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<p>I am experimenting with a recommendation systems for articles (news, magazines etc). Is there any dataset available for the same which includes the demographic information of users as well? </p>
<p>I am actually trying to incorporate demographic information as well in recommending, hence looking for such a dataset. I really don't want to simulate such data as I think real data would give much more interesting insights than simulated one. Anyone aware of such?</p>
<p>I found one <a href="http://contest.plista.com/" rel="nofollow">http://contest.plista.com/</a> but unfortunately its has german dataset and demographic information seems to be missing. Would appreciate any information here.</p> | 73,626 | [
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<p>I have a problem that I can't seem to solve:</p>
<p>The prior: $\beta_h \sim \mathcal{N}(\bar{\beta},D)$.</p>
<p>Somehow the posterior is $\beta_h \sim \mathcal{N}(M, \Omega)$, where $M=(D^{-1}+X'X)^{-1}(D^{-1}\bar{\beta}+X'p)$ and $\Omega=(D^{-1}+X'X')^{-1}$, where $X$ is a data matrix and $p$ is a data vector.</p>
<p>How can I prove $M$ and $\Omega$ are as such? What would be the likelihood function? I have 7 similar 'derive' questions that make no sense to me.</p> | 73,627 | [
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<p>From what I understand hot deck imputation involves 2 parts</p>
<p>1) Choosing the donor pool: This based on variables related to the missing variable.
Maybe using a regression technique to test for association or just ask a subject matter expert.</p>
<p>2) Choosing the value to be imputed from the donor pool based on characteristics such as distance or through random sampling techniques.</p>
<p>For single stochastic imputation the process is</p>
<p>1) Determine the distribution of the dataset after listwise deletion of item nonresponding units</p>
<p>2) Use stochastic techniques to choose a value from the distribution.</p>
<p>Both these processes seem very similar to me. What exactly is the difference between the two ?</p>
<p>Thanks</p> | 73,628 | [
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<p>Are there many features in Eviews that R misses? I have heard that especially when dealing with time series R is less extensive than Eviews. Is this true? Which of the two packages contains most statistical tools (or are they comparable?)?</p> | 73,629 | [
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<p>I'm afraid that related questions didn't answer mine. We evaluate the performances of >2 classifiers (machine learning). Our Null hypothesis is that performances do not differ. We perform parametric (ANOVA) and non-parametric (Friedman) tests to evaluate this hypothesis. If they're significant, we want to find out which classifiers differ in a post-hoc quest.</p>
<p>My question is twofold: </p>
<p>1) Is a correction of p-values after multiple comparisons testing necessary at all? The German Wikipedia site on "Alphafehler Kumulierung" says that the problem only occurs if multiple hypotheses are tested on the same data. When comparing classifiers (1,2),(1,3),(2,3), data only partially overlaps. Is it still required to correct the p-values? </p>
<p>2) P-value correction is often used after pairwise testing with a t-test. Is it also necessary when doing specialised post-hoc tests, such as Nemenyi's (non-parametric) or Tukey's HSD test? This answer says "no" for Tukey's HSD: <a href="http://stats.stackexchange.com/questions/33357/does-the-tukey-hsd-test-correct-for-multiple-comparisons">Does the Tukey HSD test correct for multiple comparisons?</a>. Is there a rule or do I have to look this up for every potential post-hoc test?</p>
<p>Thanks!</p> | 73,630 | [
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<p>First off, I know little about statistics, so some of this question may seem naive.</p>
<p>I'm trying to perform linear regression to model the relationship between x and y where:</p>
<p>-x is a company's daily stock volume on a date</p>
<p>-y is variable that is taken from the same date, however is something unrelated to stock volume. It is the volume of activity on that wikipedia for that company.</p>
<p>I assume that the variables need normalising. Specifically, x needs to be normalised as overall index volume fluctuates. My first thoughts were to divide the daily volume by the total index volume. I'll do the same with the y variable. </p>
<p>I just wondered if this seems sensible? Thanks</p>
<p>EDIT:</p>
<p>I've just noticed a typo in the question, the Y variable description has changed.</p> | 73,631 | [
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<p>I have data sets of the returns of two indexes in the same market (two different sets of stocks constituting each index), with 496 observations for each. I want to compare if the means are statistically different. I believe the variances are different, so I think I have to check if the variances are statistically different first. How would I do these things?</p> | 36,032 | [
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<p>I don't really have a motivation for this - but I was thinking about this and couldn't work it out. </p>
<p>Suppose I have a random variables $X$ and $Y$ which are correlated. Is it possible that the partial correlation between $X$ and $X\cdot Y$ is zero after taking into account Y? In other words, would a regression of $X$ on $Y$ and $X\cdot Y$ possibly result in a zero coefficient on $X\cdot Y$?</p> | 36,033 | [
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://stats.stackexchange.com/questions/298/in-linear-regression-when-is-it-appropriate-to-use-the-log-of-an-independent-va">In linear regression, when is it appropriate to use the log of an independent variable instead of the actual values?</a> </p>
</blockquote>
<p>I am running a series of multiple mediation models. Each model includes one IV, two mediators, and a DV. I’m using a macro created for SPSS (provided by Preacher and Hayes) that uses bootstrapping to examine the indirect effects of the mediators. My DV’s are depression and social anxiety (each run in a separate model) and are both positively skewed. Normally I would perform a log transformation on these variables, however, bootstrapping is a nonparametric resampling procedure that does not hold the assumption of normality of the sampling distribution. Therefore, my question is: Is it necessary to transform positively skewed DV’s even though I am using bootstrapping? </p>
<p>Note: I have run my models with the log transformed means vs. untransformed means for the DV’s and the pattern of results are essentially the same. However, I would prefer to use the untransformed means as the unstandardized regression coefficients more strongly support my predictions. </p> | 49,325 | [
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<p>Let's say I have 1 success in 4 bernoulli trials, and I wish to plot the distribution of the parameter $p$ of the corresponding binomial distribution. I'm using R.</p>
<p>The probability of seeing 1 sucess and 3 failures in 4 tests for $p=0.25$ is, for these parameters:</p>
<pre><code>> n <- 4
> p <- 0.25
> dbinom(1, n, p)
[1] 0.421875
</code></pre>
<p>To get the distribution for the parameter, I use a beta distribution $Beta(k+1, n-k+1)$. But when I try to calculate the value for $p=0.25$, I get a different result:</p>
<pre><code>> k <- 1
> dbeta(p, k+1, n-k+1)
> [1] 2.109375
</code></pre>
<p>I tried to divide that by the function beta $B(k+1, n-k+1)$, but that did not work either:</p>
<pre><code>> dbeta(p, k+1, n-k+1)/beta(k+1, n-k+1)
> [1] 42.1875
</code></pre>
<p>That's exactly 100 times the result I expected. I am certainly missing something - maybe something basic, I'm no expert.</p>
<p>Another thing that intrigues me: <code>dbeta</code> region sums to 1 without dividing by the beta function.</p> | 47,532 | [
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<p>Is it possible to do discriminant analysis with random effects?
Is there an R package for this?</p>
<p>Context: </p>
<p>I have habitat use data for two species of frogs from radio telemetry, but nested within 'species' the data is for individuals with highly autocorrelated data. </p>
<p>For example, I have ~280 relocations for species 1, with a mean of 20 relocations per individual, and ~ 210 relocations for species 2, with a mean of 13 relocations per animal. Relocations per animal are highly autocorrelated. At each relocation I collected structural habitat data, and I would like to identify which parameters are most strongly identified with each species.</p>
<p>My preference is to have this autocorrelation accounted for in the analysis, but my alternatives with DA, I think, are to:</p>
<ol>
<li>Use mean values for each individual, however then I would be
breaking assumptions of sample size as I would have fewer samples
than variables (therefore not a viable alternative); or</li>
<li>Cut relocations from individuals with lots of data points. </li>
</ol>
<p>I've done some searching through CranR, docs, etc, but haven't had much success. The MASS package does discriminant analysis and random effects, but RE in DA? I'd be grateful to be pointed in the right direction (or told that I'm completely out to lunch!) </p> | 29,245 | [
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<p>I have a time series data set of photon arrival times from a detector and need to know whether the arrival time is uniform.It is a continuous distribution?</p>
<p>I have calculated the maximum $D$ between the normalized CDF of the photon arrival times. Then what should I do? There is a "$Pr(k\le x)$" in the <a href="http://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_test" rel="nofollow">Wiki link</a>. What does it stand for in my question? Could somebody tell me the basic definition of ks-test?</p>
<p>In fact, I can calculate ks-test probability via <a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.kstest.html" rel="nofollow">scipy.stats.kstest</a>. Does anybody know the meaning of <code>args</code> for a uniform distribution? And the two output values?</p>
<pre><code>>>> stats.kstest(sample, 'uniform',args=(1,2,3,4,5,6))
(1.0, 0.0)
>>> stats.kstest(sample, 'uniform',args=(0.1,0.2,0.3,0.4,0.5,0.6))
(1.0, 0.0)
>>> stats.kstest(sample, 'uniform',args=(0.1,0.2))
(1.0, 0.0)
>>> stats.kstest(sample, 'uniform',args=(1,2))
(0.98999999999999999, 0.0)
>>> stats.kstest(sample, 'uniform',args=(1.1,2.1))
(0.98499999999999999, 0.0)
</code></pre>
<p><strong>about uniform</strong>
I think I should compare two cdf:the normalised real data and the cdf of a uniform distribution that the photons arrive uniformly.<br/></p>
<p>Please take a look at my plot.The green points are from real data.There are hundreds of green points.Every green point means an arrival of a new photon.x-axis is time and y-axis is normalised,in fact,it is the percent(cumulative arrival photons/total photon number).The red straight line stands for the cdf of uniform distribution.
stats.uniform picks random values every time.Is stats.uniform appropriate? <br/>
<img src="http://i.stack.imgur.com/yvUBz.png" alt="enter image description here"></p>
<p><strong>about ks-test</strong>
I took an image of the 2rd version Numerical Recipes in C.<br/>
What is the relation between 14.3.9 and wikipedia's Pr(k<=x)?Just an approximation,right?<br/>
The significance should be decided only by two values max(D) and sample size,right?
Pr(k<=x) is the cdf of D?How to define x?<br/>
I can not get a consistent result with stats.kstest().<br/>
You mean if I use the real time data which is not normalised,I should use two-sample ks-test,right?<br/>
<img src="http://i.stack.imgur.com/hGMz5.jpg" alt="NumerialRecipes2rdCh14"></p> | 73,632 | [
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<p>I have conducted a survey which asks respondents to indicate the informational sources regarding a product. There are 8 information sources (e.g., internet, newspaper, brochure and so on) and people can choose more than one source.</p>
<p>I want to use information source a predictor variable in a multiple regression.
However, because people can choose more than one information source, it does not seem possible to to treat it as a single categorical variable. </p>
<p><strong>How can a categorical variable where respondents can choose more than one response be used as a predictor in multiple regression?</strong></p> | 73,633 | [
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<p>I am developing a physiological test using R that requires some parameters optimised. In comparing the new method against the existing method, the values of individual readings correlate in a linear way but are very heteroscedastic - the variance approximately proportional to the mean. </p>
<p>I would like to compare the effects of various parameter changes by examining the goodness-of-fit of the linear models compared with each other. Confidence intervals around the linear model parameters are not needed. Comparing R squareds does not seem appropriate given the heteroscedasticity. Would distance correlation or R squared after HCCM correction be appropriate ways to test if one method is superior to another ?</p> | 39,335 | [
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<p>Given a hierarchical model $p(x|\phi,\theta)$, I want a two stage process to fit the model. First, fix a handful of hyperparameters $\theta$, and then do Bayesian inference on the rest of the parameters $\phi$. For fixing the hyperparameters I am considering two options.</p>
<ol>
<li>Use <strong>Empirical Bayes (EB)</strong> and maximize the marginal likelihood $p(\mbox{all data}|\theta)$ (integrating out the rest of the model which contains high dimensional parameters).</li>
<li>Use <strong>Cross Validation (CV)</strong> techniques such as $k$-fold cross validation to choose $\theta$ that maximizes the likelihood $p(\mbox{test data}|\mbox{training data}, \theta)$.</li>
</ol>
<p>The advantage of EB is that I can use all data at once, while for CV I need to (potentially) compute the model likelihood multiple times and search for $\theta$. The performance of EB and CV are comparable in many cases, and often EB is faster to estimate.</p>
<p>Question: Is there a theoretical foundation that links the two (say, EB and CV are the same in the limit of large data)? Or links EB to some generalizability criterion such as empirical risk? Can someone point to a good reference material?</p> | 73,634 | [
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<p>I am developing a method to do something with permutation testing. I have two permutation / randomization schemes and do not know which one is better than the other. Can I find the confidence interval for each permutation scheme? If so, is the one with the narrower confidence region better?</p> | 29,254 | [
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<p>I need to calculate the sample size required for an observational study in which incidence of disease is 19-29%. Population affected is 600,000 people.</p>
<p>The study has two samples similar on baseline characteristics treated
with two different drugs.</p>
<p>Statistical analysis will be chi-square and Fisher's test.
I have to demonstrate non-inferiority of one drugs with respect of the other one.
I don't have any other info.</p>
<p>Can anyone help me to calculate the sample sizes required in order to obtain power of 0.80
with an alpha 0.05?</p>
<p>Thanks a lot in advance</p> | 47,538 | [
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<p>Lets say for example a class of students and their grades are the data set.
Lets say there are around 35 students.</p>
<p>Here is what you know:</p>
<pre><code>Your mark
The class average
The median mark
The standard deviation
</code></pre>
<p>Are there any other conclusions about this data that can be made given this information?</p>
<p>Thanks</p> | 996 | [
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<p>I have some data which works nicely with JMP's canned linear discriminant analysis (LDA), but after <a href="http://en.wikipedia.org/wiki/Linear_discriminant_analysis" rel="nofollow">reading about LDA</a> I'm not sure if the analysis is valid. The Wiki article notes a fundamental assumption of LDA is that independent variables are normally distributed. Does this also mean that I cannot use LDA if my variables have any correlation whatsoever? Also, supposing I have or transform to independent variables-- then I must also test if they are normally distributed (say, Shapiro-Wilk test) and only use those that pass in the LDA? </p>
<p>Thanks</p> | 73,635 | [
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<p>I apologize in advance if the question is rather simple, but I have been having a difficult time figuring it out. </p>
<p>I am an experimental scientist interested in modeling human disease with induced pluripotent stem cells. The disease is fairly common, but doesn't have a common genetic basis. It is mainly driven by rare genetic variants of high penetrance but in a small number of individuals. </p>
<p>For (let's say) 5 patients out of 1000 screened affected cases, we are able to strongly associate mutations in one gene with the condition. These mutations are completely absent from a control population of 5000 individuals. </p>
<p>We have made stem cells from 2 of those individuals to determine whether these mutations result in cellular dysfunction (let's call this phenotype A) when compared to controls. We have several stem cell lines per individual. In this situation, phenotype A is an 'intermediate phenotype'.</p>
<p>The big conceptual question for me is this: Am I modeling the disease or am I only modeling the effect of the disease-associated mutations on cellular function? How can I determine the sample size to test the former claim with, say, 80% power?</p> | 73,636 | [
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] |
<p>I am new to R and I have run the <code>lmer</code> in lme4. In the model summary, there is no any warning message, but when I ask for <code>confint(lmer)</code>, R gives me this message at the bottom of the output:</p>
<pre><code>Warning messages:
1: In profile.merMod(object, signames = oldNames, ...) :
non-monotonic profile
2: In profile.merMod(object, signames = oldNames, ...) :
non-monotonic profile
3: In profile.merMod(object, signames = oldNames, ...) :
non-monotonic profile
</code></pre>
<p>What does it mean? and what should I do?</p> | 73,637 | [
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<p>I recently read a <a href="http://blog.echen.me/2012/03/20/infinite-mixture-models-with-nonparametric-bayes-and-the-dirichlet-process/" rel="nofollow">fascinating article</a> describing methods for clustering data without assuming a fixed number of clusters.</p>
<p>The article even includes some sample code, in a mix of Ruby, Python, and R. However, the meat of the analysis is performed using <a href="http://scikit-learn.sourceforge.net/dev/index.html" rel="nofollow">scikit-learn</a>'s <a href="http://scikit-learn.sourceforge.net/dev/modules/mixture.html" rel="nofollow">Dirichlet Process Gaussian Mixture Model</a> to actually find clusters in some sample data taken from McDonald's menu.</p>
<p>Obviously, this a a great excuse to learn some more python, but I'm lazy and would like to find a ready-made R package that can take a dataframe and return clusters, in a manner similar to the <a href="http://stat.ethz.ch/R-manual/R-devel/library/stats/html/kmeans.html" rel="nofollow">kmeans</a> function. <a href="http://cran.r-project.org/web/views/Cluster.html" rel="nofollow">A quick search on CRAN</a> reveals the packages <a href="http://cran.r-project.org/web/packages/dpmixsim/index.html" rel="nofollow">dpmixsim</a> and <a href="http://cran.r-project.org/web/packages/profdpm/index.html" rel="nofollow">profdpm</a>. Any suggestions for the best place to start?</p> | 25,062 | [
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<p>I have some trouble with score functions in likelihood calculation. I'm not good at statistics or probability, so I'm still confused on formalism and mathematical-probabilistic language.</p>
<p><strong>Some background:</strong> I'm on particle filter, so inferring a pdf that is analytically intractable by a Monte Carlo sampling: put some random particles, evaluate them with a likelihood function, and the normalised-weighted set of particles can be an approximation of the pdf.</p>
<p>I have to give a weight to each particle and compute the likelihood with a likelihood function or score function.</p>
<p>If my hidden state described by this difficult pdf that I have to infer is denoted as $X$, and I have some observation $z$, the likelihood can be formalised by:</p>
<p>$$ p( X | z ) = \text{likelihood} $$</p>
<p><strong>What I have now:</strong> a nice distance function that give me the distance between the particle and the target. It works. It is the Bhattacharyya distance (I'm working with images, and colour histogram is a relevant feature). So that:</p>
<p>$$ d = \text{Bhattacharyya(particle, target)} $$</p>
<p>This $d$ is a distance, and for a likelihood function I need a probability, so I'm putting it into a <a href="http://www.wolframalpha.com/input/?i=e%5E%28-%28d-0%29%5E2/%282%200.4%5E2%29%29/%28sqrt%282%20pi%29%200.4%29" rel="nofollow">Gaussian with zero means and variance = 0.4</a>:</p>
<p>$$ \text{likelihood} = \frac{e^{-\frac{(d-\mu)^2}{2 \sigma^2}}}{\sqrt[2]{ \pi \sigma}} $$</p>
<p><strong>What I want:</strong> Now I'd like to improve my experiments, adding similarly another score function so that the total likelihood is calculated with two score functions (let's say a shape-distance or something else) $s_1$ and $s_2$.</p>
<p>I remember from school (but don't remember exactly why) that if you want to combine 2 probabilities, you have only to multiply, not sum. So I know that:</p>
<p>$$ \text{likelihood} \propto s_1 s_2 $$</p>
<p>where $s_1$ is the Gaussian with the Bhattacharyya with the colour histogram, and $s_2$ is the shape distance.</p>
<p>The two score functions are Gaussian, and they are not independent (they depend on the same hidden state).</p>
<p><strong>Question 1</strong>: Is it true I have to multiply them? Why? So that my final formula will be:</p>
<p>$$ \text{likelihood} = \frac{e^{-\frac{(d_1-\mu)^2}{2 \sigma^2}}}{\sqrt[2]{ \pi \sigma}}
\frac{e^{-\frac{(d_2-\mu)^2}{2 \sigma^2}}}{\sqrt[2]{ \pi \sigma}} $$</p>
<p><strong>Question 2:</strong> What if I want to empirically add some more importance to one of the two scores because I think it is more descriptive of my data? Like:</p>
<p>$$ \text{likelihood} = \alpha s_1 (1-\alpha)s_2 $$</p> | 36,045 | [
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] |
<p>I'm trying to wrap my head around mixture modelling, and I've come across a small matlab script that seems relevant. In order to familiarize myself with pymix, I've decided to try rewriting the matlab script in python. I appear to have successfully fitted/decomposed the data with the expectation maximization algorithm, but I'm not sure I understand the nature of the method's output.</p>
<p>My question is as follows:</p>
<ol>
<li>How can I replicate the second figure from the matlab code (below) with the output of <code>pymix.MixtureModel.EM</code>?</li>
<li>Can someone explain the output of the above method?</li>
</ol>
<p>I should mention that I'm horribly under-educated in statistics and mathematics in general (I'm working on it!), so please assume I know nothing =)</p>
<p>In any case, here's the matlab script:</p>
<pre><code>% Generate some data drawn from two Gaussians
data = [0.4+randn(100,1).*0.15; 1+ randn(200,1).*0.25]';
data(data < 0.05) = 0.05;
[n,x] = hist(data);
bar(x,n);
% Make the mixture model pdf
mixtureGauss = ...
@(x,m1,s1,m2,s2,theta) (theta*normpdf(x,m1,s1) + (1-theta)*normpdf(x,m2,s2));
% Set up parameters for the MLE function
options = statset('mlecustom');
options.MaxIter = 20000;
options.MaxFunEvals = 20000;
% Get max likilihood parameters for our mixture model (start with some
% reasonable guesses about the parameters)
p = mle(data, 'pdf', mixtureGauss, 'start', [0.5 0.1 0.5 0.1 0.5], ...
'lowerbound', [-Inf 0 -Inf 0 0], 'upperbound', [Inf Inf Inf Inf 1], ...
'options', options);
% Plot and print information
hold on;
x = linspace(min(data),max(data),100);
plot(x, mixtureGauss(x,p(1),p(2),p(3),p(4),p(5))*max(n), 'r', 'LineWidth', 2);
fprintf('Gauss 1: %0.2f (+/- %0.2f)\n', p(1), p(2));
fprintf('Gauss 2: %0.2f (+/- %0.2f)\n', p(3), p(4));
fprintf('Mix: %0.2f proportion first gaussian\n', p(5));
</code></pre>
<p>And here's what I've done in python so far. Note that I'm running this code in iPython with the <code>--pylab=inline</code> option, thereby importing pyplot into my main workspace:</p>
<pre><code>import numpy as np
import mixture
# Generate some data drawn from two Gaussians
data = np.concatenate((0.4 + np.random.randn(100) * 0.15, 1 + np.random.randn(200) * 0.25))
data[np.nonzero(data < .05)] = .05
print type(data), len(data)
plt = Figure()
hist(data, bins=50)
show()
# Create DataSet object
mixdat = mixture.DataSet()
mixdat.fromArray(data)
# reasonable-guess mixture, akin to random starting point in K-Means
n1 = mixture.NormalDistribution(-2, 0.4)
n2 = mixture.NormalDistribution(2, 0.6)
# Mixture model and EM clustering
mix = mixture.MixtureModel(2, [.5, .5], [n1, n2])
postmat, _ = mix.EM(mixdat, 40, 0.1)
fig = Figure()
hist(data, bins=50)
x = np.linspace(np.min(data), np.max(data), 100)
# Now what?
show()
</code></pre>
<p>Any other comments, criticisms, or explanations are more than welcome. Thanks for putting up with my ignorance ;-)</p> | 36,046 | [
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<p>I would like to compare the data of a community of species between two years. I used to compare communities based on different levels of a factor (for example, a treatment). The case of a treatment is easy because each site has a corresponding level of the treatment. </p>
<p>However, if the factor is a year, we face a paired design with each site sampled twice. In this case I cannot just assign a year to a site and, therefore, I do not know which method I should apply to analyse community differences between two years. </p> | 47,551 | [
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<p>I have a time series dataset that reports the hourly page views and social media shares of online news stories. What I hope to obtain is the relationship between the two variables. I would imagine that the more shares a story gets, the more page views it will attract, and vice versa. That means the two variables would demonstrate a similar fast/slow growth curve. </p>
<p>In terms of a single story, I can use VAR (vector autoregressive) model to estimate the coefficients. However, how could I make use of hundreds of stories to build a more generalized model? What I've thought of so far is to fit each story with the same model and then observe the distribution of the coefficients. Would it be an appropriate method? </p>
<p>That would be great if you could kindly cite some papers and/or R packages that would inspire potential solutions. Thank you!</p> | 73,638 | [
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<p>I am trying to build sparse coefficient time series models but couldn't find a good resource/book to learn from. Can anyone share with me a good resource/book? It will be great if it comes with R codes.Can anyone use this kind model? Thanks.</p> | 36,048 | [
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<p>I am using <code>R</code> and <code>e1071</code> package to tune a C-classification SVM.</p>
<p>My question is: regardless of the kernel type (linear, polynomial, radial basis or sigmoidal), is there any good criterion to choose the range in which cost and $\gamma$ parameters should range over and/or to choose what the granularity should be (that is, as an example, <code>gamma = 10 ^ (1:2)</code> or <code>gamma = 1:2</code> or <code>gamma = 100 ^ (1:2)</code>)?</p>
<p>I add a second question: can <code>tune.svm()</code> return the best kernel type, too?</p>
<p>Thanks,</p> | 73,639 | [
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<p>Suppose I am doing random forest classification of labels $A$,$B$,$C$,$D$. There is some theoretical ordering to this output such that when $A$ is more likely than $B$, $B$ is also more likely than $C$, etc. Also, if $P(D) > P(C)$, we also have that $P(C) > P(B) > P(A)$. There are other such conditions that need to be met.</p>
<p>The issue is that a real random forest may give something silly that completely violates the above constraints, <em>even if</em> it is able to predict the most likely outcome successfully. For my use case the ordering is important since decisions are made not only on the most likely outcome.</p>
<p>It also seems intuitive that I should be able to improve generalization if I can somehow enforce this prior knowledge into the model. </p>
<p>How do I account for this in a decision forest? Despite this structure to the output I do not think it is possible to construct a real-valued response variable since they are <em>still class labels</em> with no natural real value, even if there is some type of ordering to them.</p> | 73,640 | [
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<p>I have two <em>finite</em> samples $s_1$ and $s_2$ and two distributions $p_1(s_1)$ and $p_2(s_2)$ that are associated to these samples. I'm essentially interested to measure the distance or similarity between these two distributions. I'm currently using the Jensen-Shannon (JS) distance, which involves in calculating the entropies of the two distributions separately and jointly.
I need to bin the data for calculating the basic entropy functions and it looks like the resulted JS distance is also a function of the data binning strategy that I use. It sounds quite arbitrary and I don't know how much I can trust the results.
Is there any way around this? How can I measure the distance between $p_1(s_1)$ and $p_2(s_2)$ in a more rigorous way that needs no data binning or any other sort of arbitrariness?</p> | 73,641 | [
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<p>I was wondering if you could share your experience in reporting chi-square tests for complex survey data in journal publications. Normally Chi-square tests are reported as $\chi^2_1(2,\text{ N} = 90)= 0.89, \text{ p} = .35$. (for example, although I guess there can be some variations). However the concept of N becomes rather tricky with complex survey design, and I'm not sure whether I should report the probability weighted sample size or just the sample size.I'm also interested in whether people would report different Ns if the sample was just subject to probability weighting (e.g. for example if strata or cluster information was unfortunately missing) or probability weighting with clustering and stratification. And if the sample size was reported in the format above should this be reported as n rather than N?</p>
<p>Just to give an example: Lumley's R package returns the following:</p>
<pre><code>data(api)
dclus1<-svydesign(id=~dnum, weights=~pw, data=apiclus1, fpc=~fpc)
svychisq(~sch.wide+stype,dclus1, statistic="Chisq")
Pearson's X^2: Rao & Scott adjustment
data: svychisq(~sch.wide + stype, dclus1, statistic = "Chisq")
X-squared = 11.94, df = 2, p-value = 0.005553
</code></pre>
<p>Would you report as N </p>
<pre><code>sum(xtabs(~sch.wide+stype, data=apiclus1)) #or
sum(svytable(~sch.wide+stype, dclus1))
</code></pre>
<p>See <a href="http://faculty.washington.edu/tlumley/survey/html/svychisq.html" rel="nofollow">this</a> page for details on computation and Rao-Scott corrections to the Pearson chisquared test.</p>
<p>Very interested in your opinion.
Many thanks</p> | 73,642 | [
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<p>I'm looking to use a multivariate regression for prediction, but making use of (possibly) superior estimates of variance for both the independent and extraneous variables.</p>
<p>My approach is to standardize the dependent and extraneous variables (by dividing their respective standard deviations derived from the full data history). Once I have the standardized regression coefficients, I use these, together with my separately sourced variance estimates, to get back to an equation that will be used for generating the predictions. Do I simply multiply each coefficient by my separately sourced variance estimate? But what about the dependent variable variance estimate?</p>
<p>As background info, my separate sourcing of variances estimates is because I believe I have better (more up-to-date) estimates than available from the full data history (let's say, because the variances aren't stable through time, I can estimate a more timely measure of variance using higher frequency data over a shorter, recent period).</p>
<ul>
<li>Is this approach a sensible standard practice?</li>
<li>How to go from the standardized betas, to un-standardized ones using the high frequency variance estimates?</li>
</ul>
<p>I read here (http://stats.stackexchange.com/questions/29781/when-should-you-center-your-data-when-should-you-standardize) about WHEN to standardize, but not clear to me if this covers the case of standardizing both dependent and extraneous variables. </p>
<p>Thank you!</p> | 39,441 | [
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<blockquote>
<p>Let $X$ be a random varaible from a distribution with pdf
$$
f(x) = \theta x^{\theta-1}, \quad 0< x < 1.
$$</p>
<p>a) Name the distribution of $U=-\ln(X)$ by first finding its density </p>
<p>b) Let $X_1, X_2, \ldots,X_n$ be independent and identically distributed random variables with pdf given by earlier with $\theta$= 3. Using the result from a) and by the central limit theorem (CLT)</p>
<p>i) find an approximation to $P(X_1 \cdot X_2 \cdot \ldots\cdot X_{30} \leq 1.85 \cdot 10^{-5})$</p>
</blockquote>
<p>i.e. for the probability of the product of the r.v's.</p>
<p><strong>My attempt</strong></p>
<p>I found part a) by doing the transformation, and got an exponential with parameter $\theta$ where my pdf is:
$$
f(x)=\theta e^{-u\theta} .
$$
Now where I am struggling is with part i) where I am supposed to find an approximation using the CLT and together with the mean equal to $1/3$ and variance equal to $1/9$. I am able to show that with 30 observation we just take the product of every mean and variance from each individual observation giving us: </p>
<p>mean = $(\frac{1}{3})^{30}$<br>
variance = $(\frac{1}{9})^{30}$</p>
<p>and then we can just substitute these into the z score by using central limit theorem
$$
P(X_1 \cdot X_2 \cdot \ldots \cdot X_{30} \leq 1.85 \cdot 10^{-5})
= P\left(\frac{X -\mu }{\sigma}\leq \frac {1.85 \cdot 10^{-5} - (\frac{1}{3})^{30}}{(\frac{1}{9})^{15}} \right)
$$
Hence giving me an answer of
$ P(Z \leq 3,808,985,943)$ which definitely cannot be correct. Would appreciate it if somebody could point out my mistake.</p>
<p><strong>Reattempt:</strong> </p>
<p>Using the hint i got i managed to deduce the following </p>
<p>$P(X_1 \cdot X_2 \cdot \ldots \cdot X_{30} \leq 1.85 \cdot 10^{-5})$</p>
<p>$P(log X_1 \cdot log X_2 \cdot \ldots \cdot log X_{30} \leq log 1.85 \cdot 10^{-5})$</p>
<p>P($\sum_{k=1}^{30} log X_i \leq log 1.85 \cdot 10^{-5})$</p>
<p>And since X random variable can be normally distributed X~ N( $\frac{1}{3}$ , $\frac{1}{9}$)</p>
<p>Substitute into the Z score </p>
<p>$ P(\frac{ log X -\mu }{\frac{\sigma}{\sqrt(n)}})\leq \frac { \frac{log1.85 \cdot 10^{-5}}{30} - (\frac{1}{3})}{(\frac{\frac{1}{3}}{\sqrt(n)})} $</p>
<p>$P(Z \leq 11.45)$</p>
<p>Am I on the right track? Is it correct to use $\mu$ = $\frac{1}{3}$ and $\sigma$ = $\frac{1}{3}$ in the z score?</p> | 16,625 | [
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<p>If I'm not wrong, likelihood functions are sensitive to the size of the sample, i.e. the larger the sample, the lower the likelihood value. Given a sample $x$ of a random variable $X \sim f(\theta)$, and a parameter estimate $\hat\theta$, suppose I want to test the hypothesis that the likelihoods of different subsamples of $x$, let's call them $x_a$ and $x_b$ are equal.</p>
<p>The problem is $x_a$ and $x_b$ have a different number of elements, say $n_a$ and $n_b$ respectively, and $n_a \neq n_b$, so I assume the likelihoods must be normalized in some way. Is it enough to divide by the sample size? For instance, can I use a test statistic such as</p>
<p>$T = \frac{\ell(\hat\theta|x_a)}{n_a} - \frac{\ell(\hat\theta|x_b)}{n_b}$</p>
<p>and then test the hypothesis that $T = 0$. A related question would be how do I find the probability distribution of the above statistic, but that is another story.</p> | 36,056 | [
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<p>In a panel regression using fixed effects, is it correct to use an instrument that does not vary by year? To use an old but simple example, Angrist and Kruger 1991 use quarter of birth as an instrument for education. If one had access to similar data that was in panel form, is it still correct (and I don't mean specifically quarter of birth, I know there are problems with the validity of this IV) to use quarter of birth (same for each respondent regardless of panel wave) as an instrument in the panel IV regression? Why or why not?</p> | 36,057 | [
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<p>I am currently working on biomass estimates using satellite imagery. I'll quickly define the background of my question, and then explain the statistical question I am working on.</p>
<p><strong>Background</strong></p>
<p><em>Problem</em> </p>
<p>I am trying to estimate biomass over an area in France. My response is the steamwood volume density (in $m^3/ha$), which is more or less proportional to biomass (depending on the wood densities...).</p>
<p>The independent variables that I have are vegetation indices derived from measured reflectances over this area (the satellite used in the study is MODIS for those who know it). These indices are for example NDVI, EVI, etc. I have maps of the indices, and the resolution of the maps are 250m.</p>
<p>There are strong correlations between these indices and the volume in a same forest type (biome and climate). So I am trying to regress the volume density against these indicators (actually their time series) on inventory plots where I know the volume.</p>
<p><em>Forest inventories</em></p>
<p>The volume on these plots is estimated with the following sampling method:</p>
<ol>
<li>Inventory nodes are placed on a regular grid covering the area.</li>
<li>A plot is attached to each node, and the inventory process (tree types, volumes, canopy height, etc.) occurs on this plot. Of course I am interested only in the inventory plot and the values of my vegetation indices is the value of the pixel containing the plot.</li>
<li><p>The inventory process on a plot is the following: </p>
<p><img src="http://i.stack.imgur.com/qcHtu.png" alt="http://i.stack.imgur.com/DeHdC.png"></p>
<ul>
<li>Measure of the trees that have a diameter > 37.5cm in the 15m radius circle</li>
<li>Measure of the trees that have a diameter > 22.5cm in the 9m radius circle</li>
<li>Measure of the trees that have a diameter > 7.5cm in the 6m radius circle</li>
</ul></li>
</ol>
<p>The volume density is then calculated using expansion factors.</p>
<p>For each plot I have access to the data for all the measured trees. </p>
<p>Moreover, for each single tree, I have an uncertainty on the volume due to the use of allometric equations (let us say 10%).</p>
<p><strong>Where statistics are important...</strong></p>
<p>For my regressions to be more accurate, I need for each estimate of volume the variance/CI of this measure. This depends, IMO, on the number of trees sampled and the volume density found.</p>
<p>So I have two problems:</p>
<ol>
<li><p>How to account for the fact that my vegetation indices are measured over a pixel of 250m ?</p>
<blockquote>
<p>I can assume that the volume density is constant over one pixel, and that I sample this pixel with one inventory plot.</p>
</blockquote></li>
<li><p>How to estimate the variability of my volume density? </p>
<blockquote>
<p>I think I could use bootstrapping on the tree population. But my total number of trees measured can be pretty small (from 7 to 20...). Moreover, how can I take into account the fact that I am measuring the trees on different circles depending on their sizes ? And how should the variability change if I am looking on an entire pixel ?</p>
</blockquote></li>
</ol>
<blockquote>
<p>I was also thinking that I could use a Monte Carlo Simulation to simulate a forest, and then randomly sample this forest with plots to see what is going on...</p>
</blockquote>
<p>I do not have a strong statistical background, so I am a little bit lost!</p> | 36,058 | [
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<p>I am aware that the "prediction interval", as defined in most textbooks on linear models, is focused on the uncertainty in the model being fit and is used to estimate an output prediction range for exact inputs. However, as is normally the case, what about situations where the input isn't exact? How do you calculate a "prediction interval" that accounts for both the uncertainty in the model and the uncertainty in the input data?</p>
<p>For example,</p>
<p>Assume the model is: <code>y = a0 + (a1 * x1) + (a2 * x2)</code></p>
<p>Where <code>y</code>, <code>x1</code>, and <code>x2</code> are time series vectors. </p>
<p>I only have one observation of the <code>y</code> time series with its associated <code>x1</code> and <code>x2</code> time series. That data is used to fit the model. However, I also have 1000 additional observations for <code>x1</code> and <code>x2</code>. I can easily calculate individual "prediction intervals", using the model and each <code>x1</code> <code>x2</code> pair, however I want to estimate a "prediction interval" that allows for all <code>x1</code> and <code>x2</code> observations. To be more specific, I generated the example below. The questionable code is below the <code>#======</code> comment line.</p>
<p>Basically, I used <code>lm(..)</code> to fit the <code>y</code> vector to its associated <code>x1</code> and <code>x2</code> vectors. Next, I used <code>predict.lm(...interval="prediction", level=alpha)</code> to generate its typical <code>fit</code>, <code>lwr</code>, and <code>upr</code> vectors for each additional <code>x1</code> <code>x2</code> pair (see Graph 1, <code>fit</code> is the solid line, <code>upr</code> and <code>lwr</code> are the dashed lines for two observations). I then collected these vectors for all <code>x1</code> <code>x2</code> pairs and used <code>alpha</code> to extract the upper and lower tails of all of the <code>lwr</code> and <code>upr</code> vectors (see Graph 2).</p>
<p>Is this scheme valid? Does the <code>alpha</code> that was used in <code>predict.lm(... level=alpha)</code> apply directly to counting-up/sorting the results to generate a "prediction interval" that allows for all <code>x1</code> <code>x2</code> pairs? Can a 5% range from a competing model (for example an ARIMA model) be compared to this 5% "prediction interval"?</p>
<p>I'm fairly sure that the following scheme isn't right, but so far, I haven't figured out what I need to fix.</p>
<pre><code>set.seed(1)
numpoi <- 10 #Number of data points in a time series vector
#First independent variable "x1", first observation
x1mea <- 0.03
x1sta <- 0.05
x1 <- cumsum(rnorm(numpoi, mean=x1mea, sd=x1sta))
#Second independent variable "x2", first observation
x2mea <- -0.01
x2sta <- 0.1
x2 <- cumsum(rnorm(numpoi, mean=x2mea, sd=x2sta))
#Dependent variable "y", first observation
a0 <- 3
a1 <- 2
a2 <- 1
noimea <- 0.0
noista <- 0.1
y <- a0 + (a1 * x1) + (a2 * x2) + rnorm(numpoi, mean=noimea, sd=noista)
#Build a data frame of the "first observation" data
datfra <- data.frame(y=y, x1=x1, x2=x2)
#Fit the model for the "first observation"
mod <- lm(y ~ x1 + x2, data=datfra)
summary(mod)
#Set up desired alpha value
alpha <- 0.95
onetai <- (1 - alpha)/2 #Convert the two tail "alpha" to a one tail value for use later
#Generate some new data "a" for a second observation of "x1" and "x2".
x1a <- cumsum(rnorm(numpoi, mean=x1mea, sd=x1sta))
x2a <- cumsum(rnorm(numpoi, mean=x2mea, sd=x2sta))
datfraa <- data.frame(y=rep(NA, numpoi), x1=x1a, x2=x2a)
modprea <- predict(mod, newdata=datfraa, interval="prediction", level=alpha)
#Generate some new data "b" for a third observation of "x1" and "x2".
x1b <- cumsum(rnorm(numpoi, mean=x1mea, sd=x1sta))
x2b <- cumsum(rnorm(numpoi, mean=x2mea, sd=x2sta))
datfrab <- data.frame(y=rep(NA, numpoi), x1=x1b, x2=x2b)
modpreb <- predict(mod, newdata=datfrab, interval="prediction", level=alpha)
#Plot the results for both new data "a" and "b"
plot(modprea[, 1], type="l", ylim=c(min(modprea, modpreb), max(modprea, modpreb)), main="Graph 1 - Second and Third Observations for x1 and x2", lwd=2, col="red")
lines(modprea[, 2], lwd=2, lty=2, col="red")
lines(modprea[, 3], lwd=2, lty=2, col="red")
lines(modpreb[, 1], lwd=2, col="green")
lines(modpreb[, 2], lwd=2, lty=2, col="green")
lines(modpreb[, 3], lwd=2, lty=2, col="green")
#===========================================================================
#The code below is where my question lies. Is this the appropriate method
#to account for all observations?
#Run the above calculation scheme on "all" observations.
numtri <- 1000 #All observations
modprecfit <- matrix(0, nrow=numpoi, ncol = numtri) #Matrix to hold all "fit" vectors
modpreclwr <- matrix(0, nrow=numpoi, ncol = numtri) #Matrix to hold all "lwr" vectors
modprecupr <- matrix(0, nrow=numpoi, ncol = numtri) #Matrix to hold all "upr" vectors
#Fill up the modprecfit, modpreclwr, and modprecupr matricies.
for (i in 1:numtri) {
#Generate the new data and put it in a dataframe
x1c <- cumsum(rnorm(numpoi, mean=x1mea, sd=x1sta))
x2c <- cumsum(rnorm(numpoi, mean=x2mea, sd=x2sta))
datfrac <- data.frame(y=rep(NA, numpoi), x1=x1c, x2=x2c)
#Predict the new "y" for new input data
modprec <- predict(mod, newdata=datfrac, interval="prediction", level=alpha)
#Store the "ft", "lwr", and "upr" vectors so they can be processed later
modprecfit[, i] <- modprec[, 1]
modpreclwr[, i] <- modprec[, 2]
modprecupr[, i] <- modprec[, 3]
}
#Extract the average "fit", the lower quantile "lwr", and the upper quantile "upr"
modprecfitfin <- apply(modprecfit, 1, quantile, 0.5)
modpreclwrfin <- apply(modpreclwr, 1, quantile, onetai)
modprecuprfin <- apply(modprecupr, 1, quantile, (1 - onetai))
plot(modprecfitfin, type="l", ylim=c(min(modpreclwrfin), max(modprecuprfin)), main="Graph 2 - All Observations for x1 and x2", lwd=2, col="red")
lines(modpreclwrfin, lwd=2, lty=2, col="red")
lines(modprecuprfin, lwd=2, lty=2, col="red")
</code></pre>
<p><img src="http://i.stack.imgur.com/dHaNa.png" alt="enter image description here">
<img src="http://i.stack.imgur.com/oMcGL.png" alt="enter image description here"></p> | 47,564 | [
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<p>I'm trying to assess the difference between two algorithms. They are stochastic, so I've run them multiple times against the same input files and noted their results. I want to determine whether my algorithm offers a statistically significant improvement over a previous approach. From my (potentially flawed) understanding this sort of situation is where I should (or rather could) use the Wilcoxon Sign Rank test. </p>
<p>The data is naturally paired, so I can join together outputs of both algorithms by the particular input problem they used. Since I want to test that my algorithm is not just different, but actually better (in this case returning lower values) than the other algorithm this appears to be a one-tailed assumption. </p>
<p>I'm using the R <code>wilcox.test</code> function to perform the test and I'm slightly confused about how I should interpret the results. I have read the help page for <code>wilcox.test</code> and it doesn't seem to offer much information about the results, more focus is made to the function's arguments. I've made a minimal working example with a small subset of my data:</p>
<pre><code>x <- structure(list(instance = structure(c(1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L), .Label = c("competition01", "competition02",
"competition03", "competition04", "competition05", "competition06",
"competition07", "competition08", "competition09", "competition10",
"competition11", "competition12", "competition13", "competition14",
"competition15", "competition16", "competition17", "competition18",
"competition19", "competition20"), class = "factor"), nhoods = structure(c(1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("nhoods1", "nhoods2",
"nhoods3", "nhoods4", "nhoods5"), class = "factor"), run.no = structure(c(1L,
1L, 2L, 2L, 3L, 3L, 4L, 4L, 5L, 5L), .Label = c("1", "2", "3",
"4", "5"), class = "factor"), partition = structure(c(1L, 2L,
1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L), .Label = c("Hard-Soft", "Full"
), class = "factor"), VNS = c(984L, 1445L, 1033L, 1445L, 1035L,
1318L, 1058L, 1445L, 913L, 1445L), `VNS-Skip` = c(1083L, 1425L,
1099L, 1230L, 1077L, 1363L, 1102L, 1442L, 1093L, 1252L)), .Names = c("instance",
"nhoods", "run.no", "partition", "VNS", "VNS-Skip"), row.names = c(NA,
10L), class = "data.frame")
wilcox.test(x[,5], x[,6], paired = TRUE, conf.int = TRUE, alternative = "greater")
</code></pre>
<p>My algorithm's results are in the 6th column and the original ones are in the 5th column. Since I want to assess whether my algorithm is better I've used the alternative = "greater" option which should mean that the test is checking for 1st arg > 2nd arg. </p>
<p>This results in the output:</p>
<pre><code> Wilcoxon signed rank test
data: x[, 5] and x[, 6]
V = 22, p-value = 0.7217
alternative hypothesis: true location shift is greater than 0
95 percent confidence interval:
-72 Inf
sample estimates:
(pseudo)median
-21
</code></pre>
<p>In this case the p-value is not less than 0.05 so there is not enough evidence to discard the null hypothesis.</p>
<p>What does having infinity as the upper bound of a confidence interval mean? Is this because I'm using the one-tailed version of the test? All the tests I've run on my data always have the upper confidence interval as Inf. If the p-value were less than 0.05 would that mean I would be justified in saying "with a 95% confidence x[,5]'s mean will be within -72 of x[,6]'s?" </p>
<p>What does the V value mean with regard to my data? From what I can see it is the difference between <code>median(x[,5])</code> and <code>median(x[,6]</code> but how would describe that in prose? Does anyone actually use the V value is the discussion of their data analyses? </p> | 47,566 | [
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<p>I'm familiar with using tools like SVMs and decision trees for discrete classification problems. But one detail that I have not encountered in that domain is: what do you do if your classifier must conserve some quantity when it is predicting outcomes for new input data?</p>
<p>For example, suppose that you took all teams in the NFL and broke them into quintiles (20% buckets) based on their rushing yards per game (or say you took teams from the EPL and broke them down into quintiles based on their time-of-possession or some other statistic). Further let's say you are doing this on a weekly basis, so every week you collect your stats and then rank the teams 1 to N, chop them into quintiles, and each team's "class label" is its quintile.</p>
<p>Now let's say you build a bunch of features for each team that you think will predict the team's quintile for next week. It could be the team's historical quintile, coaching changes, injuries to key players, whatever. But the point is you can make a feature vector for each team and you want to train a classifier that will predict which class label (1 to 5) to assign based on the features.</p>
<p>What are some common or empirically effective ways to constrain the classifier so that the output makes sense? That is to say, it should only be possible to classify 20% of the teams in any particular quintile, and the classifier should not be able to logically contradict itself by putting more teams in a quintile than 20% of the total. (That is, the theory behind the classifier ought to demonstrate how we can <em>know in advance</em> that the classifier won't make contradictions).</p>
<p>I'm not looking for post-hoc hacky ways to do rounding or anything, and I am also specifically trying to avoid the situation where you build a regression model of the underlying continuous quantity and then just predict the quantity and manually assign quintiles yourself. I want the classifier to discretely choose quintiles for each feature vector while respecting external constraints on the class labels.</p>
<p>More generically you could wonder, how do you train an SVM-like classifier such that it has internal rules like "Only M of the N objects can receive label L, and I need to take that into account all the time for <em>every other</em> label that I assign too..."</p>
<p><strong>Some thoughts:</strong></p>
<p>(1) Use something like simulated annealing to shuffle the boundary points for the quintile after prediction. That is, use the trained classifier to classify every team's quintile. Use the distance from the margin as the "energy function" to be minimized, and then start randomly shuffling members of over-populated quintiles to nearby under-populated quintiles. You either accept or reject such a shuffling based on the extent to which it worsens the overall distance from the margin.</p>
<p>I don't like this solution because it probably would be computationally inefficient after you already solve the SVM optimization problem. Also, it feels like you're actually just using the margin distance as a continuous quantity to determine the classification, at which point you might as well try to derive a more model-driven or physically plausible continuous quantity and just do regression or something and chop the predicted output into quintiles at the end, which is something I wanted to avoid.</p> | 73,643 | [
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<p>I am doing multiple imputation on a database of observations on hospital patients. There is one observation of many covariates per patient. There are 2 binary outcome variables:</p>
<ol>
<li><p>Alive/Dead after 30 days</p></li>
<li><p>Died in hospital, or survived/discharged</p></li>
</ol>
<p>Two seperate analysis models (logistic regression), with identical covariates, are to be run, each with one of these outcomes as the response. There are 7 covariates in the analysis models.</p>
<p>There is missing data of between 3 and 11% in the covariates and the outcomes. </p>
<p>In addition there are 7 further covariates that are to be used in the imputation model to predict the missingness in the covariates and outcomes.</p>
<p>My questions concerns the imputation of the two outcome variables. They are to be used as predictors for missingness in the covariates, as per standard practice, but they are highly collinear with each other. Is this a concern for the imputation model ? Is it valid/recommended to impute them both in the same model (to generate several complete datasets all containing both outcomes) or should seperate imputations be performed for each of the outcomes (to generate two distinct sets of complete datasets, each distinct set having one of the outcomes) ? Any other suggestions for how to proceed would be welcome.</p> | 47,568 | [
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] |
<p>Suppose, the data below shows the mean response time on a task for respondents among four different groups:</p>
<pre><code>A B C D
1.2 2.3 4.5 6.7
</code></pre>
<p>In order to assess which one of the means are different from one another I do a multiple comparisons test (after an omnibus ANOVA test is cleared) and the multiple comparisons test tells me that the mean for group D is significantly different from the ones for groups A and B and no other pair of differences is significantly different.</p>
<p>What is the best way to present this information visually? </p> | 6,799 | [
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<p>I am trying to implement a test as described in a paper in R. The aim is to calculate enrichment for a particular type of mutation that occurs in a given base in a given sequence context.</p>
<p>I quote</p>
<blockquote>
<p>Statistical evaluation of the over-representation of APOBEC signature mutations in each sample was performed using a one-sided Fisher's exact test comparing the ratio of the number of cytosine-to-thymine or cytosine-to-guanine substitutions and guanine-to-adenine or guanine-to-cytosine substitutions that occurred in and out of the APOBEC target motif (TCW or WGA) to an analogous ratio for all cytosines and guanines that reside inside and outside of the TCW or WGA motif within a sample fraction of the genome.</p>
</blockquote>
<p>Reference - <a href="http://www.nature.com/ng/journal/v45/n9/full/ng.2702.html" rel="nofollow">http://www.nature.com/ng/journal/v45/n9/full/ng.2702.html</a></p>
<p>This means they calculate enrichment by comparing CtoT or CtoG mutations in the base context TCW to those outside that context to the number of Cytosines found in and out of the TCW context in the genome.</p>
<p>So we've got the following values.</p>
<pre><code>TCW.mutations = the number of C to T or G mutations in the context TCW
non.TCW.CtoTG.mutations = the number of C to T or G mutations outside the context TCW
TCW.cytosines = the number of cytosines in the base context TCW in the human exome
nonTCW.cytosines = the number of cytosines outside the base context TCW.
</code></pre>
<p>I need to do a one-tailed fisher's exact test comparing the following using the fisher.test function in R</p>
<pre><code>TCW.mutations/non.TCW.CtoTG.mutations to TCW.cytosines/nonTCW.cytosines
</code></pre>
<p>How is my input matrix supposed to look?</p> | 36,060 | [
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<p>I have 6,000 points for which I have all pairwise distances in a distance matrix. I want to get an idea whether these data were generated by a mixture of Gaussian distributions so I'm trying to get a visualization. I am trying to apply multidimensional scaling in 2 dimensions using sklearn in Python. </p>
<p>I have four questions: </p>
<ol>
<li>In all the examples I found, the number of points were very limited (around 20). Is it possible to apply MDS with 6,000 points?</li>
<li>If not, is there any way I can get a better idea whether my data were generated by a mixture of Gaussians? (I want to cluster this data using GMM.)</li>
<li>sklearn uses the function <a href="http://scikit-learn.org/stable/modules/generated/sklearn.manifold.MDS.html" rel="nofollow">manifold.MDS</a>. One of the parameters of this function is 'random state'. What does it represent?</li>
<li>In <a href="http://scikit-learn.org/stable/auto_examples/manifold/plot_mds.html" rel="nofollow">this example</a>, the matrix used (X_true) has dimension 20x2. Shouldn't MDS take a distance matrix (i.e., a square matrix)?</li>
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<p>This question regards the basic statistics of a normal distribution, but I can't figure it out. I have been given the mean and 95% confidence intervals for a distribution, but would like to know the standard deviation. In my example:</p>
<p>$$
\mu=53.4\quad
95\%\ c.i.=(52.3, 54.3)
$$</p>
<p>I had thought that the solution for $\sigma$ would be something like:</p>
<p>$$54.3=53.4+(SE*1.96)$$
$$SE=(54.3-53.4)/1.96=0.46$$
and then,
$$SE=\frac{\sigma}{\sqrt{n}}$$
$$\sigma=0.46*\sqrt{n}$$</p>
<p>So, if I don't know the $n$, is this possible?</p> | 49,618 | [
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<p>I was able to reproduce table 3.1 from ESL. However, when I tried to reproduce table 3.2, my estimated coefficients were way off (shown below):</p>
<pre><code> [,1]
[1,] 0.4292
[2,] 0.5765
[3,] 0.6140
[4,] -0.0190
[5,] 0.1448
[6,] 0.7372
[7,] -0.2063
[8,] -0.0295
[9,] 0.0095
</code></pre>
<p>The results from table 3.2 in ESL are as follow:
<img src="http://i.stack.imgur.com/epSz4.png" alt="enter image description here"></p>
<p>I have attached my code here: </p>
<pre><code>res <- read.table("prostate.data", sep = "")
fix(res)
XTraining = subset(res, train)
XTesting = subset(res, train == FALSE)
nrow = dim( XTraining )[1]
p = dim( XTraining )[2] - 1 # the last column is the response
D = XTraining[,1:p-1] # get the predictor data
# This gives the raw data for Table 3.1 from the book:
#
print(cor(D),digts=3)
library(xtable)
xtable( cor(D), caption="Duplication of the values from Table 3.1 from the book", digits=3 )
#
# Duplicate Table 3.2 from the book
#
# Append a column of ones:
#
Dp = cbind( matrix(1,nrow,1), as.matrix( D ) )
lpsa = XTraining[,p]
library(MASS)
betaHat = ginv( t(Dp) %*% Dp ) %*% t(Dp) %*% as.matrix(lpsa)
# this is basically the first column in Table 3.2:
#
print('first column: beta estimates')
print(betaHat,digits=2)
</code></pre>
<p>Does anyone have similar issues ? I would like to know what went wrong with my output. </p> | 73,645 | [
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<p>I am currently reviewing some work and have come across the following, which seems wrong to me. Two mixed models are fitted (in R) using lmer. The models are non-nested and are compared by likelihood-ratio tests. In short, here is a reproducible example of what I have:</p>
<pre><code>set.seed(105)
Resp = rnorm(100)
A = factor(rep(1:5,each=20))
B = factor(rep(1:2,times=50))
C = rep(1:4, times=25)
m1 = lmer(Resp ~ A + (1|C), REML = TRUE)
m2 = lmer(Resp ~ B + (1|C), REML = TRUE)
anova(m1,m2)
</code></pre>
<p>As far as I can see, <code>lmer</code> is used to compute the log-likelihood and the <code>anova</code> statement tests the difference between the models using a chi-square with the usual degrees of freedom. This does not seem correct to me. If it is correct, does anyone know of any reference justifying this? I am aware of methods relying on simulations (Paper by Lewis et al., 2011) and the approach developed by Vuong (1989) but I do not think that this is what is produced here. I do not think that the use of the <code>anova</code> statement is correct.</p> | 73,646 | [
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<p>I am trying to learn some statistics using the book, Biometry by Sokal and Rohlf (3e). This is an exercise in the 5th chapter which covers probability, the binomial distribution, and Poisson distribution.
<img src="http://i.stack.imgur.com/T0Tth.jpg" alt="enter image description here"></p>
<p>I realize there is a formula to produce an answer to this question:
$$
n = \frac 4 {( \sqrt{p} - \sqrt{q} )^2}
$$
However, this equation is not in this text. I'd like to know how to calculate sample size knowing only the probability, the desired level of confidence, and the binomial distribution. Are there any resources covering this topic that I can be pointed to? I've tried Google, but what I've seen so far requires information I don't have access to in this problem.</p> | 73,647 | [
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<p>Here is an example case:</p>
<ul>
<li>I have a population of 10,000 items. Each item has an unique id. </li>
<li>I randomly pick 100 items and record down the ids </li>
<li>I put the 100 items back into the population </li>
<li>I randomly pick 100 items again, record down the ids and replace. </li>
<li>In total, I repeat this random sampling 5 times</li>
</ul>
<p>What is the probability that $X$ number of items appear in all 5 random samplings?</p>
<p>I am not very well versed in statistics. Would this be correct for $X = 10$?</p>
<ul>
<li>For each sampling, the number of possible combinations of 100 items from 10,000 is ${\rm binom}(10000, 100)$</li>
<li>Out of all possible combinations of 100 items, ${\rm binom}(9990, 90) * {\rm binom}(100, 10)$ combinations contain 10 specific items</li>
<li>The probability of having 10 specific items is $({\rm binom}(9990, 90) * {\rm binom}(100, 10)) / {\rm binom}(10000, 100)$</li>
<li>The calculated probability to the power of 5 would represent 5 indepenent samplings. </li>
</ul>
<p>So essentially we are just calculating 5 independent hypergeometric probabilities and then multiplying them together? I feel like I am missing a step somewhere.</p> | 73,648 | [
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<p>This is a homework question and I need suggestion how to approach it. We have given the transitions </p>
<ol>
<li>$\ i\rightarrow i+1$ with rate $\lambda(i)$ where $\ i \ge 1$ </li>
<li>$\ i\rightarrow i-1$ with rate $\mu(i)(i-1)$ where $\ i \ge 2$</li>
</ol>
<p>I am starting the forward equation like this:</p>
<p>$$\ p_j(t) = [1-(\lambda_jh+\mu_jh +o(h))p(t)]+ \lambda(j-1)p(j-1)(t)h + ...$$</p>
<p>and I cannot really continue from here. I need to get to the point where I can show that </p>
<p>$$\ G(z, t) = \sum P(N(t)= j|N(0) = a) z^j $$</p>
<p>satisfies</p>
<p>$$\frac{\partial G}{\partial t}
= z \left( z-1\right) \left(\lambda\frac{\partial G}{\partial z}- \mu\frac{\partial^2 G}{\partial z^2}\right)$$</p> | 36,067 | [
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<p>I've used rjags to run MCMC on a model, specified in the JAGS language. Is there a good way to extract that model and perform predictions with it (using the posterior distributions of my parameters)? I can re-specify the model in R and plug in the modes of my parameter posteriors; I'm just wondering if there's a less redundant way of doing this.</p>
<p>I believe <a href="http://sourceforge.net/p/mcmc-jags/discussion/610037/thread/0ecab41c" rel="nofollow">http://sourceforge.net/p/mcmc-jags/discussion/610037/thread/0ecab41c</a> is asking the same question.</p> | 47,486 | [
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<p>I've been looking at numerous questions on this site regarding bootstrapping and confidence intervals, but I'm still confused. Part of the reason for my confusion is probably that I'm not advanced enough in my statistics knowledge to understand a lot of the answers. I'm about half-way through an introductory statistics course and my math level is only about mid-Algebra II, so anything past that level just confuses me. If one of the knowledgeable people on this site could explain this issue at my level it would be extremely helpful.</p>
<p>We were learning in class how to take resamples using the bootstrap method and use those to build up a confidence interval for some statistic we'd like to measure. So for example, say we take a sample from a large population and find that 40% say they'll vote for Candidate A. We assume that this sample is a pretty accurate reflection of the original population, in which case we can take resamples from it to discover something about the population. So we take resamples and find (using a 95% confidence level) that the resulting confidence interval ranges from 35% to 45%.</p>
<p>My question is, what does this confidence interval actually <em>mean</em>?</p>
<p>I keep reading that there's a difference between (Frequentist) Confidence Intervals and (Bayesian) Credible Intervals. If I understood correctly, a credible interval would say that there's a 95% chance that in <em>our situation</em> the true parameter is within the given interval (35%-45%), while a confidence interval would say that there's a 95% that in <em>this type of situation</em> (but not necessarily in our situation specifically) the method we're using would accurately report that the true parameter is within the given interval.</p>
<p>Assuming this definition is correct, my question is: What's the "true parameter" that we're talking about when using confidence intervals built up using the bootstrap method? Are we referring to (a) the true parameter of the <em>original population</em>, or (b) the true parameter of the <em>sample</em>? If (a), then we'd be saying that 95% of the time the bootstrap method will accurately report true statements about the original population. But how could we possibly know that? Doesn't the whole bootstrap method rest on the <em>assumption</em> that the original sample is an accurate reflection of the population it was taken from? If (b) then I don't understand the meaning of the confidence interval at all. Don't we already know the true parameter of the sample? It's a straightforward measurement!</p>
<p>I discussed this with my teacher and she was quite helpful. But I'm still confused.</p> | 73,649 | [
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] |
<p>I computed a feature <code>x</code> that I use to predict <code>y</code> which is a <strong>probability</strong> of being a certain class.</p>
<p><strong>Raw data in R format for (x,y) is pasted here:</strong>
<a href="http://tny.cz/a97b3fd0" rel="nofollow">http://tny.cz/a97b3fd0</a>
(500 samples)</p>
<p>plot(x,y) looks like this:</p>
<p><img src="http://i.stack.imgur.com/sKoJo.png" alt="enter image description here"></p>
<p>It seems similar to a <a href="http://stats.stackexchange.com/questions/83554/linear-regression-not-fitting-well">previous question</a> I asked, so I am tempted to try <a href="http://stats.stackexchange.com/a/83613/21720">this advice</a>, which I understand is the "Least Squared Fit"on log(y) (because y is a probability).</p>
<p>Am I correct?</p>
<p>(My objective is to minimize the MSE.)</p> | 49,921 | [
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<p>I'm working on my final project, and it's a QUEST algorithm, and it uses the chi-square test. I have a problem where the expected value = 0. </p>
<ol>
<li>What should I do? </li>
<li>What does it imply to the chi-square test or to the QUEST algorithm?</li>
</ol> | 73,650 | [
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<p>I am interested in the following sampling problem, which I will try to describe by a motivating example. </p>
<p>Suppose we want to estimate how many people in a certain area, has blue eyes, how many have them has brown eyes etc.(think of a color scale) We do have an estimate on total number eye colors that the population contains (let's say 100 colors). </p>
<p>We then sequentially observe samples - in a motivating context let's say a cruise arrives from that region each month. We disrupt those passengers and examine the eye color of each of them. The cruise does not always contain same number of passengers, and we don't know the decision rule on putting those people on that cruise. A reasonable assumption is that each person has an equal chance (p) of being in that cruise and reasonably we tend to see more the people with common eye colors. </p>
<p>The problem is</p>
<ol>
<li><p>Can we estimate total number of people living on the area?</p></li>
<li><p>Can we estimate the proportion or chance "p" ?</p></li>
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<p>I am attempting to build a model to forecast attendance in a given week in the current year based on this year's attendance values up until the present, and data from two previous years. My data looks like this:</p>
<pre><code> Week 11-12 Cumulative ADA 12-13 Cumulative ADA 13-14 Cumulative ADA
1 0.9941 0.9941 0.9914
2 0.9907 0.991 0.989
3 0.9888 0.9888 0.9879
4 0.9877 0.987 0.9869
5 0.9869 0.9865 0.9867
6 0.9862 0.985 0.9859
7 0.9856 0.9842 0.9857
8 0.9856 0.984 NA
9 0.9852 0.9839 NA
10 0.9848 0.9834 NA
</code></pre>
<p>Any guidance on how to predict the three NAs based on the past two years data and this year's values would be much appreciated.</p>
<p>Thanks!</p> | 36,071 | [
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<p><strong>Study Design:</strong><br>
Below is a clinical trial in a longitudinal dataset. All subjects (n=34) attended <code>V1</code> (baseline) and then they were assigned to either a <code>Placebo</code> (n=15) or a <code>Drug</code> (n=19), both then were investigated at visit <code>V2</code>. Based on an investigation's result at <code>V2</code> called <code>grpVar1</code> they were grouped into two groups: <code>grpVar1=P</code> (n=16) and <code>grpVar1=N</code> (n=18).<br>
Those <code>N</code> were routed for visit <code>V3</code>, whereas those <code>P</code> were routed for visit <code>V4</code> and later visit <code>V5</code>.<br>
<code>Par1</code> was measured in all of the visits for all subjects at two anatomical sites: <code>site1</code> and <code>site2</code>. So each subject has two measurements at the two sites in all of the visits. Additionally, <code>Days</code> variable is the number of days of subsequent visits based on the baseline. Even though the visit is the same, different subjects attended the visit at different days and that was recorded. </p>
<p><strong>It looks like this:</strong> </p>
<pre><code>> head(df,12)
id id_site Gender Visit Days grpVar1 Therapy Par1
1 1 site1 F V1 0 P Placebo 0.61030187
2 1 site2 F V1 0 P Placebo 0.43833820
3 1 site1 F V2 244 P Placebo 7.45492517
4 1 site2 F V2 244 P Placebo 0.63105623
5 1 site1 F V3 322 P Placebo 0.22600916
6 1 site2 F V3 322 P Placebo 0.23180883
7 2 site1 M V1 0 P Drug 0.18130448
8 2 site2 M V1 0 P Drug 0.14165622
9 2 site1 M V2 223 P Drug 1.02354748
10 2 site2 M V2 223 P Drug 2.05987466
11 2 site1 M V3 314 P Drug 0.10194901
12 2 site2 M V3 314 P Drug 0.22315864
</code></pre>
<p><strong>Class of variables</strong></p>
<pre><code>> sapply(df, class)
id id_site Gender Visit Days grpVar1 Therapy Par1
"factor" "factor" "factor" "factor" "numeric" "factor" "factor" "numeric"
</code></pre>
<p><strong>Conception:</strong><br>
So as you can see, repeated measures design with a twist; there is some kind of routing of subjects based on <code>V2</code> results, I call it "bifurcation of subjects" into two different routes of visits after <code>V2</code>.<br>
Clearly there should be some individual variations that need to be accounted for by allowing both intercept and slope to change. Another source of variation I believe is the anatomical site that need to be accounted for alike. So <code>Par1</code> is measured in a hierarchy of site and subjects. Both <code>id_site</code> and <code>id</code> can be looked at as contextual variables; therefore, they can be treated as the random effects in a mixed model.<br>
Although there were 5 visits as shown in <code>Visit</code> variable, but can we make use of the related <code>Days</code> variable to account for variation in the time as days after the baseline. I wonder how one can let the model account for this also? </p>
<p><strong>My trial in R</strong> </p>
<pre><code>library(nlme)
lm_form_1 <- formula (Par1 ~ Visit + Gender + Therapy + id_site + grpVar1)
mod1 <- lme(lm_form_1, random = ~ 1|id , data = df)
</code></pre>
<p><strong>Question:</strong><br>
How to account for variation of <code>id</code>, <code>id_site</code>, and <code>Days</code> as random effects. How to set the var-covar structure of <code>pdMat</code> class based on this study design. Is the layout of the dataset fit for modeling with <code>lme()</code> function or should be modified, what would be suitable? I would be very grateful to suggestions by the statistics community. Please limit your answer to the <code>nlme</code> R package and not <code>lme4</code>. </p> | 73,651 | [
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<p>I have set of time series data tuples: {$(1,22), (2, 25), (3, 18), (4, 26), ...$ so on}</p>
<p>I want to estimate $Y_{t+1}$ using support vector machine regression technique. I have found numerous publications that mostly refer to <a href="http://alex.smola.org/papers/2003/SmoSch03b.pdf" rel="nofollow">Smola's paper</a>. I want to understand the technique to implement it in my programming. </p>
<p>There are numerous examples available for simple regression techniques, but is there any simple example available that solves the problem of finding regression with support vector machine on a given data set using the equations and also shows the steps? </p> | 47,585 | [
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<p>I have accuracy vectors of two classifiers. How can I make a t-test for them on Matlab and is there a good plot type to show it?</p> | 36,075 | [
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<p>I am using Wilcoxon test to compare two paired sets of data for whether their means differ. Besides the p-value, I would also like to know the power of this test. How to compute it in R? Thank you in advance.</p> | 36,078 | [
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<p>I am trying to ascertain if a relationship exists between <strong>hours of play</strong> and <strong>number of friends</strong>. I have two contexts for the study: "at school" and "at a place other than the school".</p>
<p>My data set relates to the "at school" context and the correlation r=0.8766 (significant). </p>
<p>Now the difficult part....</p>
<p>As I want to focus on the <strong>same group of students</strong> for the "at a place other than the school" context, I have asked a question that filters my respondents and puts them in the "at a place other than the school context".</p>
<p>The question is: Did you make any friends in the last three weeks? The answer can be either "yes" or "no". If it is yes, then I have asked them to indicate whether they made the friends "at the school", "at a place other than the school" or "at both places". </p>
<p>So I have four data sets as follows: </p>
<ol>
<li>Those who did not make any friends</li>
<li>Those who made one or more friends at the school</li>
<li>Those who made one or more friends at a place other than the school</li>
<li>Those who made one or more friends at both places (i.e. school and a place other than the school)</li>
</ol>
<p>I have ignored data set 1 because there is obviously no relationship between hours of play and number of friends because no new friends are made.</p>
<p>I have also ignored data set 2 because I already have this finding (in the correlation above, which was at the school)</p>
<p>I have also ignored data set 4 because it does not distinguish between "at school" and "at a place other than the school".</p>
<p>I have used data set 3 and worked out the correlation, which is 0.7687 (significant). My interpretation of this finding is the relationship between hours of play and number of friends exists at the school and also outside the school.</p>
<p>Does this make sense? </p> | 73,652 | [
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<p>This may be too simple a question for this forum - it is possibly a very basic statistics question as commonly found in biomedical research. But since scientists often lack good understanding of statistics, I would appreciate a lot if I could hear the thoughts from expert statisticians on this forum and be educated a little bit.</p>
<p>I want to test if the treatment X affects the parameter P in a sample group of subjects. The design is paired: each subject is tested with no treatment (negative control) and with treatment X (order is randomized). To analyze such data, a paired t-test is obvious. However, I also have a positive control group - which is a separate independent group of subjects with sort of intrinsically different level of P, the one we would expect if treatment X works. So now I have three groups of measurements - two are paired, and one is un-paired. For three groups, I would need to use 1-way ANOVA. However, this will treat three groups as independent. How can I test if there is a difference in means between these three groups. Which test to use? Is it always appropriate to treat paired samples as un-paired? I understand that this leads to lower power, however - is this the only problem with this approach and is it still correct?
Thank you!</p> | 73,653 | [
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<p>I have a waveform, for which most people will measure either a peak amplitude or a slope. I have included the area under the curve and several other measures involving the same original waveform. I now have 10 measures on such waveforms (and I have measured these waveforms in 500 patients). Is it legitimate to put all these measures side by side in one big principal component analysis (PCA) to distil a smaller set of principal components. My worry is about the fact that some of the measures are inherently interdependent (for example, peak amplitude will be inherently correlated with area under the curve), so I was afraid it might fail to meet some of the assumptions behind PCA, such as independence of measures. Is there another analysis method I should use instead of PCA? Independent Component Analysis? Another multi-dimensional scaling method? Cluster analysis? Thanks very much!</p>
<p>A bit more detail: In my case, I have made 9 raw measures, <em>x1</em> .. <em>x9</em>, in each patient. I already know that <em>x2</em> and <em>x4</em> are highly correlated, but their difference has important prognostic implications. On one hand, I am afraid PCA would fail to note this difference (because <em>x2</em> and <em>x4</em> are so correlated), so I would like to include <em>x2-x4</em> as a 10th measure. However, I am bothered by the fact that I am thus introducing trivial correlation, which will inflate the importance of <em>x2</em> and <em>x4</em> and any noise in them. Thanks again.</p> | 73,654 | [
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<p>I've known that, in orthogonal rotation, if the rotation matrix has determinant of -1 then reflection is present. Otherwise the determinant is +1 and we have pure rotation. May I extend this "sign-of-determinant" rule for non-orthogonal rotations? Such as orthogonal-into-oblique axes or oblique-into-orthogonal axes rotations? For example, this matrix</p>
<pre><code> .9427 .2544 .1665 .1377
-.0451 -.0902 -.9940 -.0421
.3325 .3900 .1600 .8437
.4052 .8702 .2269 .1644
</code></pre>
<p>is an oblique-to-orthogonal rotation (I think, because sums of squares in rows, not in columns, are 1). Its determinant is -0.524. May I state that the rotation contains a reflection? Thanks in advance.</p> | 73,655 | [
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<p>Suppose I have a random symmetric matrix W of size $n\times n$, with i.i.d. coefficients uniformly distributed in [0,1], and I set $W_{ii} = 0$.</p>
<p>Then I apply a Multidimensional Scaling of dimension $k$, which I define as minimizing the quantity:
$H=n^{-2}\sum_{i,j} (W_{ij} - ||x_i-x_j||^2)^2$
with respect to the $n$ points $x_i \in R^k$. Say I denote $H^*$ the minimum.</p>
<p>The question is : what is the behavior of $\mathbb{E}[H^*]$ as a function of $k$ and $n$ ?</p>
<p>Is there a mathematical article out there dealing with this question ? or is it an open question ?</p>
<p>Thanks.</p> | 73,656 | [
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<p>I have a data which contains several columns which I later reduced using a PCA algorithms to two different components. I then applied the k-means algorithms to the data.<br>
Now, how can I verify that my data clustered well into each group? Or how do I determine misclassification rate?</p>
<p>For instance, using R, if I check the cluster vector say k$cluster against the labels of the data I had previously before clustering can I just draw a confusion matrix from that and assume that 1 in the clustered vector is equivalent to 1 in my labels?</p>
<pre><code>col3 col2 Col1 lables
123 2.32 2.50 0
124 2.81 3.10 1
125 2.72 3.09 2
126 2.92 3.03 3
127 2.32 2.95 4
</code></pre>
<p>Please note this is a hypothetical data; my data is way bigger than this.</p> | 73,657 | [
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<p>I'd like to test how well my data can be modeled by an <a href="http://en.wikipedia.org/wiki/Exponentially_modified_Gaussian_distribution" rel="nofollow">Exponentially modified Gaussian distribution (Wikipedia)</a> or <a href="https://en.wikipedia.org/wiki/Normal-exponential-gamma_distribution" rel="nofollow">Normal-exponential-gamma (NEG) Distribution</a>. However, the parameter estimation (which involves Skewness) is not very robust when there are outliers in the data set.</p>
<p>I've good experiences with Median based parameter estimation on this data set (see the related question <a href="http://stats.stackexchange.com/questions/48864/estimating-parameters-of-a-normal-distribution-median-instead-of-mean">Estimating parameters of a normal distribution: median instead of mean?</a> ).</p>
<p>Do you know a Median-based or similarly robust parameter estimation for the ExGaussian / NEG distributions? I've already tried trimming my data set, the results were clearly better afterwards. Yet, this obviously introduces a bias, that I would need to correct somehow.</p> | 73,658 | [
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<p>I have $n$ dice with $m$ sides. The $i^{th}$ dice will show value $0 \leq x_i \leq m-1$ with probability $0 \leq D_i(x_i) \leq 1$. What is the probability that the sum of the dice equals $\alpha$</p>
<p>Is there some approximation for $P(\alpha)$</p> | 73,659 | [
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<p>I use SPSS, but am forced to use R for exact logistic regression. So I'm brand new to R (and hating it so far) and also new to logistic regression. I've read the original elrm paper and looked at examples of its use. However, I can't find information on the questions below (after the data description).</p>
<p>The fit of two models of cognitive processing was compared for each subject in each of 3 conditions. My binary dependent variable is whether the difference in model fits was significant or not (my "Success" variable below). I have three experimental Conditions: 0, 1, and 2. 0 is my reference group. My question is: is there an overall effect of Condition? If so, which conditions differ? The specific alternative hypothesis is that the proportion/probability of "success" should be greater in conditions 0 and 1 than in condition 2. My data look like</p>
<p><img src="http://i.stack.imgur.com/OAFtP.gif" alt="original data"></p>
<p>...and so on. SPSS actually creates the dummy variables for you on the fly but they are easy enough to create explicitly.</p>
<p><strong>Question 1:</strong> I have read that to use elrm you have to enter the data such that the response variable represents success/number of trials. And as far as I can tell elrm doesn't create dummy variables automatically. I've seen examples of tables representing this data structure, but can't find any step-by-step examples of getting raw data into that format, espescially given a one-variable 3-levels situation. Is there an example out there that I'm missing? If not, is this what the data should look like? </p>
<p><img src="http://i.stack.imgur.com/aVxOL.gif" alt="reformated data"></p>
<p>I'm not sure how I'd enter the dummy variables into the formula...just as separate variables?</p>
<p><strong>Question 2:</strong> I can see how I can get the tests of the coefficients of the dummy variables. But I can't figure out how to get a test of the overall effect of the independent variable. I need to evaluate the overall effect of Condition before looking at individual conditions. Is there a way to get that out of elrm? (I found an example of this done for the aod package which runs regular logistic regression but not exact logistic regression.)</p>
<p><strong>Question 3:</strong> I can't find a description of what the p-value for individual coeffeicients represents in elrm. Is this is for the Wald test?</p> | 73,660 | [
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<p>I am doing a study of how legal need relates to a number of predictors.</p>
<p>Outcome Variable: Legal Need (Yes or No)<br>
Possible Predictors: Age, Gender, Race, Ethnicity, Language, Clinic, Insurance Status.<br>
Predictors based on bivariate analysis: Age, Language, Clinic, Insurance Status. All ORs were around 1.6 and were significant, typical 95CI between 1.2-2.0.<br>
Number of subjects: 8803 </p>
<p>I suspect that the one variable that is going to fall out of a multiple regression analysis would be Clinic, as the Asthma Clinic (vs the well-visit clinic) has in general, older children who don't speak English and are more on Medicaid (the other predictors from bivariate analysis). </p>
<p>Knowing all of this, I still can't figure out how to run a multiple regression in Excel. </p>
<p>I keep getting Pearson's coefficients like 0.06, which it then says is significant. </p>
<p>Either way I think I need to go beyond this, maybe a stepwise forward or backward analysis? </p>
<p>It's difficult for me to grasp when the outcome is a 0 (no) or 1 (yes), this doesn't really result in anything linear when the percent "yes's" are typically in the 15-30% range. </p>
<p>Am I missing something? Besides years of stats training? </p> | 36,086 | [
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<p>I have two variables measured concurrently at 3 time points, let's call them wealth (<code>W1</code>, <code>W2</code>, <code>W3</code>) and anxiety (<code>A1</code>, <code>A2</code>, <code>A3</code>). Suppose that wealth and anxiety are uncorrelated. Now, I'm interested whether <em>change</em> in anxiety is related to <em>change</em> in wealth. What would be the recommended way of testing this? Naively I would just create 4 new variables <code>W2-W1</code>, <code>W3-W2</code>, <code>A2-A1</code> and <code>A3-A2</code> and look at correlation coefficients between <code>W2-W1</code> vs. <code>A2-A1</code> and between <code>W3-W2</code> vs. <code>A3-A2</code>. Somehow this approach seems silly, since I want a single model that would look at the overall change. Should I be looking at mixed/multilevel models? Specifically which model? Thanks!</p> | 73,661 | [
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<p>As a little experiment, I am extending a nice, interpretable AR/MA relationship between a security $r$ that is variably influenced by the previous $k$ time points over another security $f$. These relationships ("lags") are represented by $l$. I want to pump up the "realism" by making both securities move with stochastic volatility: </p>
<p>$
\begin{bmatrix} r_t \\
f_t \end{bmatrix} =
\begin{bmatrix} l_{r,1} & ... & l_{r,k} \\
l_{f,1} & ... & l_{f,k} \end{bmatrix} \Theta_t
+ \Sigma_t u
$</p>
<p>$u \sim N(0,1)$</p>
<p>$
\log(\Sigma_t) =
\begin{bmatrix} \log(\sigma_{r,t}) \\
\log(\sigma_{f,t}) \end{bmatrix} =
\begin{bmatrix} 1 & \phi_r \\
1 & \phi_t \end{bmatrix}
\begin{bmatrix} \omega_r & \omega_f \\
\log(\sigma_{r,t-1}) & \log(\sigma_{r,t-1}) \end{bmatrix}
+ \begin{bmatrix} \eta_{r,t} \\
\eta_{f,t}) \end{bmatrix}
$</p>
<p>$\eta_{i,t} \sim N(0,\sigma_{\eta_i})$</p>
<p>$
\Theta_t =
\begin{bmatrix} f_t \\
f_{t-1} \\
... \\
f_{t-k} \end{bmatrix} =
I
\begin{bmatrix} f_{t-1} \\
f_{t-2} \\
... \\
f_{t-k-1} \end{bmatrix}
+ \begin{bmatrix} \sigma_{f,t-1} \\
\sigma_{f,t-2} \\
... \\
\sigma_{f,t-k-1} \end{bmatrix}
$</p>
<ol>
<li><p>Does this look right to better trained eyes, before I whip out a prototype? Especially, suggestions on parameters that might to be worth consolidating (i.e., params not adding much explanatory "value")? </p></li>
<li><p>Any suggestions for how to approach the "lag" selection more rigorously (e.g., model selection procedure)? </p></li>
<li><p>Does anyone see shortcuts for consolidating the two transition equations ($\log(\Sigma_t)$ and $\Theta_t$) into the typical "state space representation," i.e., the $\Theta$, $F$, $G$, $V$, $W$ referred to in the literature. For some special cases the equations can be simplified substantially: e.g., traditional MA log volatility models, a log transformation of the master equation simplifies out that pesky $u$ stochastic term.</p></li>
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<p>I have 20 years of data from observing dolphins. When a group is seen, it gets an unique number identifying it, and all identified (marked) dolphins were also registered. So I had a table like</p>
<pre><code>Group Dolphin
1 1
1 10
1 14
2 10
2 23
</code></pre>
<p>I got about 20,000 groups and 500 dolphins. I made a matrix with groups in rows and dolphins in columns, with 1 where a dolphin is in a group, 0 where it's not. So I've ran a multivariate analysis (prcomp in R), and it gave me two very distinct blocks.</p>
<p><img src="http://i.stack.imgur.com/CjplT.png" alt="PCA"></p>
<p>I know that the vertical axis (PC2) is related with the size of the group, the small groups are below, in the bottom of the triangles. But the two blocks are separated in the horizontal axis (PC1), and I didn't figured yet what it's about. I suppose the dolphin population might be separated into two "clans" or something like that, but couldn't discover yet. I colored the points according to group size, water level, place of sight, but all patterns appear equally on both sides. The block on the right has about 2400 points.</p>
<p>My questions are: such a separation must mean something, right? What other tools can I use to understand what is going on?</p>
<p>Thanks very much!</p> | 36,088 | [
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<p>I'm trying to help out a not-for-profit organization and made an error that I'm trying to fix. They've been doing a non scientific survey of their Board of Directors for a number of years regarding board engagement. They asked me to help them convert the survey format from an unfriendly Excel file to something web based, handle the results and do some analysis for them.</p>
<p>In past years, they've used what I'm going to call a weighted scale (Very good = 5, Good = 3, Fair = 2, Poor = -1). This year, we mistakenly included an extra level by allowing a 5, 4, 3, 2, or 1 response. (That is, the previous questionnaires had 4 options, but this one has 5.) </p>
<p>I'm trying to figure out how to conform the scales to be roughly equivalent. I had been thinking that I could let 5 = 5, 4 = 3, 3 = 2.5, 2 = 2 and 1 = -1. However, I realize that this doesn't work and will skew everything lower.</p>
<p>Can anyone recommend a good way to handle this?</p> | 73,662 | [
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<p>I am looking at two populations on which I have measured 4 independent variables ($X_1$, $X_2$, $X_3$, $X_4$) and one dependent variable ($Y$) along with each measurement or observation. I suspect that the two populations are different in the sense that the second population's $Y$ shows a dependence on an additional non-considered factor (I expect $Y$ to be systematically lower, in fact).
Considering that:</p>
<ul>
<li>the dependent variables are highly correlated;</li>
<li>the dependence of $Y$ on the $X$'s is unknown and arguably non-parametric;</li>
<li>the number of observables/measurements is small (~100 for the first group, ~30 for the second).</li>
</ul>
<p>I feel that multi linear regression would assume some kind of underlying structure and would bias my analysis, so I would like to avoid it. I tried to use PCA on both and compare the PC's: nothing significant comes out in the sense of dimensionality.
Could you suggest a test that would check if the two populations are really different in respect to $Y$ while keeping at a minimum the number of assumptions on its functional dependence?</p>
<p>Thank you very much,</p>
<p>P.</p> | 73,663 | [
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<p>I am trying to model weekly disease counts in 25 different regions within 1 country over a ten year period as influenced by temperature. The data is zero inflated and over dispersed. </p>
<p>I am most familiar with Stata but I don't think that there is any option amongst the <code>gee</code>, <code>xtmixed</code>, <code>xtmepoisson</code> etc. commands that allows me to account for the zero inflation and over dispersion issues as well as the autocorrelation. </p>
<p>I log transformed the incidence data and used a SARIMA model but the residuals are not quite normal. I think that there are versions of the ARIMA model for integer data like disease counts but I can't find a program for it. </p>
<p>I was also thinking that I could create a hierarchical model with random intercepts for each region and random effects of temperature in each region, while also accounting for the regular seasonal disease cycle. I believe that I could model this in R using a package like <a href="http://admb-project.org/examples/r-stuff/glmmadmb" rel="nofollow">glmm.admb</a> but due to my limited statistical and R knowledge I am not entirely sure how to do use it. I am mainly confused about accounting for the autocorrelation and seasonal cycle part of the data using a program like this. </p>
<p>Any advice on how to best do this?</p> | 36,091 | [
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<p>I'm new to both R and Bayesian statistics, and I have a problem where I have a normally distributed prior that elicits a mean and standard deviation. The introduced likelihood function is also normally distributed with a mean and standard deviation that can be drawn from a sample.</p>
<p>Now I understand that a posterior is formed that will also be normally distributed. I have been asked to generate this in R, but I cannot find an example of R code where the posterior is formed from a normally distributed prior and likelihood function. </p>
<p>Could someone please point me in the right direction. Thanks. </p> | 73,664 | [
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<p>I am new to PCA and wanted to do a bit of experimentation on my data set just to see what it looked like (using R). I am not able to give access to the data here since it is confidential. However, if there is some other kind of statistic/visualization you would like to see that would help you answer my questions please let me know and I will provide it.</p>
<p>I found the following information about the explained variance:</p>
<pre><code>Component Prop.Var
1 0.911804348
2 0.033618098
3 0.020827269
4 0.011772988
5 0.006611746
6 0.005372772
7 0.004464788
8 0.003436401
9 0.002091589
</code></pre>
<p>This raises the following questions:</p>
<ol>
<li>Am I justified in removing the other 8 principal components? </li>
<li>How do I interpret 91% of explained variance on one component?</li>
<li>If I only kept one component what would be the best way to visualize the data?</li>
</ol>
<p>Below is how the graph of the first two principal components looks. The spread of the data like this is not surprising given how little of the variance is on the second component.</p>
<p><img src="http://i.stack.imgur.com/g9wXP.png" alt="Principal Components 1 and 2"></p>
<p>As I mentioned, I am new to PCA so I really do not know if there is even any useful information to be found from this kind of dimensional reduction. Any insight would be appreciated.</p> | 73,665 | [
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<p>$\newcommand{\E}{\mathrm{E}}$
I don't understand why Baum-Welch algorithm is an instantiation of EM algorithm.</p>
<p>Indeed, why computing $\alpha_t(i)$ and $\beta_t(i)$ corresponds to Expectation step. Expectation step corresponds to compute expectation over the latent variable of log-likelihood of observed variable given the parameter: $\E_{Z|X,\theta^{t-1}}[L(X|\theta)]$. </p>
<p>I don't understand the link. </p> | 73,666 | [
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<p>I'm performing a web based a/b test where there is a control and one treatment. The results are not as simple as "converted" or "didn't convert." A user can "convert" anywhere between 0-10 times. I have all of the data from both the control and the treatment (how many times each user converted from both the control and the treatment). The sample sizes aren't the same size (about 1900 vs 2100) and the variances are different (7.12 vs 6.02). The mean of the treatment is about 11% higher than the control.</p>
<p>The goal of the experiment is to find out if the treatment can increase converts per user. The numbers are showing an 11% increase in conversions per user. To find out if the result is statistically significant I've been trying to use a Welch's t test. When I use the equation for a Welch's t test found on <a href="http://en.wikipedia.org/wiki/Welch%27s_t_test">this wikipedia page</a> I get the following results:</p>
<pre><code>t-score: 2.26
degrees of freedom: 4025.82
</code></pre>
<p>On the wikipedia page it says I can use a <code>t-distribution</code> to test the null hypothesis (my null hypothesis is that the means of the control and treatment are the same). But I'm not sure how to go about using a <code>t-distribution</code>. I'm guessing it has something to do with using a t distribution table.</p>
<p>Questions:</p>
<ul>
<li>Is using a Welch's t test a good approach for this situation?
<ul>
<li>If not what other method would you suggest?</li>
</ul></li>
<li>With my results from the Welch's t test, how do I use a <code>t-distribution</code> to determine if I have a significant result and with how much confidence?</li>
</ul> | 36,094 | [
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<p>I have a vector $v=(v_1,...,v_J)$, which is jointly normal. I then need to take the expectation of this vector. This should give me something like this:</p>
<p>1)$$E(v)=(E(v_1),...,E(v_J))$$</p>
<p>However, I want to write up the integral for this expectation, but I'm unsure how to do this. My guess is something like this:
$$E(v)=\int v \phi(v)dv$$</p>
<p>How does this relate to the expectation I have in 1)? $\phi(.)$ is the joint pdf, but to compute something like $(E(v_1),...,E(v_J))=$, I guess I need the marginal distribution:
$$E(v_1,...,v_J)=(\int v_1 \phi(v_1),\int v_2 \phi(v_2),...,\int v_J \phi(v_J))$$ </p>
<p>Thanks</p> | 73,667 | [
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<p>Suppose that you are running a linear regression model with outcome $Y$ and explanatory variables $X_1$ and $X_2$. You also run a linear regression model with a quadratic transformation of $X_1$: $$E[Y] = \beta_0 + \beta_{1}X_{1}+\beta_{2}X_{1}^{2} + \beta_{3}X_{2}$$ </p>
<p>If $|\beta_2| \approx 0$ can we drop it from our model?</p> | 73,668 | [
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<p>Which method would you suggest for estimation an univariate regression ($y = a + bx + e$) which comprise a lot of $0$ values in the dependent variable (actually kind of censored data). My experience hints at the use of the <strong>Tobit model</strong>. But There is a problem connected with the normal distribution and homoscedasticity of the error term. In my case I'm suspecting a <em>violation</em> of these basic assumptions for using Tobit. In particular the behaviour of latent $y$ under the zero is not anticipating. </p>
<p>Do you know some method (literature) for handling this kind of problems?</p> | 73,669 | [
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<p>I would like to calculate Student's t test of two normal distribution data.
However, I do not have the data at all, but only mean and standard deviation of each population.
So, how can I simulate those data in R and calculate the t.test among both?</p>
<p>These are the values (mean and SD):
Population 1: 6,62 +- 0.52 years
Population 2: 6.31 +- 0.49 years</p>
<p>Thanks in advance
Mario</p> | 73,670 | [
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<p>I am new to Neural Networks and trying to implement RBM. I am stuck on initializing the visible layer's bias value. Is it supposed to initialize to some random number or there is some probabilistic distribution by which it should be initialized. In python I am seeing: </p>
<pre><code>> "vbias = theano.shared(value =numpy.zeros(n_visible,
> dtype = theano.config.floatX), name='vbias') "
</code></pre>
<p>but don't know what is happening here in this line.</p> | 73,671 | [
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<p>I have run a logistic regression using several predictor variables (call them p1 p2 p3 p4) to predict a binary dependent variable (call it y). P1 is a significant predictor of y in the regression. However, a Mann-Whitney test of p1 shows no significant difference by category of y.</p>
<p>Is it normal to have a significant logistic regression predictor that doesn't significantly differ by groups, or is there potentially something screwy with the data?</p> | 73,672 | [
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<p>I wonder if it is fair is to compare the gini coefficient of two discrete distributions with different number of elements. If not, how can I adjust the coefficients for a fair comparison. </p>
<p>In particular, I'm interested in the case when the sum of values in both distributions are equal. For example, minutes played by players of two teams in a basketball game if they have different number of players (10 players in one team, 12 players in the other team) but for both teams sums plays 48 minutes x 5. </p>
<p>Other example, different partitioning of some surface in different regions, how to compare inequality for different partitioning if they have different number of subareas. </p> | 22,257 | [
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<p>I'm looking to test for equality of means across different sample sizes of data, but know that the data is not normally distributed and heteroscedastic.
Can anyone suggest anything?</p> | 49,583 | [
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<p>Let's say I have two models. One has cumulative lift on test data 4.322578, second 2.84488. The only advantage of the second over the first consists in the quality of having the cumulative lift curve nearly identical for both train and validate sets. </p>
<p>For the first model the curve of cumulative lift looks as you can see below.</p>
<p><img src="http://i.stack.imgur.com/GtD7X.png" alt="enter image description here"></p>
<p>Sorry for non-english elements on the plot, but that's the only SAS Enterprise Miner version I have access to.</p>
<p>Mean standard error for the model from the plot - the first one - for train, validate and test sets are: 0.038389, 0.04999 and 0.055314.
For the second one: 0.070393, 0.071889 and 0.07727.</p>
<p>First model seems to be obviously better in terms of accuracy. But at the same time it is less stable, more sensitive to data changes. </p>
<p>My question is whether those stability issues are here big enough to discredit that model in favor of the second one? How to measure instability and at which point it renders a model unusable?</p>
<p>If it is important, the models in question are neural networks.</p> | 36,103 | [
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<p>I did some research and didn't find what I was looking for: I have a data set x = 10,100,1000 and y1, y2, y3 respectively, and I want to plot those points. </p>
<p>But what is happening is that in the x axis the values that are appearing are 10, 200, 400, 600, 800 and 1000. How can I set the scale so that it only appears the values I specified above? What I'm doing is:</p>
<pre><code>y_values <- c(9, 9.6, 9.7, 9.8)
x_values <- c(10,100,1000)
plot(x_values, y_values)
</code></pre>
<p>Thank you.</p> | 73,673 | [
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<p>Please help me proving this:</p>
<p>Suppose that $Y_1,\ldots,Y_n$ are i.i.d. nonnegative RV's with CDF $F$ and $E(Y_i)=\mu<\infty$. Let $y_1,\ldots,y_n$ be a realization from which an EDF $\hat{F}$ is defined:
$$
\hat{F}(y)=\frac{1}{n}\sum_{i=1}^nI(y_i\leq y).
$$
<strong>Want to show</strong>:
$$
\text{plim}_{n\to\infty}\left(n^{1/2}\int_0^\infty y(\hat{F}(y)-F(y))d(\hat{F}-F)(y)\right)=0.
$$
Please state any further necessary assumptions.</p>
<hr>
<p>EDIT responding to GUNG'S comment:</p>
<p>This result is a small step in a bigger argument in Russell Davidson 2009's paper on the Gini index. The author must have considered it obvious because he mentions it without proof. </p>
<p>I have some understanding of asymptotic theory such as some laws of large numbers, some variants of the CLT, various modes of convergence, Slutsky Theorem, measure theory in general and probability theory in particular, and some stochastic calculus.</p>
<p>My problem is I've been learning asymptotic theory on my own and I haven't done a lot of exercises in this. So while I want to understand the author's reasoning, I don't know where to start with this one.</p> | 73,674 | [
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<p>149 students each sat two tests. My null hypothesis is that the product-moment correlation coefficient is 1, because each test should be an accurate indicator of current attainment. The actual PMCC for the data is 0.912152856.</p>
<p>Please could you show (and explain) how to test if this is a significant result?</p> | 73,675 | [
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<p>I recently came across a predicting problem (0-1 outcome, with more than 80 variables), I decided to use GBM (Gradient Boosting Machine by Friedman)to handle this job. I let the GBM use only 70% of the dataset, and within this training set, 60% are used at each iteration. </p>
<p>During this process I found a big problem of GBM: there was one predictor (AAA) that was so important (nearly causal) that this single predictor can predict the outcome with precision=40% at recall=40% (0-1 unevenly distributed, with 0: 80%, and 1: 20%), and this single predictor model was better than the GBM with 80 predictors including it (AAA). I wonder why this could happen, I would like to hear you thought on it. </p>
<p>From a 'linear regression' perspective, I suspect multicollinearity, that GBM splits many other spurious predictors that correlated to AAA, gradually missing the predictive power of AAA. Additionally, I found GBM cut each of my predictor in a very 'overfitting' way (predictor sometime positive, sometime negative affect the fitted value). To tackle this problem, my strategy was to use a parameter of GBM called 'var.monotone' (it takes three values, 1 for positive correlation, -1 for negative, 0 for arbitrary). I selected 22 out of the original 80 predictors based on there association with the outcome, and used var.monotone to force their relationship with the outcome. the model was slightly better. </p>
<p>I would like to know if force each predictors relationship with the outcome is a good strategy to mitigate overfitting, what's the better way from your perspective? More importantly, do you think a blackbox with 80 predictors really work? how about a logistic regression, or a L1 regularized one, with only 5 highly important (or causal) predictors?</p>
<p>Thanks,
Hicham Hu</p> | 36,513 | [
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<p>I have to validate the data in one database by comparing it to data from a validated application system. The solution I came up with was (at least in theory) creating a statistical method that would define the number of random samples needed to check on a table of the database, in order to say, that with a 95% chance the number of errors is representative for that table. Then, with the probability of the errors I could consider if the data is valid or not.</p>
<p>The binomial distribution doesn't help, since I don't have any knowledge about the probability at which an error could be found. My statistical knowledge is pretty rusty and I can't figure it out right now.</p>
<p>Just to clarify again:
Given N the number of entries in a table I want to know what number n for random samples I have to chose in order to be able to say after testing, that the probability of the error is p, at a 95% accurateness.</p>
<p>I would be very helpful for every helping idea I could get. Any references to literature or sites covering this would also be greatly appreciated. Thanks in advance!</p> | 73,676 | [
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<p>I am applying a linear model to my data:
$$
y_{i}=\beta_{0}+\beta_{1}x_{i}+\epsilon_{i}, \quad\epsilon_{i} \sim N(0,\sigma^{2}).
$$</p>
<p>I would like to estimate the confidence interval (CI) of the coefficients ($\beta_{0}$, $\beta_{1}$) using bootstrap method. There are two ways that I can apply the bootstrap method:</p>
<ol>
<li><p>Sample paired response-predictor: Randomly resample pairs of $y_{i}-x_{i}$, and apply linear regression to each run. After $m$ runs, we obtain a collection of estimated coefficients ${\hat{\beta_{j}}}, j=1,...m$. Finally, compute the quantile of ${\hat{\beta_{j}}}$.</p></li>
<li><p>Sample error: First apply linear regression on the original observed data, from this model we obtain $\hat{\beta_{o}}$ and the error $\epsilon_{i}$. Afterwards, randomly resample the error $\epsilon^{*}_{i}$ and compute the new data with $\hat{\beta_{o}}$ and $y^{*}_{i}=\hat{\beta_{o}}x_{i}+\epsilon^{*}_{i}$. Apply once again linear regression. After $m$ runs, we obtain a collection of estimated coefficeints ${\hat{\beta_{j}}}, j=1,...,m$. Finally, compute the quantile of ${\hat{\beta_{j}}}$. </p></li>
</ol>
<p>My questions are:</p>
<ul>
<li><strong>How are these two methods different?</strong></li>
<li><strong>Under which assumption are these two methods giving the same result?</strong></li>
</ul> | 73,677 | [
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<p>Presumably this has been discussed already, but I wanted to get some sense of how prevalent is the use of R for biostatistics publications. On PubMed I did find a number of research papers that were conducted using R (as mentioned in the Methods or Statistical Analysis sections of the documents). However, the majority were done using SAS/SPSS and also an appreciable number using Stata.</p>
<p>There has been a lot of talk about R in recent years and I am looking for some data that can corroborate the fact that R has been rising in popularity in the commercial area. In my experience, however, I have been seeing some resistance for firms to switch to R from SAS, even though there is so much more that you can do with R compared to SAS. There is also the concern that FDA "prefers results in SAS" ... although I have not seen anything officially mentioned by FDA to this effect.</p>
<p>I understand that SAS has been there for decades, it is what many R&D departments are most comfortable working with, etc., etc., ... and am looking for real-world examples of who are instead using R for professional research and/or publications.</p> | 73,678 | [
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<p>Hi i am trying to use AIC value for comparing logit and probit model where in each model the data and the number of covariates are same (say, covariate= 3 for each model)</p>
<p>Does AIC value increases while increasing sample size?</p>
<p>Which one better to use as a tool for comparing logit and probit, AIC or MSPE?</p> | 73,679 | [
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<p>Logistic regression essentially means taking the logit of your response proportions, p, and then doing standard regression. Consider the case where one p is 1. </p>
<p>logit(1) = log(1/(1-1)) = infinity. How can you do regression with infinity?</p>
<p>That is, if one of your observed proportions p is 1, then you are trying to find the line that minimises the sum of squared differences from a set of points that include infinity. How does this not drive the regression line to always have infinite slope?</p> | 36,114 | [
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<p>I have a data set of recorded elephant locations for the span of 6 years (elephantdata). Some of the entries are duplicates of the same day. I want to create a subset of my 'elephantdata' and create a new matrix that only has one data point before noon and one data point after noon for each day. I would like that data point to be selected randomly from the data points offered.</p>
<p>For example:</p>
<pre><code>elephantdata
Row Date Time Breeding_H E1 E2 E3
1 11/01/06 08:38 1 0 0 0
2 11/01/06 18:00 1 0 0 0
3 12/01/06 05:38 1 0 0 0
4 02/02/06 08:58 1 0 0 0
5 02/02/06 16:30 1 1 1 1
6 02/02/06 17:15 1 1 1 1
7 03/02/06 08:45 1 0 0 0
</code></pre>
<p>For Breeding_H I want to find that if the 'Date' is a duplicate AND two entries are in the morning (before 12:00) or in the evening (after noon) I want R to randomly chose one of the entries. So Row 6 and 7 are both after noon and on the same day, so I would like to only have one of those data entries.</p>
<p>Any suggestions? Would really appreciate any help you've got. I've looked up the 'unique' and 'duplicated' function but I don't know how to write the actual code to make this happen. </p> | 73,680 | [
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<p>Good evening everyeone,</p>
<p>I am currently working on a set of self-study questions which relate to true/false answers. I am currently faced with a question where the answer claims for it to be false, but I find it true. Not sure if there is an error in the answer. Appreciate some help and advice please.</p>
<blockquote>
<p>A confidence interval is an estimate for which there is a specified degree of certainty that the sample statistic will be in the interval. </p>
</blockquote>
<p>My take is that the above <strong>statement is true</strong> as the confidence interval tells us with a specific degree of confidence how likely a value will fall within the range. </p>
<p>Appreciate some advice please.</p>
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<p>According to the <a href="http://en.wikipedia.org/wiki/Approximate_Bayesian_computation" rel="nofollow">Wikipedia article</a>, we have the scenario shown below, but how can ABC generate simulation datasets from samples of $\theta$ without knowing or evaluating the likelihood function?</p>
<p>For example, how would this method work for a normal $N(\mu, \sigma)$ distribution? Assuming that the parameter to estimate is $\mu$ and that $\sigma$ is known, how would it generate the simulations without evaluating $N(\mu, \sigma)$?</p>
<p><img src="http://i.stack.imgur.com/pkpG0.png" alt="enter image description here"></p> | 36,117 | [
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0.03303150087594986,
-0.06711449474096298,
0.007111826911568642,
-0.018200865015387535,
-0.005163668654859066,
0.011494315229356289,
-0.019672788679599762
] |
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