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<p>I am trying to cluster cells (1×1km) over a specific area. Each cell is composed of various habitats defined by a code. (Each habitat consists of 3 parameters, so a habitat code looks like e.g. 1-3-15. There are around 100 different habitats, i.e. max number of combinations of these 3 parameters).</p>
<p>I now try to define clusters according to:</p>
<ul>
<li>Number of habitats per cell</li>
<li>1st largest habitat covering the cell</li>
<li>2nd largest habitat covering the cell and</li>
<li>Rarest habitat in the cell (I developed a global rarity index for each habitat, and one habitat having the lowest index is chosen per cell).</li>
</ul>
<p>So the last 3 in the list refer to a specific habitat per cell, and the first is more a quantitative measure of how many are in each cell.</p>
<p>Based on this they'd like to perform a cluster analysis, but I am wondering whether there is a mix up between categorical and quantitative data.</p>
<p>Could anyone please give some advise on what to method to use, e.g. in R?
Thanks.</p> | 36,119 | [
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<p>My boss gave me this do file but I have never worked with dprobit. I also need to interpret it, this is the result:</p>
<pre><code> xi: dprobit apoyado $X, robust nolog
i.fuerza _Ifuerza_1-9 (_Ifuerza_1 for fue~a==Comando General omitted)
note: _Ifuerza_8 != 0 predicts success perfectly
_Ifuerza_8 dropped and 1 obs not used
note: _Ifuerza_2 dropped because of collinearity
note: _Ifuerza_9 dropped because of collinearity
Probit regression, reporting marginal effects Number of obs = 592
Wald chi2(5) = 33.04
Prob > chi2 = 0.0000
Log pseudolikelihood = -387.38545 Pseudo R2 = 0.0433
------------------------------------------------------------------------------
| Robust
apoyado | dF/dx Std. Err. z P>|z| x-bar [ 95% C.I. ]
---------+--------------------------------------------------------------------
_Ifuer~3*| -.1759987 .1586211 -1.10 0.273 .162162 -.48689 .134893
_Ifuer~4*| -.3915721 .1314311 -2.56 0.011 .155405 -.649172 -.133972
_Ifuer~5*| -.2404857 .1450899 -1.60 0.110 .533784 -.524857 .043885
_Ifuer~6*| .0252801 .1673778 0.15 0.881 .087838 -.302774 .353335
_Ifuer~7*| .0776492 .1834521 0.41 0.681 .038851 -.28191 .437209
---------+--------------------------------------------------------------------
obs. P | .5675676
pred. P | .5723459 (at x-bar)
------------------------------------------------------------------------------
(*) dF/dx is for discrete change of dummy variable from 0 to 1
z and P>|z| correspond to the test of the underlying coefficient being 0
</code></pre> | 73,681 | [
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<p>I created a criterion for my financial data-set for classify data to two classes for other processing (like <code>neural network binary classificatio</code>). After calculating this criterion (between 0 and 1) the distribution of output is like <code>exponential</code> (but between <code>0</code> and <code>1</code> - something like <code>beta distribution</code>). Now i want set a <code>threshold</code>to create two classes from these samples. </p>
<p>I can set every threshold (<code>70% - (0.7)</code> was good in <code>classification accuracy</code>) but I want i want a logic for that. for example in <code>normal distribution</code> we can set <code>68–95–99.7 rule</code>. I want set this default value in my program because different samples are inserting in my system in the feature.</p>
<p>Thanks.</p> | 73,682 | [
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] |
<p>I am trying to select a prior for the covariance parameters of my Gaussian Process (GP) and have been running into numerical problems with my MCMC code. My model is the following:</p>
<p>$$Y = D\beta + GP(0,\sigma^2R(\psi))$$</p>
<p>where $R$ is the following correlation matrix:</p>
<p>$$R_{i,j}(\psi)=\exp(\psi(x_i-x_j)^2)$$</p>
<p>My priors for $\beta$ and $\sigma^2$ are the following:</p>
<p>$$p(\beta)\propto 1$$ and
$$\sigma^2\sim IG(a,b)$$</p>
<p>so what I am trying to figure out is what are possible appropriate choices of prior for $\psi$.
So far I have been trying to place an inverse gamma prior on $\psi$ but that has not been going very well. </p>
<p>Here is an update: Here is further problem formulation if it helps</p>
<p>Likelihood: $$f(\beta,\sigma^2,\psi|x)\propto|\sigma^2R(\psi)|^{-1/2}\exp(-\frac{1}{2}(Y-D\beta)'R(\psi)^{-1}(Y-D\beta))$$
Prior: $$p(\beta,\sigma^2,\psi)=p(\beta|\sigma^2,\psi)p(\sigma^2|\psi)p(\psi)\propto\sigma^{-a-1}\exp(-b/\sigma^2)p(\psi)$$</p>
<p>Now, based on my posterior under this prior, I have been trying to code up a Metropolis within Gibbs sampler with the following full conditions:</p>
<p>$$\beta|\sigma^2,\psi,Y\sim N(\hat\beta,D'(\sigma^2 R(\psi))^{-1}D)$$
$$\sigma^2|\beta,\psi,Y\sim IG(a,b)$$
$$\psi|\beta,\sigma^2,Y\propto |R(\psi)|^{-1/2}\exp(-\frac{1}{2\sigma^2}(Y-D\beta)'R(\psi)^{-1}(Y-D\beta))p(\psi)$$</p>
<p>So I sample $\beta$ and $\sigma^2$ within a gibbs step and then use a M-H step for sampling from $\psi$ but I am having horrible numerical problems when sampling from $\psi$ (basically my acceptance ratio is 0/0). Finally, I'll post some code to if that helps.</p>
<p>Code: </p>
<pre><code>x = sort(runif(5,0,1))
y = exp(-1.4*x)*cos(7*pi*x/2)
plot(x,y,type='l',ylim=c(-1,1))
tau = as.matrix(dist(x,upper=T,diag=T))
corrR = function(psi,tau){
R = exp(-tau^2*psi)
return(R)
}
psi.cond = function(psi,r,sig,D,beta,Y){
d = .01
e = .01
ans = det(r)^(-.5)*exp(-.5/sig*t(Y-D*beta)%*%solve(r)%*%(Y-D*beta))*psi^-(d+1)*exp(-e/psi)
#ans = -.5*log(det(r))-.5/sig*t(Y-D*beta)%*%solve(r)%*%(Y-D*beta)-(d+1)*log(psi)-e/psi
return(as.real(ans))
}
D = rep(1,length(x))
Y = as.matrix(y)
m = length(x)
a = .01
b = .01
B = 100
beta = rep(NA,B)
sigma = c(1,rep(NA,B-1))
psi = c(120,rep(NA,B-1))
for(i in 1:B){
R = corrR(psi[i],tau)
bhat = as.real(solve(t(D)%*%solve(R)%*%D)%*%t(D)%*%solve(R)%*%Y)
beta[i] = rnorm(1,bhat,t(D)%*%solve(sigma[i]*R)%*%D)
sigma[i+1] = 1/rgamma(1,(m+2*a)/2,(as.real(t(Y-D*beta[i])%*%solve(R)%*%(Y-D*beta[i]))+2*b)/2)
log.xi = rnorm(1,log(psi[i]),.1)
xi = exp(log.xi)
u = runif(1)
R.xi = corrR(xi,tau)
R.psi = corrR(psi[i],tau)
temp = (psi.cond(xi,R.xi,sigma[i],D,beta[i],Y)*(1/psi[i]))/(psi.cond(psi[i],R.psi,sigma[i],D,beta[i],Y)*(1/xi))
alpha = min(1,temp)
if(u <= alpha){
psi[i+1] = xi
}else{
psi[i+1] = psi[i]
}
}
</code></pre> | 73,683 | [
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<p>I have $2\times 3$ repeated measures design.</p>
<ul>
<li>2 conditions(a and b)</li>
<li>3 intensities (low, medium and high).</li>
</ul>
<p>I am concerned only with the a to b differences at the corresponding intensity. For example I would like to compare:</p>
<ul>
<li>A low and b low</li>
<li>A medium and b medium</li>
<li>A high and b high.</li>
</ul>
<p>I am not concerned with comparing A low to A medium to A high as physiologically we know that they are different and it does not answer my research question.
I don't care about how the 2 variables interact, but I may be wrong.
My inclination is to say the paired T -tests are fine as </p>
<p><strong>Should I perform 3 paired t-tests for the comparisons of interest or a $2\times3$ Repeated measures ANOVA?</strong></p> | 36,125 | [
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<p>I have 3 variables A, B and C, which are all markedly skewed. Below, I indicate correlations between two variables, e.g., A and B as $r_{ab}$.
Using the following test with with $n-2$ degrees of freedom</p>
<p>$$t= \frac{r\sqrt{n-2}}{1-r^2}$$</p>
<ul>
<li>$r_{ac}$ is positive but not significantly different from zero, </li>
<li>$r_{bc}$ is positive but not significantly different from zero, and </li>
<li>$r_{ab}$ is significantly different from zero.</li>
</ul>
<p>Then using <a href="http://books.google.de/books?id=5WFohzuwzP0C&pg=PA381&lpg=PA381&dq=howell+williams+t+correlation&source=bl&ots=oRJeJ1RsdQ&sig=k0H8uDGDJbMhzUrsk_OKGUi5ufQ&hl=de&sa=X&ei=s1jwUZ7uD4rEswba54HoBA&ved=0CFcQ6AEwBQ#v=onepage&q=williams&f=false" rel="nofollow">Williams t test</a> </p>
<ul>
<li>$r_{ac}$ and $r_{bc}$ are not significantly different from each other.</li>
</ul>
<p>How can this be possible?
<strong>Shouldn't the difference between two positive correlations always be non-significant when they are both not significantly different from zero?</strong></p> | 73,684 | [
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<p><strong>UPDATE</strong> Original question was confused and poorly worded. I thought about it more and don't think I have a question any longer. After thinking a bit more I came up with:</p>
<p>For a distribution, such as the normal for example, the probability that the variable falls in a certain range is:</p>
<pre><code>P(a<=X<=b|X ~ N(mu, sigma^2))
</code></pre>
<p>Using Bayes' Theorem I can infer:</p>
<pre><code> P(a<=X<=b|X ~ N(mu, sigma^2)) = P(a<=X<=b, X ~ N(mu, sigma^2)) / P(X ~ N(mu, sigma^2))
</code></pre>
<p>Interpreting this statement I could say:</p>
<p>P(X ~ N(mu, sigma^2)) is the prior probability that the random variable X ~ N(mu, sigma^2) (based on whatever information we have), and P(a<=X<=b, X ~ N(mu, sigma^2)) is the prior probability that X ~ N(mu, sigma^2) <strong>and</strong> within the interval [a,b]. Then, if it is revealed to us that X is in fact distributed N(mu, sigma^2), or if we assume it to be so, the probability that it falls within the interval [a,b] is the ratio of the prior probabilities, as stated above.</p>
<p>The above statement doesn't depend at all on what the particular pdf is that you're dealing with. I think I was hoping to see a connection between the two, but they seem to be unrelated ideas.</p> | 73,685 | [
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<p>How can I interpret the main effects (coefficients for dummy-coded factor) in a Poisson regression?</p>
<p>Assume the following example:</p>
<pre><code>treatment <- factor(rep(c(1, 2), c(43, 41)),
levels = c(1, 2),
labels = c("placebo", "treated"))
improved <- factor(rep(c(1, 2, 3, 1, 2, 3), c(29, 7, 7, 13, 7, 21)),
levels = c(1, 2, 3),
labels = c("none", "some", "marked"))
numberofdrugs <- rpois(84, 10) + 1
healthvalue <- rpois(84, 5)
y <- data.frame(healthvalue, numberofdrugs, treatment, improved)
test <- glm(healthvalue~numberofdrugs+treatment+improved, y, family=poisson)
summary(test)
</code></pre>
<p>The output is:</p>
<pre><code>Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 1.88955 0.19243 9.819 <2e-16 ***
numberofdrugs -0.02303 0.01624 -1.418 0.156
treatmenttreated -0.01271 0.10861 -0.117 0.907 MAIN EFFECT
improvedsome -0.13541 0.14674 -0.923 0.356 MAIN EFFECT
improvedmarke -0.10839 0.12212 -0.888 0.375 MAIN EFFECT
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
</code></pre>
<p>I know that the incident rate for <code>numberofdrugs</code> is <code>exp(-0.023)=0.977</code>. But how do I interpret the main effects for the dummy variables? </p> | 49,412 | [
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<p>Let $X$ be a random variable from $f(x; \theta)$, where $\theta =(\theta_1,\theta_2)$.
I want to:</p>
<p>take a sample from this distribution using Metropolis Hastings algorithm and update the parameters simultaneously.</p>
<p>The proposal distribution is a bivariate normal distribution with mean the current value of the parameter $\theta$ and covariance matrix $\Sigma$.</p>
<p>Steps:</p>
<p>Given $\theta$</p>
<p>Step 1: Generate $\theta^{can}$ from the proposal distribution.</p>
<p>Step 2: Take $\theta$ = $\theta^{can}$ with probability
$\alpha(\theta,\theta^{can}) $ </p>
<p>where $\alpha(\theta,\theta^{can})$ = $ min \left( \frac{f(\theta^{can})}{f(\theta)}∗ \frac{proposal(\theta)}{proposal(\theta^{can})}, 1\right)$</p>
<p>I know that </p>
<p>$proposal(\theta^{can}) = \frac{1}{\sqrt{(2\pi)^k|\boldsymbol\Sigma|}} \exp\left(-\frac{1}{2}({\theta^{can}}-{\theta})^T{\boldsymbol\Sigma}^{-1}({\theta^{can}}-{\theta}) \right)$.</p>
<p>I would like to ask if $proposal(\theta) = 0$.</p>
<p>Thank you very much.</p> | 29,780 | [
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<p>was wondering if someone could help clarify an ANCOVA for me, or maybe post me in the right direction.</p>
<p>I have a set of outcome measures that have been administered pre treatment and post treatment. I do not have a control group. My data is in a long format (i.e. each individual has data on 2 rows, one for pre treatment one for post treatment). </p>
<p>I want to do an ANCOVA with baseline scores as a covariate. Time is my fixed factor. I've been told to have my data in the long format (by someone quite senior), but I'm wondering whether I need to transform it into wide format, and then use outcome score as my DV. </p>
<p>I'm using SPSS for the analysis.</p> | 73,686 | [
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<p>I have a screen shot and the question asks if the sample size is blocked out, what is the most likely sample size that was used to generate these results. How do I do this? The possible answers are 5, 10 , 20 and 25 and 25 is the correct answer. It gives the mean 8.08, median 7, sd=6.22 skew=0.83 at the top.</p> | 73,687 | [
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<p>What kind of data analysis technique / formula would you use to describe which is the fastest OS in this chart, Windows or Linux? </p>
<p><img src="http://i.stack.imgur.com/uleOH.png" alt="enter image description here"></p>
<p>If Linux and Windows had equal speed on all tests, all bars would be 50% blue, 50% green.</p>
<p>The data is duration in milliseconds. Each number (e.g. Linux Startup) represents the mean of 1000 individual duration tests on that scenario. The results of each test individually is covered in separate charts. </p>
<p>This data represents an overview of the one set of data (Linux over the course of these 5 tests) and how it relates to the second set of data (Windows over the course of these 5 tests). The aim is to be able to say:</p>
<p>Over the 5 tests we Windows is faster. (You can see this in the chart because there is less green, but this is to prove it statistically).</p>
<p>Note:</p>
<p>The chart below shows the same data in real value terms, showing that one test dominates the others. While this is an important result, it does not weigh on the current question as the two results in the 'Refreshing Desktop' test still bear the same relation to each other as those in the other tests.</p>
<p>In the comments there has been some discussion on how to represent this data. The reason I represent it in stacked bars is because I want to show it <em>without</em> the overshadowing effect of the one anomalous data. Is there a preferred method to show this relationship?</p>
<p><img src="http://i.stack.imgur.com/NqQNC.png" alt="enter image description here"></p> | 36,130 | [
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<p>What I mean is, constructing a decision tree where each node is not a single feature instead composition of multiple features, therefore the evaluation criteria should consider a metric over multiple numbers instead of single number. For the original case of decision tree we are looking for a feature's value comparing its ordinal relation < or > to other instances. But I am expecting to compare multiple value like $x_1,\cdots,x_n$ with new instance's values $x_1,\cdots,x_n$ at each node selection. It is like to have an vector of values selected for each decision-tree node.</p> | 36,131 | [
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<p>Consider the following m regression equation system:</p>
<p>$$r^i = X^i \beta^i + \epsilon^i \;\;\; \text{for} \;i=1,2,3,..,T$$</p>
<p>where $r^i$ is a $(T\times 1)$ vector of the T observations of the dependent variable, $X^i$ is a $(T\times k)$ matrix of independent variables, $\beta^i$ is a $(k\times1)$ vector of the regression coefficients and $\epsilon^i$ is the vector of errors for the $T$ observations of the $i^{th}$ regression</p>
<p>If the above is an SUR model (seemingly unrelated regressions), does it make sense to compute the BIC (Bayesian Information Criterion) for the model?</p>
<p>If so, how would that be computed? Should the dependent variables be stacked into one vector, in order to get only one regression equation?</p>
<p>Any help would be appreciated! Thank you!!!</p> | 73,688 | [
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] |
<p>Previously I've read that adjusted-$R^2$ is not a measure of fit. Recently, though, I wanted to substantiate that piece of knowledge by understanding the reason why but I couldn't find any substantive sources to back this up. </p>
<p>The Wikipedia article on it states "while $R^2$ is a measure of fit, adjusted $R^2$ is instead a comparative measure of suitability of alternative nested sets of explanators" but does not provide a citation.</p>
<p><a href="http://en.wikipedia.org/wiki/Coefficient_of_determination" rel="nofollow">http://en.wikipedia.org/wiki/Coefficient_of_determination</a></p> | 36,133 | [
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] |
<p>I was comparing the performance of pROC and AUC libraries when performing auc() calculations on random data:</p>
<pre><code>library("pROC");
library("AUC")
predictor <- rnorm(10000, 5);
outcome <- rnorm(10000) > 0;
print ("pROC:::auc() time & output")
system.time(x <- pROC:::auc(outcome, predictor))
print(x);
print ("AUC:::auc() time & output")
system.time(x <- AUC:::auc(AUC:::roc(predictor, factor(outcome))))
print(x);
</code></pre>
<p>AUC:::auc seemed to perform substantially faster, but what I found strange is that the compute different auc values for the same dataset:</p>
<pre><code>> system.time(x <- pROC:::auc(outcome, predictor))
user system elapsed
1.00 0.01 1.31
> print(x);
Area under the curve: 0.5058
> print ("AUC:::auc() time & output")
[1] "AUC:::auc() time & output"
> system.time(x <- AUC:::auc(AUC:::roc(predictor, factor(outcome))))
user system elapsed
0.19 0.00 0.18
> print(x);
[1] 0.4942452
</code></pre>
<p>I thought the Auc() function was deterministic so they should produce the same number. </p>
<p>Yet pROC produces 0.5058 and AUC produces 0.4942452 .</p>
<p>Am I misusing either function?</p>
<p>EDIT: FYI I tried making the number semi random and the functions now give identical results (bar rounding errors):</p>
<pre><code>predictor <- runif(10000);
outcome <- as.integer((predictor + runif(10000)) > 0.5);
</code></pre> | 690 | [
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<p>I have a series of numbers, which are some survival probabilities that form a decaying curve. I would like to fit them with a "Pareto" distribution. I expect to have a smooth fitted curve, thus I can extrapolate it and have a rough prediction.</p>
<p>My data are like <code>1, 0.987, 0.972, 0.965, ...</code>.</p>
<p>How can I achieve my goal?</p> | 36,136 | [
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<p>I am currently working on a retrospective analysis where I am looking at patients to see if immune sensitization prior to a procedure has any bearing on outcomes after the procedure. The immune sensitization is a categorical variable (Hi vs Lo). </p>
<p>In regards to outcomes, one of the things I am looking is survival analysis (time to death). I ran a Kaplan-Meier analysis broken down by immune sensitization and there seems to be a statistically significant (p<.05) difference in regards to the time to death.</p>
<p>My questions are these: </p>
<ol>
<li>I ran a Cox regression analysis with the sensitization status as the only covariate and noted the p-value to be .35. Why is there such a big difference in the statistical significance and which one should I choose? (if it helps, from a visual inspection, only patients in the Hi category died)</li>
<li>When analyzing my patient characteristics, I noted that there was a gender difference in the two sensitization categories (p<.05). I ran a Cox Regression model with the sensitization and gender as the covariates and noted that p-value of 0.955 for the sensitization status and 0.5 for the gender. Am I correct in interpreting that neither covariate has any bearing on the time to death?</li>
</ol>
<hr>
<p><em>As requested, here is some of my output</em> </p>
<p>Original Kaplan Meier analysis (PRA_Categ represents the sensitization status):</p>
<p><img src="http://i.stack.imgur.com/ba1aJ.png" alt="Original Kaplam Meier Results (PRA_Categ represents the sensitization status)"></p>
<p>The Corresponding COX regression with only one covariate (PRA_Categ): </p>
<p><img src="http://i.stack.imgur.com/4Eabs.png" alt="The corresponding COX regression with only one covariate (the PRA_Categ)"></p>
<p>COX regression with two covariates (PRA_Categ and Gender): </p>
<p><img src="http://i.stack.imgur.com/R2Bht.png" alt="COX regression with two covariates (PRA_Categ and Gender)"></p> | 18,991 | [
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<p>I would like to run a negative binomial regression, but also controlling for one of the variables. Similar to what you would do with a hierarchical regression. I am trying to predict violence (never, once, 3 times ...); and the literature says I should control for age, as aggression decreases with age.
Would welcome your thoughts, thanks in advance.
sharon</p> | 20,443 | [
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<p>I'd like to see how not adjusting for confounders affects estimated coefficients in linear regression. Here is what my lecture notes say:</p>
<ol>
<li>Un-adjusted model: $E[Yi] = \beta_0 + \beta_1X_i$</li>
<li>Adjusted model: $\quad\ E[Yi] = \gamma_0 + \gamma_1X_i + \gamma_2W$, where $W$ is the confounder.</li>
</ol>
<p>Let $\hat{\beta_1}$ be the OLS estimate of $\beta_1$. Then under the adjusted model we have:</p>
<p>$$
E[\hat{\beta_1}] = \gamma_1 + r_{XW}\sqrt{\frac{{\rm var}(W)}{{\rm var}(X)}}\gamma_2
$$</p>
<p><strong>How $E[\hat{\beta_1}]$ was calculated?</strong></p> | 48,671 | [
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<p>I have created a vector of length 400 with 6 unique values of relatively equal proportions (1-6). I have drawn two random samples from the vector, each $n=26$, 10,000 times, performed $t$-tests, added the $p$-values to a list and output a histogram of the $p$-value frequency. The histogram of the $p$-values shows a cyclical clumping effect for $p$-values greater than $0.7$. I would like to know why this occurs.</p>
<p>Here is my R-code:</p>
<pre><code>set.seed(117)
cover1<-rep(1,100)
cover2<-rep(2,63)
cover3<-rep(3,59)
cover4<-rep(4,74)
cover5<-rep(5,56)
cover6<-rep(6,48)
landscape=c(cover1,cover2,cover3,cover4,cover5,cover6)
sample.size<-26
x<-10000
pval.list <-vector("list", length(x))
alpha <- 0.05
conf.level <- 1 - alpha
for(i in 1:x){
s1 <- sample(landscape, size = sample.size, replace = TRUE, prob = NULL)
s2 <- sample(landscape, size = sample.size, replace = TRUE, prob = NULL)
result.t.test <- t.test(s1,s2, conf.level=conf.level)
pval.list[i] <- result.t.test["p.value"]
}
s<-pval.list
pvalue<-as.numeric(s)
hist(pvalue, main = paste("Histogram of" , "p-value"), breaks= 100)
</code></pre>
<p><img src="http://i.stack.imgur.com/Hz4pH.jpg" alt="Histogram of p-values"></p> | 73,689 | [
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<p>Say I have a data matrix of size $N \times P$ where $N$ is the number of samples and $P$ is the number of features. Now, if I do principal component analysis, I get another data matrix of size $N \times K$ where $K$ was chosen according to some criteria. My question: if I pick a row (sample) from the $\text{PCA}$ matrix, does it still point to the <em>same</em> sample as in the original data matrix?</p>
<p>In my study the data on each row is from one subject, so I want to know if the correspondence still exists if I use $\text{PCA}$ for feature selection. (I think this is correct but better safe than sorry...!)</p> | 73,690 | [
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<p>In the <a href="http://en.wikipedia.org/wiki/Pitch_%28card_game%29" rel="nofollow">game of Pitch</a> what are the odds of the jack of trump being dealt in the 24 cards?</p> | 73,691 | [
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] |
<p><strong>Variogram</strong> is simple but effective way to investigated the spatial variation in the variable of interest in the field being studied. However it has been reported that variogram cannot be considered as the most satisfactory model especially where there are curvature <em>(e.g., permeable channels in reservoir engineering)</em> in the medium being studied. That is different patterns could have more and less exact copy of the same variogram.<br>
A suggestion for development an approach was <strong>multi-point statistics</strong> (<strong>geostatistics</strong>), in which for example, a <strong>training image</strong>, a 2D matrix template is being used for inference of spatial variation. It was shown in the literature that training images are useful to dictate the output the desired pattern honoring conditioning data and being based on stochastic approaches to satisfy statistical inferences. </p>
<ul>
<li>Questions:</li>
</ul>
<blockquote>
<p><strong>Q1:</strong> What else about advantages and or disadvantages of multi-point statistics ?<br>
<strong>Q2:</strong> How to obtain training images?<br>
__<strong>Q2.1:</strong> How to generate training images using existing knowledge etc?<br>
<strong>Q3:</strong> How about 3D and further dimensions?<br>
<strong>Q3:</strong> What is the next stage after training image? </p>
</blockquote> | 73,692 | [
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<p>I've got two time-series, S (stress in a railway track) and T (temperature).
The time-series are several months long. The relationship is linear, however, it can change subtly or 'jump' at some points, due to work done on the rails.</p>
<p>Currently, I'm doing linear regression on a per-day basis, and then temperature-correcting S based on that days models. However, changes in the relationship do happen within each day, so this is not perfect.</p>
<p>I guess I'm trying to figure out how to best fit multiple linear models between S/T over time. How would I go about doing that? I've just started out with R, though I'm also good with Python.</p> | 40,061 | [
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<p>I have a data set of 903 continuous observations, that I graphically visualize with a histogram. The bin and width values could be optimized, but it is logical from the distribution that I have a Gaussian function.</p>
<p>When I do the fitting, I use the frequency values of the data as the Y-values. For example, if the observations are ${(2,3,3,3,4,4,5)}$, and the user-defined bin width is 1.0, then the corresponding y-values would be $(1,3,3,3,2,2,1)$, assuming that the first bin limit will be assigned as the minimum value.</p>
<p>I am not obtaining statistical significance with a Gaussian fitting, in terms of goodness of fit ($Q$) with the Chi-squared test ($\chi^2$). In other words, my null hypothesis is rejected making that a Gaussian model does not represent the experimental data.</p>
<p>Now, I am doing the same test but using an averaged shifted histogram version of my x-values and the frequency for those averaged bins as the y-values for each observation, I now obtain good results in terms of goodness of fit.</p>
<p>I need to clarify if it is valid to realize a Goodness of fit for an averaged shifted histogram, or if there is clear bias for data overfitting.</p>
<p>Here it is a q-q plot of the data:</p>
<p><img src="http://i.stack.imgur.com/gRHTp.jpg" alt="QQ Plot"></p> | 73,693 | [
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<p>I only found a example in which the constraind on $\beta_i, \ i=1,...k$ would make them sum up to one as well introduces a constraind such that all $\beta_i$ are all greater or equal zero. Since I dont need a condition for the summation of the $\beta_i$ I'm not quite sure how to deal with this problem.</p>
<p>Since in this context a matrix $C$ of constraints is introduced such that $C\beta = c$, I'm not sure how to deal with $C\beta \geq 0$.</p>
<p>Any suggestions are very welcome!</p> | 36,146 | [
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<p><strong>The short question:</strong></p>
<p>Are there any studies of systems described by several hidden stochastic time dependent variables and observed variables that are given by known deterministic functions of hidden variables?</p>
<p><strong>More Details:</strong></p>
<p>I have a time dependent stochastic process in which $n$ real-valued variables depend on time: $x_i(t)$. These variables cannot be observed directly ($i.e.$ they are hidden variables). However, we can observe a deterministic (not stochastic) function of these hidden variables: $y(t) = y(x_{i}(t))$ (in my particular case $y(t) = \sum_{i=1}^n x_{i}(t)$). Moreover, we can observe another variable that is a function of hidden variables. This second function is also deterministic but it combines hidden variables corresponding to different times: $z(t) = x_{0}(t) + x_{1}(t-\Delta t) + x_{2}(t-2 \Delta t) + ... + x_{n}(t-n \Delta t)$.</p>
<p>In addition to that we know that subsequent vectors representing the hidden variables are related in a stochastic way: $x_{i}(t) = \psi[x_{i}(t - \Delta t)]$. The exact form of $\psi$ is not known.</p>
<p>We also always know $x_0(t)$ and we set the value of $x_{n}(t)$.</p>
<p>The goal is to find the stochastic relation $\psi$ and to chose such values of $x_{n}(t)$ that $x_{t}=0$ (we choose $x_{n}$ now and what to keep $x_{0}=0$ in the future). We also want to avoid $y=0$.</p>
<p>My question is how to approach this problem and if there are some results for such systems (or what are the name of such systems).</p>
<p>The closest that I can think of are Markov hidden process but, as you can see, it is something different.</p> | 73,694 | [
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<p>I am doing a one-way ANOVA of a response variable (Y) on a treatment factor (T) of 7 levels. However, for each treatment, I have only 2 observations (or replicates). The ANOVA result shows the the means across the treatment are highly significant (p<0.001). I have check the normal and constant-variance assumptions and seems that my data does not violate these assumptions.</p>
<p>My question is: Can I trust the result of ANOVA, even if the sample size is extremely small (n=2*7=14)?</p>
<p>The first question that comes to my mind is the power of my test. Since my ANOVA has obtained an effect size of 0.9. I conducted a power analysis (using Q*Power.3) to see how many samples are needed to obtain such effect size with significance level of 0.05 and power of 0.8. The result showed that I need at least 28 samples. Since I have much fewer samples than required, does it mean that my ANOVA results are not reliable? </p> | 36,148 | [
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<p>Which of the following is the correct code for fitting a GARCH-M(1,1) model where the ARMA(0,0) is "removed"? Or what is the correct code?</p>
<ol>
<li><p><code>modm11 = ugarchspec(variance.model=list(model="sGARCH", garchOrder=c(1,1)),
mean.model=list(archm=T, archpow=2, include.mean=F))</code></p></li>
<li><p><code>modm11 = ugarchspec(variance.model=list(model="sGARCH", garchOrder=c(1,1)),
mean.model=list(armaOrder=c(0,0), archm=T, archpow=2,
include.mean=F))</code></p></li>
<li><p><code>modm11 = ugarchspec(variance.model=list(model="sGARCH", garchOrder=c(1,1)),
mean.model=list(armaOrder=c(0,0), archm=T, archpow=2))</code></p></li>
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<p>This seemed to me to be basic, but I can't seem to find a solution online, so I wondered what I might be missing.</p>
<p>I wish to include the output of an lm summary object inside an Sweave (.Rnw) document. I can either output the summary.lm as is, or use the xtable/Hmisc packages (through xtable or latex commands). Is there something like xtable that also gives the summary information which available from outside the table? ($R^2$, F statistics etc...?)</p>
<p>Thanks.</p> | 73,696 | [
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<p>I'm concerned with Box-Jenkins-models and especially the first step, the prewhitening to obtain meaningful crosscorrelations for identifying transfer functions and building regression models.</p>
<p>I'm working with SAS and here one has to identify a suitable ARIMA-model for the input series to achive white noise and afterwards the response series is automatically filtered by the same model.</p>
<p>Now I'm wondering about two things:</p>
<ol>
<li>If I have two series A and B and I do not know which one is the input and which one the response series (and there can be feeback maybe), do I have to set at first series A as input and filter it with a suitable ARIMA-model (and the series B is filtered like that) and I can only have a look at positive lags (and lag 0) of the crosscorrelation function (CCF) that will show how series A affects B. And as a second step do I have to choose series B as input and do the same (set a suitable ARIMA-model for B, A is filtered with the same parameters, look at the positive lags (and lag 0) of the CCF to see how B affects A) ? It seems a little bit weird to me, but it seems to be right in a logical way. But then I ask myself what to do with two different lag 0 values for example? (In some cases I got significant results in one case and when I changed input and response like described it wasn't significant)</li>
<li>What if I decided that there is a deterministic trend in one of the series (let's say series A) and I have to detrend by polynomial subtraction? In this case in SAS the response series (let's say series B) isn't filtered in the same way. Is it right to take the detrended series from A and the original series B for computing the CCF?</li>
</ol>
<p>I would be very glad if someone can help me.</p>
<p>Greetings,
Daniela</p> | 73,697 | [
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<p>I'm attempting to answer a general question about a method of musical comparision which is generalizable beyond western music but uses western music scales as a nearly sufficient subspace for dimensional reduction. What is a good probability model of the distribution of frequencies as represented by western sheet music for SATB and instruments?</p> | 73,698 | [
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<p>1)
Suppose, I have 25 sample values. I have no idea as to which distribution, the observation comes from. How will I proceed?</p>
<p>2)
With regard to the same question:
Suppose, though I have no idea, I pretend that it comes from normal distribution and estimate its mean and variance, do a P-P or an Anderson-Darling and conclude that it comes from normal density. Precisely, does it essentially mean that the data follows normal distribution. Aren't I just trying to fit my data to a convenient distribution?</p>
<p>In short, given a continuous sample, how do I decide its original parent distribution??</p> | 73,699 | [
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<p>I have a random forests model with which I am trying to predict species presence or absence.<br>
This is my code:</p>
<pre><code>#read in dataframe containing observations of species presence/absence & predictor variables
mydata <- read.csv('mydata.csv')
#fit random forests model
fitmodelA <- randomForest(SPECIESA ~ var1 + var2 + var3 + var4 + var5 +var6 + var7 + var8 +
var9 + var10, data=mydata, mytry=3, ntrees=500, replace=T, importance=T, keep.forest=T)
#predict to new data
predictmodelA <- predict(fitmodelA, newdata, type="prob")
# save as raster image
writeRaster(predictmodelA,"predictSPECIESA.tif")
</code></pre>
<p>Apparently I should get back a matrix that has the probability for both classes, i.e., in two columns. Do I understand correctly that it is also possible to add the "index" argument to predict only one class? </p>
<p>With my code the way it is, my output raster produced one layer with probabilities 0 to 1, but no other attributes – <strong>what class is this predicting?</strong> I am more interested that my map show predictions of presence rather than absence.
Probably a simple solution to this...? Thanks! </p> | 73,700 | [
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<p>I have a merged database from two cross-sectional surveys for distinct years ($t_1$ and $t_2$). If all questions were exactly the same, I could just stack the data horizontally and run a normal panel data OLS.</p>
<p>The problem is that some variables exist only for $t_1$, while other variables exist only for $t_2$. So my question is: should I just do the same as above and disregard these variables, should I run cross-sectional OLS on each separate databases using all variables available for that year (and then there is a way to "aggregate" the results?) or could I run a SUR model where for each year I use all available variables and constrain the coefficients to be the same?</p> | 17,840 | [
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<p>I am implementing the ARIMAX model and need to implement feature selection. I have >100 features and a lot of data, so I need a method that isn't too computationally expensive. I tried a wrapper, backward feature selection algorithm but that was too expensive. Is there a less computationally expensive approach towards feature selection? Perhaps like a filter feature selection method.</p> | 37,223 | [
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<p>When running an OLS regression with a squared term,
$$
y = a + b_1(X) + b_2(X^2) + e
$$
I know that the partial effect of $X$ is $b_1 + 2b_2(\bar X)$ to get the overall effect of $X$ on $Y$ evaluated at the mean. Using</p>
<pre><code>reg y x c.x#c.x
margins, dydx(*) atmeans
</code></pre>
<p>does this in Stata and it also includes a 95% CI for the overall effect. My question now is: how does <code>margins</code> calculate the standard error and the 95% CI of the overall effect of $X$ at the mean?</p> | 36,152 | [
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<p>I am working on classification of audio files. It is a binary classification and I plan to use SVM. I have used SVM before for face matching and other image analysis and retrieval stuff. </p>
<p>I have extracted the required feature vectors from the audio files, i.e., the training and test dataset and reduced their dimensionality by using Principal Component Analysis. I would like to know whether there are any more steps which are necessary before applying SVM classification and prediction? Should the test and training dataset obtained after applying PCA be normalized or centered? Would the results be different (better / worse) after applying the normalization / centerization? Or are there any more methods that can be used to pre-process data before SVM is applied on it? </p> | 73,701 | [
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<p>I have 5 years worth of mean wind speed meteorological data. I want to compare the observed wind speed data against a Weibull distribution on a graph of <strong>the probability density distribution.</strong></p>
<p>I have read about the different methods to find parameters $k$ (shape) and $c$ (scale) of a Weibull distribution, and I found that the maximum-likelihood method is better but I am confused. What should my steps be?</p> | 49,339 | [
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<p>Given an (infinite) data population from which you repeatedly draw samples of a fixed size. On each sample you learn a classifier which you then evaluate by computing the prediction error on a large independent test set.
The prediction error is defined as the average over all instances in the test set of the zero-one loss function $\mathcal{L}(y,\hat{y})$. (The zero-one loss function $\mathcal{L}(y,\hat{y})=0$ if the predicted label $\hat{y}$ of an instance equals the true label of the instance y, and is 1 otherwise.)</p>
<p>My question is whether the central limit theorem holds in this situation, so that the distribution of the prediction error over the samples approximates a normal distribution, given a sufficient number of samples?</p>
<p>I know that the theorem holds for a sufficiently large number of <em>independent</em> random variables. So I am in doubt because the individual predictions for one test set originate from the same classifier, and the classifiers vary over the samples. </p> | 73,702 | [
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<p>I am doing a project on sexual selection (male-male competition) in the turquoise killifish Nothobranchius furzeri. </p>
<p>There are two morphs of male in the population from which my fish are obtained from- one has a red tail and the other has a yellow tail. </p>
<p>My null hypothesis is: Tail colour is not related to dominance/competitive ability. </p>
<p>I will be putting one yellow-tailed male and one red-tailed male in an arena and recording the number or aggressive interactions that take place within 5 minutes and the winner of each. I have 8 red males and 8 yellow males all of similar colour intensity. I originally thought I had about 30 of each and I was going to rank for size and pair them up (i.e. largest red with largest male etc.)which would control for size (the larger fish are more dominant). However with a sample size of only 8 this would not be sufficient to get significant results. </p>
<p>How could I redesign the experiment and which statistical tests could I use? </p>
<p>I don’t have access to any more fish.</p> | 73,703 | [
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<p>How does a computer algorithm set up to take as input an arbirary bivariate probability density function, generate pairs of numbers from that distribution? I have found a routine called simcontour that is part of LearnBayes in R that performs that operation. </p> | 36,154 | [
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] |
<p>I found a formula for pseudo $R^2$ in the book <a href="http://www.maths.bath.ac.uk/~jjf23/ELM/" rel="nofollow">Extending the Linear Model with R, Julian J. Faraway</a> (p. 59).</p>
<p>$$1-\frac{\text{ResidualDeviance}}{\text{NullDeviance}}$$. </p>
<p><strong>Is this a common formula for pseudo $R^2$ for GLMs?</strong></p> | 73,704 | [
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<p>I am having trouble understanding the different estimators that can be used in an impact evaluation. I know that the intention-to-treat (ITT) estimator compares differences between eligible individuals without the program, and eligible individuals with the program, regardless of compliance. However, I thought the average treatment effect (ATE) also measured the same thing. However, it seems that the ATE takes into consideration the compliance. Therefore, it compares outcomes between those eligible and taking up treatment with those who are not eligible. Is this correct? </p> | 73,705 | [
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<p>I would like to find a reference, preferably free on the internet, where I can read about the theoretical or practical justification for the use of parametric / analytic probability distributions.</p>
<p>By parametric distributions I mean the named ones like Normal, Weibull, etc. </p> | 36,156 | [
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<p>I have a nested-case control study that I have been using for analysis. At the end of my work I have deduced a set of variables that I use later to to classify new cases. One example of a simple classifier I am using is a naive Bayes, which will output simply a probability. </p>
<p>So here is my question:</p>
<p>Could I make my probabilities reflect the real world? In my specific example, the condition that I am testing for has a prevalence of 33% in my study, but a it has a population prevalence of only 10%. Bayes factors have been suggested to me as a way to achieve this, however I am little unsure how to set up the problem. </p>
<p>As an example I have seen a Bayes factor as a logit between the true vs. study prevalence of the outcome. The classifier however was a logistic regression, and in that case the Bayes factor was just added to the linear predictors. I think the example there was very specific, and perhaps an inappropriate method for probabilities of a naive Bayes. Instead what I did was add the logit Bayes factor to the logged probabilities, but I am also not convinced this is right either. I also think a simpler solution would be to use Bayes theorem directly, but there I am not sure how to represented my study vs.population prevalences. The method below isn't quite right, but gets at what I want:</p>
<pre><code> p_final = classier_posterior*(population_prev)/(study_prev)
</code></pre>
<p>I should contextualize that I use the probabilities to establish a threshold for classification down stream.</p> | 73,706 | [
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<p>I guess this means that omitting some variables in a certain interval, say, $(x_1, x_2, x_3, x_4, x_5) \to (x_1, x_5)$ in AR(4) model. </p>
<p>Is it right? Or does this means eliminating autocorrelations by adjusting autocorrealated variables by a certain method?</p>
<p>Thanks in advance!</p> | 73,707 | [
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<p>I would like to conduct a multivariate meta-analysis (multiple treatment arm meta analysis) comparing the effect of different drugs. My outcome measure is discrete and describes the number of occurrences of a specific side effect during the period of observation. The studies that i would like to include report the odds ratio (OR) and their 95%-CI of this side effect for every drug relative to a “baseline drug”. The problem is that studies defined different drugs to be the baseline.</p>
<ul>
<li>Is it valid to just transform my OR to bring them to a common
baseline drug? </li>
<li>Is it valid to transform the 95%-CI of the OR in the
same way?</li>
<li>There is typically no 95%-CI reported for the baseline drug. Thus<br>
when I transform this baseline drug, I have no 95%-CI. Is there a way
to derive a 95%-CI in this case?</li>
</ul>
<p>Here is some dummy data:</p>
<pre><code>structure(list(study = structure(c(2L, 2L, 2L, 2L, 2L, 3L, 3L,
3L, 3L, 3L, 1L, 1L, 1L, 1L, 1L), .Label = c("Liu", "Mark", "Smith"
), class = "factor"), drug = structure(c(1L, 2L, 3L, 4L, 5L,
1L, 2L, 3L, 4L, 5L, 1L, 2L, 3L, 4L, 5L), .Label = c("A", "B",
"C", "D", "E"), class = "factor"), OR = c(1, 1.5, 1.7, 1.8, 2.5,
2.8, 1.1, 1, 2.3, 1.2, 1.8, 1.2, 2.5, 1, 1.8), ci_lb = structure(c(13L,
5L, 4L, 9L, 11L, 12L, 2L, 13L, 10L, 1L, 6L, 3L, 8L, 13L, 7L), .Label = c("0.5556",
"0.6225", "0.7619", "1.2628", "1.365", "1.4212", "1.5758", "1.6208",
"1.7048", "1.7435", "1.9497", "2.3531", "NA"), class = "factor"),
ci_ub = structure(c(13L, 2L, 7L, 5L, 10L, 11L, 1L, 13L, 9L,
4L, 8L, 3L, 12L, 13L, 6L), .Label = c("1.5775", "1.635",
"1.6381", "1.8444", "1.8952", "2.0242", "2.1372", "2.1788",
"2.8565", "3.0503", "3.2469", "3.3792", "NA"), class = "factor")), .Names = c("study",
"drug", "OR", "ci_lb", "ci_ub"), row.names = c(NA, -15L), class = "data.frame")
> my_data
study drug OR ci_lb ci_ub
1 Mark A 1.0 NA NA
2 Mark B 1.5 1.365 1.635
3 Mark C 1.7 1.2628 2.1372
4 Mark D 1.8 1.7048 1.8952
5 Mark E 2.5 1.9497 3.0503
6 Smith A 2.8 2.3531 3.2469
7 Smith B 1.1 0.6225 1.5775
8 Smith C 1.0 NA NA
9 Smith D 2.3 1.7435 2.8565
10 Smith E 1.2 0.5556 1.8444
11 Liu A 1.8 1.4212 2.1788
12 Liu B 1.2 0.7619 1.6381
13 Liu C 2.5 1.6208 3.3792
14 Liu D 1.0 NA NA
15 Liu E 1.8 1.5758 2.0242
my_data_1 <- my_data[my_data$study=="Mark",]
my_data_2 <- my_data[my_data$study=="Smith",]
my_data_3 <- my_data[my_data$study=="Liu",]
my_data_2$OR <- my_data_2$OR * 1/my_data_2$OR[my_data_2$drug=="A"]
my_data_3$OR <- my_data_3$OR * 1/my_data_3$OR[my_data_3$drug=="A"]
my_data_2$ci_lb <- my_data_2$ci_lb * 1/my_data_2$OR[my_data_2$drug=="A"]
my_data_3$ci_lb <- my_data_3$ci_lb * 1/my_data_3$OR[my_data_3$drug=="A"]
my_data_2$ci_ub <- my_data_2$ci_ub * 1/my_data_2$OR[my_data_2$drug=="A"]
my_data_3$ci_ub <- my_data_3$ci_ub * 1/my_data_3$OR[my_data_3$drug=="A"]
my_data_new <- rbind(my_data_1, my_data_2, my_data_3)
my_data_new
my_data_new$OR <- round(my_data_new$OR, 2)
my_data_new$ci_lb <- round(my_data_new$ci_lb, 2)
my_data_new$ci_ub <- round(my_data_new$ci_ub, 2)
> my_data_new
study drug OR ci_lb ci_ub
1 Mark A 1.00 NA NA
2 Mark B 1.50 1.36 1.64
3 Mark C 1.70 1.26 2.14
4 Mark D 1.80 1.70 1.90
5 Mark E 2.50 1.95 3.05
6 Smith A 1.00 2.35 3.25
7 Smith B 0.39 0.62 1.58
8 Smith C 0.36 NA NA
9 Smith D 0.82 1.74 2.86
10 Smith E 0.43 0.56 1.84
11 Liu A 1.00 1.42 2.18
12 Liu B 0.67 0.76 1.64
13 Liu C 1.39 1.62 3.38
14 Liu D 0.56 NA NA
15 Liu E 1.00 1.58 2.02
</code></pre> | 73,708 | [
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<p>I'm writing an essay on the effects of M&A announcements on stock prices. I understand most of the requirements perfectly fine, but I'm stumped on one particular part of the essay.</p>
<p>I have for every target and acquiror stock prices in the range [-170, 10] days, where day 0 is the announcement date. I use [-170, -71] to calculate the abnormal returns in [-10, 10] which is the event window I'm interested in. The next part confuses me:</p>
<p>The idea underlying the in-between period [-70, -11] is that for each firm/stock 4 variables can be con-structed, that is the stock-price runup = stock return [-70, -11], the stock-sigma = stock vola-tility [-70, -11], the market-price runup = market return [-70, -11], and the market-sigma = market volatility [-70, -11]. </p>
<p>Following this, I'm supposed to use these four variables for both univariate and multivariate regressions for CAR[K,L] where [K,L] will be chosen depending on the number of days for which a significant announcement effect has been found. </p>
<p>My question is: why would I want to have this in my essay, I have literally no idea why this would be interesting. What is the purpose of the four variables, and why can the be used to regress on the CAR?</p>
<p>I know this is quite an economical question, but I think the theory is statistical in nature, and there is not an economics stackexchange-site, so I decided to ask this question here. If anyone could provide any assistance, even the smallest hint, I would be most grateful. Thank you for any help you can give!</p> | 73,709 | [
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<p>I'm reading about convolutional neural networks. As I understood a feature map is a set of neurons (i.e like a single hidden layer in traditional ANN). So why feature maps are indexed by (i,j)? Shouldn't a feature map be indexed only by one index because it's just a set of neurons?</p>
<p>In the following picture layer C1 has 6 feature maps. The picture says that a feature map is 28 by 28. But why?! Why 2D?!</p>
<p><img src="http://i.stack.imgur.com/V79IH.png" alt="enter image description here"></p> | 36,160 | [
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<p>I am running into an error </p>
<pre><code>Error in node Y1[5]
Observed node inconsistent with unobserved parents at initialization
</code></pre>
<p>trying the following bugs model in JAGS accessed from R:</p>
<p>Apparently <code>Y1[5] = 2</code> causes problems in <code>dcat</code>. But I can't seem to figure out why.
Any help kindly appreciated.</p>
<h3>DATA</h3>
<pre><code>d1 <- matrix(c(1,1,1,1,2,2,2,3,3,3,3,3,4,4,5,5,5,
0,0,0,0,0,0,1,0,0,1,1,1,1,1,0,1,1),ncol=2)
d2 <- matrix(c(1,1,1,2,2,3,3,3,4,4,5,5,5,
0,0,0,0,0,0,0,1,1,1,1,1,1),ncol=2)
d3 <- matrix(c(1,1,1,1,1,2,2,2,2,3,3,3,
0,0,0,0,0,0,0,1,1,1,1,1),ncol=2)
bugdata <- list(
N1 = 17,
N2 = 13,
N3 = 12,
ncat1 = 4,
ncat2 = 5,
ncat3 = 3,
Y1 = d1[,1],
Y2 = d2[,1],
Y3 = d3[,1],
D1 = d1[,2],
D2 = d2[,2],
D3 = d3[,2]
)
</code></pre>
<h3>INITS</h3>
<pre><code>buginit <- list (
list (
ta=1, tb=1,
a=0.5, b=2, al2=0.1,
alpha1 = 0.5, alpha2 = 0.5, alpha3 = 0.5,
beta1 = 2, beta2 = 2, beta3 = 2,
theta1_0=c(-.5,0,1),
theta2_0=c(-.5,0,1,2),
theta3_0=c(-.5,0)
)
)
</code></pre>
<h3>MODEL</h3>
<pre><code>model{
# SET d1
for (i in 1:N1) {
for (j in 1:(ncat1-1)) {
probit(Q1[i,j]) <- (theta1[j] - beta1*D1[i])/exp(al2 + alpha1*D1[i])
}
p1[i,1] <- Q1[i,1]
for (r in 2:(ncat1-1)) {
p1[i,r] <- Q1[i,r] - Q1[i,(r-1)]
}
p1[i,ncat1] <- 1 - Q1[i,(ncat1-1)]
Y1[i] ~ dcat(p1[i,1:ncat1])
}
# SET d2
for (i in 1:N2) {
for (j in 1:(ncat2-1)) {
probit(Q2[i,j]) <- (theta2[j] - beta2*D2[i])/exp(al2 + alpha2*D2[i])
}
p2[i,ncat2] <- 1 - Q2[i,(ncat2-1)]
p2[i,1] <- Q2[i,1]
for (r in 2:(ncat2-1)) {
p2[i,r] <- Q2[i,r] - Q2[i,(r-1)]
}
Y2[i] ~ dcat(p2[i,1:ncat2])
}
# SET d3
for (i in 1:N3) {
for (j in 1:(ncat3-1)) {
probit(Q3[i,j]) <- (theta3[j] - beta3*D3[i])/exp(al2 + alpha3*D3[i])
}
p3[i,ncat3] <- 1 - Q3[i,(ncat3-1)]
p3[i,1] <- Q3[i,1]
for (r in 2:(ncat3-1)) {
p3[i,r] <- Q3[i,r] - Q3[i,(r-1)]
}
Y3[i] ~ dcat(p3[i,1:ncat3])
}
# PRIORS...
for (t in 1:3) {theta1_0[t] ~ dnorm(0, 0.1)}
theta1[1:3] <- sort(theta1_0)
for (t in 1:4) {theta2_0[t] ~ dnorm(0, 0.1)}
theta2[1:4] <- sort(theta2_0)
for (t in 1:2) {theta3_0[t] ~ dnorm(0, 0.1)}
theta3[1:2] <- sort(theta3_0)
alpha1 ~ dnorm(a,ta) T(-10,10)
alpha2 ~ dnorm(a,ta) T(-10,10)
alpha3 ~ dnorm(a,ta) T(-10,10)
beta1 ~ dnorm(b,tb)
beta2 ~ dnorm(b,tb)
beta3 ~ dnorm(b,tb)
al2 ~ dnorm(0.0, 0.1) T(-10,10)
a ~ dnorm(0.0, 0.1) T(-10,10)
b ~ dnorm(0.0, 0.1)
ta ~ dgamma(0.01, 0.01)
tb ~ dgamma(0.01, 0.01)
}
</code></pre> | 37,450 | [
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<p>@Dmitrij Celov posted an answer to the question <a href="http://stats.stackexchange.com/questions/8303/how-to-do-logistic-regression-subset-selection">How to do logistic regression subset selection</a> saying that <a href="http://www.jstor.org/discover/10.2307/2531779?uid=3739256&uid=2&uid=4&sid=21102415674961" rel="nofollow">this paper</a> was a good reference. I was wondering if anyone knows if any of these authors ever created an R package based on it.</p> | 73,710 | [
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<p>I recently read the article "<a href="http://scholar.google.com/citations?view_op=view_citation&hl=de&user=TeaZX90AAAAJ&citation_for_view=TeaZX90AAAAJ%3ad1gkVwhDpl0C" rel="nofollow">Is It Really Robust?</a>" (Schmider, E., Ziegler M., Danay, E., Beyer, L. & Bühner M., 2010)
The authors of the article come to the conclusion that an ANOVA is quite robust against violations of the normality assumption. </p>
<p>However the study focusses on one-way ANOVAs. I would like to know if these findings can be generalized on a two-way repeated measures ANOVA?</p>
<p>References to peer-reviewed articles are highly appreciated!</p>
<hr>
<h3>References</h3>
<p>Schmider, E., Ziegler M., Danay, E., Beyer, L. & Bühner M. (2010). Is It Really Robust?.<em>Methodology, 6 (4),</em> 147 - 151.</p> | 36,162 | [
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<p>I have near about 50 files(each file corresponds to a patient) with 4 columns -</p>
<pre>chromosome start.position stop.pos value</pre>
<p>First 3 columns in all 50 files are same and fourth column is value which is different (or can be same for some) for all patients. Basically this value corresponds to copy number (structural variation in genome). I want to apply some test (or if you can suggest any other procedure) to find out values which are deviating as compared to others. Example-</p>
<pre>file1</pre>
<pre>chromosome start.position stop.pos value
1 10 110 4
2 100 200 5
2 500 600 0.5
</pre>
<p>file2</p>
<pre>chromosome start.position stop.pos value
1 10 110 2.5
2 100 200 6
2 500 600 0.6
</pre>
<p>file3</p>
<pre>chromosome start.position stop.pos value
1 10 110 3
2 100 200 5.5
2 500 600 3.5
</pre>
<p>file4</p>
<pre>chromosome start.position stop.pos value
1 10 110 2
2 100 200 0.9
2 500 600 3
</pre>
<p>file5</p>
<pre>chromosome start.position stop.pos value
1 10 110 8
2 100 200 4.5
2 500 600 2.5
</pre>
<p>So in the output, file5 has significant value (as compared to same position of other files) at row1, file4 has significant value at row2 and file1 and file2 has significant value at row3.</p>
<p>I have 1 solution in my mind- pick a row from each file and take the average of values. Then compare this average with each file and return the position if it is significant as compare to average. But I feel there should be some better solution for this. Can you please suggest any test or any other procedure that you will use to complete this task.</p>
<p>Thanks in advance.</p>
<p>EDIT: After reading Joel's comment.</p>
<p>Yes I have a specific question in my mind. As I mentioned these files corresponds to each patient, so I am trying to find if a patient has significantly increase(or decrease) in value at certain position (i:e row). Ok we can talk about only 1 row now. Just consider 1 position (1 row), take the values ( in this case, for first row we will have 5 values as we have five files) and from these values check which value is significantly deviating from others. So if you can suggest me solution for 1 row, I can do it for all the rows one by one. Please let me know if it is not clear.</p> | 36,163 | [
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<p><em>(Apologies for the ASCII tables, Stackexchange doesn't allow HTML tables and since I'm not supposed to link to an image, this is the only way I know of showing the data)</em></p>
<p>I'm learning about ANOVA F-testing and stumbled upon this problem:</p>
<p>There exists the following set of data regarding four teaching methods and the scores of students who were subject to each teaching method:</p>
<pre>
Method 1 Method 2 Method 3 Method 4
----------------------------------------
65 75 59 94
87 69 78 89
73 83 78 80
79 81 62 88
81 72 83
69 79 76
90
------------------------------------
</pre>
<p>$\bar{x} = 75.67$ $78.43$ $70.83$ $87.75$<br>
$s = 8.17$ $7.11$ $9.58$ $5.80$<br></p>
<p>Where $\bar{x}$ is the mean of all scores for each teaching method and $s$ is the standard deviation for each method.</p>
<p>After conducting an ANOVA, I derive the following ANOVA table:</p>
<pre>
Source | Deg. Freedom | SS | MS | F |
-------------------------------------------------------------
Treatment | 3 | 712.59 | 237.53 | 3.77 |
Error | 19 | 1196.63 | 62.98 | - |
Total | 22 | 1909.22 | - | - |
</pre>
<p>Now the question is: Test a level $\alpha = 0.05$ The null hypothesis is that there is no difference in mean achievement for the four teaching techniques.</p>
<p>So to restate:</p>
<p>$H_0$: Teaching technique <em>does not</em> have an influence on mean achievement of students <br>
$H_1$: Teaching technique <em>does</em> have an influence</p>
<p>I work out the critical f value to be $f_{3,19;0.95}$ from an F-distribution table to be $3.1274$</p>
<p>The next step is what I don't understand.</p>
<p>We can claim that the teaching technique does have an influence on the mean achievement of the students (with less than 5% chance of being wrong)<br></p>
<p>The associated p-value is:</p>
<p>$p = P(X>3.77) = 0.0281$</p>
<p>and indeed, p < $0.05$ (hence reject of $H_0$)</p>
<p>But now where is this $0.0281$ from? It looks to be the probability that X > 3.77. If I'm not wrong, in this case $X ~ F_{3,19} = 3.1274$ (as calculated before) and so the p value should be the probability that 3.1274 is greater than 3.77. Now how can 3.1274 ever be greater than 3.77? </p> | 73,711 | [
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<p>Imagine picking a 1 when any real number is equally likely. What is the pdf? Does this idea have a known use? What is its name?</p>
<p>There could be a use for a uniform random real number. It could end up always being integrated. It could be a prior for a number that is completely unknown. </p>
<p>It would be like a delta function, which integrates to a finite number though it doesn't have a well-defined value at zero. The delta function is greater than any number at zero. This uniform random on (-inf,inf) would be not well-defined anywhere. It would be less than any positive number and greater than zero. What is it?</p> | 36,164 | [
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<p>I am just wondering what kind of things could cause power to be lost in general (the opposite of reducing the noise of the data to increase the power of the test). </p>
<p>Could anyone give some summary or ideas how to think of the power issue?</p> | 30,010 | [
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<p>I am working on a business research paper. The hypothesis is that the sales rep influences the customer's decisions. Independent variables consist of the sales rep's: knowledge, pushiness, friendliness, etc. Dependent variable is the customer's willingess to buy.
In all, I have 12 questions that I asked on a Likert scale ranging from 1 (not important at all) to 7 (extremely important). </p>
<p>At this point, I have all the means and standard deviations calculated but am not sure how to proceed to evaluate whether the whole set of independent variables proves my hypothesis that the rep's qualities does influence the customer to buy. </p>
<p>I've done some reading on regression, ANOVA and chi squared but would really like to understand how I can apply them to this situation. </p>
<p>Additionally, I want to know if I compute the composite score of the subgroups, i.e. men versus women, how can I compare them statistically?</p>
<p>Thanks for any and all suggestions!</p> | 36,166 | [
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<p>For homework I have been given a 20-dimensional input $x \in \mathbb{R}^{20}$, many of which are suspected to be irrelevant. I tried using L1-norm Lasso regularization to uncover which dimensions contribute to the output: </p>
<p>$$L(\beta) = \sum_{i=1}^n (y_i - \phi(x_i)^T \cdot \beta)^2 + \lambda \sum_{j = 1}^k l(\beta_j)$$</p>
<p>Please note, that instead of $|\beta_j|$ another function is used, where</p>
<p>$$l(\beta_j) = \begin{cases}
|\beta_j| - \varepsilon/2 & \textbf{if } |\beta_j| \geq \varepsilon\\
|\beta_j^2| / (2\varepsilon) & \textbf{if } |\beta_j| < \varepsilon\\
\end{cases}$$</p>
<p>With the resulting gradient:</p>
<p>$$\frac{\partial}{\partial\beta} L(\beta) = -2 \sum_{i=1}^n - \phi(x_i) \cdot (y_i - \phi(x_i)^T \cdot \beta) + \frac{\partial}{\partial\beta_m}\sum_{j=1}^kl(\beta_j)$$</p>
<p>$$
\frac{\partial}{\partial\beta_m}\sum_{j=1}^kl(\beta_j)=
\begin{cases}
0&m\gt k\;,\\
sign(\beta_m)&m\le k\;,|\beta_m|\ge\epsilon\;,\\
sign(\beta_m)/\epsilon&m\le k\;,|\beta_m|\lt\epsilon\;.
\end{cases}
$$</p>
<p>In order to find the minimum I applied gradient descent on the differentiated Lasso function and received a $\beta$ vector after 6 to 10 iterations. However, I don't see how this helps me to uncover the irrelevant dimensions. How should I proceed?</p> | 36,167 | [
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<p>We recently studied a model with a likelihood function of the form</p>
<p>$$\Pr(d_i|\omega,t_i)=(1-d_i)+(2d_i-1)\cos^2(\omega t_i),$$</p>
<p>where $d_i\in\{0,1\}$, $\omega$ is an estimation parameter, and $t_i$ are determined by the experimenter. This is a set of independent but non-identically distributed Bernoulli trials (think: trying to estimate the time-varying bias of a coin).</p>
<p>Since this was a simple one estimation parameter, one design parameter model, we could essentially employ a first principles approach to the theory and computations (the paper is here: <a href="http://arxiv.org/abs/1110.3067" rel="nofollow">http://arxiv.org/abs/1110.3067</a>).</p>
<p>Now that we plan to generalize this to multiple estimation and design parameters, I really want to make sure we are doing the most efficient thing possible. I did a bit of searching but couldn't find anything in the literature on statistical models that depend on a periodically varying design parameter $t$. Has anyone seen a model like this studied before?</p> | 36,168 | [
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<p>my project is identification of factors influencing motor bikes for home to office trip. there are some attiributes like gender,age,marital status,education qualification,job type,working sector, no. of members in household,working members in household,monthly income,total household income,no. of motor bikes,members having motor bike driving licence(D.L),no. of cars,members having car D.L,do you have D.L for motor bike, do you have D.L for car,type of house, live-in status of house, do you work from home, do you use internet for office purpose, no. of days you work from house,purpose of trip, timings of office i.e., starting and ending time, vehicle for above trip,distance from home to office,time from home to office and office to home,reason for preferring to private vehicle,likely fare (if you go by bus or shared auto),drop off any kid to school while going to office,does the school come on your way to office, spouse is working person,do you drop off your spouse to her office,city bus is accessible to your house,walking distance from home to bus stop,waiting time at bus stop... and some of these questions are related to one another like spouse is working ?? if no he should not fillup the next question. also like drop off any kid to school.. wat should i use in the related question...wheather '-' (or) 9999...also i am totally confused about the dependent and independent and categorical variables........ also wat the model we are going to use for this project wheather binary logistic (or) multinomial logistic ... </p> | 36,169 | [
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<p>For the lasso problem
$\min_\beta (Y-X\beta)^T(Y-X\beta)$ such that $\|\beta\|_1 \leq t$. I often see the soft-thresholding result
$$ \beta_j^{\text{lasso}}= \mathrm{sgn}(\beta^{\text{LS}}_j)(|\beta_j^{\text{LS}}|-\gamma)^+ $$
for the orthonormal $X$ case. It is claimed that the solution can be "easily shown" to be such, but I've never seen a worked solution. Has anyone seen one or perhaps has done the derivation? </p> | 73,712 | [
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<p>I have worked out a naive approach for clustering different variables, and I wonder what better approaches are there. I have data with many more dimensions (variables) than observations (samples), and I wish to cluster the variables by their correlation. However, the observations correspond to different groups, for example treatment and control. If I just calculate the correlation coefficient, all variables that go up in one group will have a positive correlation, and that is not what I intend; I want to cluster them by within-group effects and disregard between-group effects.</p>
<p>To give you a specific example: variables are abundances of certain substances in the serum of patients. Serum samples are the observations, and each serum sample is associated with a number of abundances (for example, abundances of amino acids, cytokines etc.). There are, say a hundred observations (serum samples), each associated with the same 1000 variables (abundances). I want to see which abundances are correlated: for example, which cytokines are correlated with which amino acids.</p>
<p>The approach that I am taking is to fit a simple linear model which explains the effect of various groups and correlate the residuals from the model. This heuristic works in the sense that it gives "reasonable" (in terms of biology) grouping of the variables, for example it clusters genes with similar functions. </p>
<p>Consider this example in R.</p>
<pre><code>groups <- factor( rep( c( "a", "b" ), each= 50 ) )
set.seed( 123 )
x1 <- rnorm( 100 )
x2 <- rnorm( 100 ) # not correlated with x1 yet
x3 <- x1 + rnorm( 100 ) # positively correlated with x1
# simulate group effect
x1 <- x1 + rep( c( 0, 2 ), each= 50 )
x2 <- x2 - rep( c( 0, 2 ), each= 50 )
x3 <- x3 - rep( c( 0, 2 ), each= 50 )
</code></pre>
<p>Now, x1 and x2 appear negatively correlated (although within each group there is no correlation), and x1 and x3 appear not correlated at all (although within each group there is a positive correlation):</p>
<p><img src="http://i.stack.imgur.com/q1lkX.png" alt="enter image description here"></p>
<p>Then, I calculate the residuals:</p>
<pre><code>x1r <- lm( x1 ~ groups )$residuals
x2r <- lm( x2 ~ groups )$residuals
x3r <- lm( x3 ~ groups )$residuals
</code></pre>
<p>The situation now is very much different and much more what I intend:</p>
<p><img src="http://i.stack.imgur.com/Ig7FJ.png" alt="enter image description here"></p>
<p>My question is this: what would be a statistically more appropriate way of achieving the same? Note that neither of x1, x2 or x3 can be treated as independent variables or response variables -- they are merely correlated, without a given as to which one is determines which other. My ultimate goal is to create clusters of variables that are correlated after removing the effects of the groups.</p> | 73,713 | [
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<p>I remember once in our Statistics class, our professor mentioned an interesting problem, that is:</p>
<blockquote>
<p>In our class, consisting of 30 students, I bet that there are two students born on an exact day of year.</p>
</blockquote>
<p>It was quite clear to all of us that he will lose the bet, but then he asked all the students to write out their birth date on the board and surprisingly three of us were born in the same day of year!</p>
<p>It was very interesting to us. He wrote the proof to his statement, showing that If there are 40 students in one classroom, the probability that at least two students are born in the same day of year is over 90 percent (as I recall).</p>
<p>A few days ago, I told my friends about this, they all laughed at me saying it is impossible. I tried to give them the proof but I failed. I've forgotten everything! </p>
<p>I guess it is a famous problem in statistics, can anyone provide the proof or any link to any docs providing the proof to this statement?</p> | 49,922 | [
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<p>I have just started learning these things, and I would really appreciate any help on this.
There are 4 nodes in a network (say $A,B,C,D$), and each node has certain failure probabilities, namely ${\rm Pr}(F_A)$, ${\rm Pr}(F_B)$, ${\rm Pr}(F_C)$, ${\rm Pr}(F_D)$.
Then, I have a $4 \times 4$ correlation Matrix which contains the correlation coefficients for every pair of nodes. </p>
<p><strong>How can I calculate ${\rm Pr}(F_A|F_B)$ or ${\rm Pr}(F_A| F_B, F_C, F_D)$?</strong></p> | 73,714 | [
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<p><img src="http://i.stack.imgur.com/gVwaj.png" alt="Probability plot of standardized residuals."></p>
<p>I go to Stat from main menu then Regression -> Regression...</p>
<p>Although I have selected almost everything I cannot plot the extra info (p-value, mean, N, etc ) above in circle. I use Minitab 16.2.0.</p> | 30,051 | [
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<p>I recently became interested in <em>Cognitive Diagnosis Modelling</em>, which classifies respondents to skill profiles based on their responses and a hypothesized relation between skills and items (Q- or Transfer-Matrix).</p>
<p>I had a look at at <a href="https://pslcdatashop.web.cmu.edu/" rel="nofollow">https://pslcdatashop.web.cmu.edu/</a> but the datasets there are quite big. Does anyone have a suggestion, where I can find <em>records of testing data with reasonable size, where a Q-Matrix is already specified</em>?</p> | 73,715 | [
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<p>In a linear mixed model, you take the covariance between data into account by adding a random intercept per cluster.</p>
<p>For example, you measure the effect of a drug campaign over time on students, and add a random intercept per school and a random intercept per student within a school:</p>
<p>$Y_{ijk}=\beta_{0}+\beta_{1}*Time+b_k+b_{jk}+\epsilon_{ijk}$</p>
<p>With Y the outcome variable "how much does he knows with drugs. We assume that the random intercepts are normally distributed with mean and variance: </p>
<p>$b_k \sim N(0, \sigma_3^2)$, $b_{jk} \sim N(0, \sigma_2^2)$ and $\epsilon_{ijk} \sim N(0, \sigma_1^2)$</p>
<p>With these variances of random intercepts we can calculate the variance of the treatment effect on the different levels, for example on the school level.</p>
<p>But what if I want to model that the campaign has not the same average increase over time in every school? I add a random slope per school:</p>
<p>$Y_{ijk}=\beta_{0}+\beta_{1}*Time+b_{0k}+b_{1k}*Time+b_{jk}+\epsilon_{ijk}$</p>
<p>Is in this model the variation of $b_{0k}$ still meaningful? Is my intuition correct that the variation between different schools increases over time, as the random slopes drive the schools further apart? </p>
<p>And as a second question, without random slope we also know that the covariance between students within the same school is given by: </p>
<p>$Cov_{school}=\frac{sigma_3^2}{sigma_1^2+sigma_2^2+sigma_3^2}$</p>
<p>What is this covariance if a random intercept is included?</p>
<p>Thank you in advance!</p>
<p>UPDATE: included a plot of the data I am working with, level 1 are the 8 repeated measurements at each measurement occasion, level 2 are the difference measurement occasions, level 3 are the patients.</p>
<p><img src="http://i.stack.imgur.com/MKt8e.jpg" alt="enter image description here"></p> | 73,716 | [
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<p>According to Bayes' theorem, $P(y|\theta)P(\theta) = P(\theta|y)P(y)$. But according to my econometric text, it says that $P(\theta|y) \propto P(y|\theta)P(\theta)$. Why is it like this? I don't get why $P(y)$ is ignored. </p> | 73,717 | [
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<p>Some authors eg Hunter et al (1982) propose that we must correct sample correlations for the measurement error.It seems measurement error need not be corrected for when we take a recourse to the meta-analysis of sample-correlations In a meta-analytic perspective, measurement error(here it is construct bias) has a little effect on the sampling error variance. </p> | 73,718 | [
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<p>We just started learning asymptotic theory, and to prove the lindberg-levy central limit theorem, weak law of large numbers etc, we 'scale and standardize' the RVs so it ends up having a standard normal distribution when sample size T tends to $\infty$. The math behind it is straightforward but can someone give a quick intuition or an example of what it means to 'scale' a RV, by $T^{1/2}$ for example?</p> | 36,178 | [
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<p>I am looking for different types of regression models for such data in which the dependent variable is always decreasing with the independent variables.</p>
<p>The two's, I know and have used so for are</p>
<pre><code>Y = C + C_a A + C_b B
</code></pre>
<p>and </p>
<pre><code>Y = C + C_a A + C_b B + C_a2 A^2 + C_b2 B^2 + C_ab A B
</code></pre>
<p>The second one give me the best fit so far. I want to try some other ones too but don't know. Please suggest some.</p>
<p>Thanks</p> | 73,719 | [
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<p><strong>Figure A</strong> demonstrates a point process (object=rectangle) with marks as the length and width of the rectangle. <strong>Figure B</strong> shows a realization of the point process regarding the information extracted from the input data.<br>
The <strong>question</strong> is:<br>
How to condition (using pre-conditioning or post-conditioning) the realization to the existing data points with marks?</p>
<p><img src="http://i.stack.imgur.com/8koYz.jpg" alt="enter image description here"></p>
<p><strong>More Explanation:</strong><br>
Figure <strong>E</strong> demonstrates point process which has location, and width and height marks added.<br>
Figure <strong>A</strong> is our point process. Figure <strong>B</strong> added marks as width and height variables. Figure <strong>C</strong> is our realization of the point process by means of information extracted from Figure <strong>A</strong>. Figure <strong>D</strong> is final marked point process, a realization.
We seek a method to condition this realization to Figure <strong>B</strong>.
<img src="http://i.stack.imgur.com/TEghN.jpg" alt="enter image description here"></p> | 73,720 | [
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<p>I want to make a linear regression where the dependent variable is the amount spent on some good and the independent variables are some characteristics of the consumer (age, gender, wage, etc). Specifically, I want to know how much this characteristics influence the annual spending on this good. </p>
<p>But the way that the survey was made is asking how much was spent on the good in the week of reference. So a lot of zero consumption was recorded (more than 90% of the records are zero). So, every regression that I make to explain the spending as a function of the consumer characteristics have no significance. What is expected if the good has some sporadic way of being consumed.</p>
<p>Is there any work around for this problem?</p> | 73,721 | [
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<p>I have a data set consisting of 166 observations on 24 variables (<code>a1</code>, <code>a2</code>, <code>a3</code>, <code>a4</code>, <code>b1</code>, ..., <code>b4</code>, ..., <code>f4</code>). Responses where made on a 6-point scale from 1 to 6:</p>
<pre><code>d <- read.table("http://pastebin.com/raw.php?i=m1ZJuKLH")
str(d)
## 'data.frame': 166 obs. of 24 variables:
## $ a1: int 7 7 7 1 1 7 7 7 7 1 ...
## $ a2: int 7 7 4 7 5 5 1 7 7 4 ...
## $ a3: int 7 7 5 1 1 7 7 3 7 1 ...
## $ a4: int 7 7 6 7 1 7 1 7 7 1 ...
## $ b1: int 1 2 5 7 1 4 1 7 4 2 ...
## [...]
## $ f4: int 6 6 4 1 7 7 7 7 7 1 ...
</code></pre>
<p>Variables with a common letter (i.e., all <code>a</code>s, all <code>b</code>s, ..., all <code>f</code>s) are of the same type.</p>
<p>I would like to test whether the latent factors behind the variable types are correlated with each other (or whether you can set the correlation to 0). An additional complication is that the latent variables <code>c</code> to <code>f</code> share a further latent variable (termed <code>c.to.f</code>) and I only want to test the correlation between <code>a</code>, <code>b</code> and <code>c.to.f</code>.</p>
<p>I would like to run a confirmatory factor analysis (which essentially is a structural equation model) in R testing this. There are at least two mature packages of doing so <code>sem</code> and <code>openMX</code>.<br>
<strong>I am interested in opinions/code on which package would be the best or perhaps easiest to specify such a model.</strong> </p>
<hr>
<p>Edit: I would like to accept an answer which includes code samples.</p> | 73,722 | [
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<p><strong>Simulated Annealing</strong> is a method of simulation in which each entity in the system is perturbed in some characteristics e.g., location due to increasing and decreasing the heat (the energy) of the entire system.<br>
My question is about the application of simulated annealing approach to conditioning simulations. For instance what are the steps to condition a simulation (for example see <a href="http://stats.stackexchange.com/questions/16780/how-to-condition-a-point-process-to-the-actual-sampling-data">conditioning point process</a>) to the existing sampling data?</p> | 73,723 | [
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<p>Our professor keeps on writing in his slides that when you test different ARIMA models on your time series, one always has to keep T fixed.</p>
<p>I assume he is talking about fitting your model using the same number of observations. If you try a model with a higher lag, you loose one observation to fit the data on. Is this correct? </p>
<p>Is this why he writes restrict your sample? We have 214 observations, should I for example to be on the safe side only use 205 observations? And how does Eviews know to always use the same number of obersations?</p>
<p>Ref screenshot:</p>
<p><img src="http://i.stack.imgur.com/93Zjo.png" alt="enter image description here"></p>
<p>Thanks in advance.</p> | 36,181 | [
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<p>So, some algorithms were motivated by theoretical work, such as in the case of boosting.
Adaboost was introduced as an <a href="http://www.face-rec.org/algorithms/Boosting-Ensemble/decision-theoretic_generalization.pdf" rel="nofollow">algorithm for solving</a> the <a href="http://www.cs.princeton.edu/~schapire/papers/strengthofweak.pdf" rel="nofollow">hypothesis boosting problem</a>.
The bounds on the training error and generalization error were formulated along many other extensions and explanations about how and why the algorithm works.</p>
<p>My questions: 1.) Regarding classification and regression tress (CART), would it be correct to say that learning a decision tree was motivated by data and not by theory?</p>
<p>2.) Regarding classification and regression tress, are there theoretical bounds on the training and testing errors? If so a reference would be great.</p> | 73,724 | [
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<p>X,Y are independent random variables.
X's pdf = f(x)
Y's pdf = g(x)
if Z= X+Y
what is the Z's pdf?
Can it be calculated?</p> | 36,182 | [
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<p>I want to measure the inner correlation of the occurrences of events i.e. I want to distinguish between the two (drawn) and say "in the second sample events occur more conglomerate compared to the first":</p>
<p><img src="http://i.stack.imgur.com/NxRBP.png" alt="enter image description here"></p>
<p>Isn't this different from burstiness (i.e. easier to compute as it doesn't invole traffic-values)?</p>
<p>I have drawn a possible representation of the expected result (for S2) in the image below the samples (just as it is in my mind now), but don't hesitate to suggest different proposals.</p>
<p>I looked out and tried different build-in functions and googled/ searched CrossValidated for R and burstiness or "inner correlation", but I didn't make progress. Maybe I am looking for the wrong search terms.
If I wanted to really measure burstiness, it seemed to me (by reading papers about burstiness) that there would be no common known measure (but many different one). I we would pick one it would be cool to justify why choosing this specific one.</p>
<p>This is how the time series is represented in R, currently:
(written by dput in file)</p>
<pre><code>c(3.256861, 3.377142, 3.941173, 4.304236, 4.485358, 4.606512,
4.707296, 5.473004, 5.714746, 5.815394, 5.835405, 5.936067, 5.957008,
6.964611, 7.045158, 7.065171, 7.165824, 7.669618, 8.17324, 8.273692,
9.503988, 9.604991, 9.624853, 9.725522, 10.237766, 10.954529,
11.378399, 12.687714, 13.291919, 13.41258, 13.67527, 14.380529,
14.743638, 15.247138, 15.851832, 15.952875, 15.972497, 16.456259,
16.476052, 17.201506, 17.463708, 18.068535, 18.309645, 18.390292,
18.410299, 18.430323, 18.531736, 18.652921, 18.793662, 19.297076,
19.639692, 19.760698, 20.768096, 20.868441, 20.990499, 21.494412,
21.856368, 22.199341, 22.219143, 22.440472, 22.481118, 23.327013,
23.447678, 23.811188, 23.843, 24.113302)
</code></pre> | 36,184 | [
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<p>I have a microarray data which I ran through a continuous covariate (say "X"). I did this using 4 different methods.</p>
<p>For the results obtained from each of the 4 methods, I have the following from each of the 4:</p>
<ol>
<li>p-value, </li>
<li>FDR significant value, </li>
<li>"Bonferonni significance" (saying "true" or "false")</li>
<li>"Holm significance" (saying "true" or "false")</li>
</ol>
<p>I wish to obtain an ROC curve showing lines for sensitivity and specificity from each of the 4 methods.</p>
<p>I kind of know what is an ROC curve, but even after reading through a few links, I dont feel clear of the concept of what kind of input it needs to create it. So I apologise if this seems to be a dummy question.</p>
<p>So my questions are:</p>
<ol>
<li><p>Can a ROC curve be created from the 4 values (p value, FDR, Bonferoni & Holm) which I have mentioned above? Or is it that I have to calculate the FP and FN first?</p></li>
<li><p>Can you suggest me an easy to use package which could do this for me, by giving me a ROC curve with lines of 4 methods using the input above?</p></li>
</ol>
<p>Your help appreciated. Thanking you in advance.</p> | 43,114 | [
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<p>I want to check various classification model like random forest, tree, knn,etc. I used some bench marking data set but now I need to simulate my own data set with a binary response variable.</p> | 73,725 | [
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<p>According to <a href="http://blog.gribblelab.org/2009/03/09/repeated-measures-anova-using-r/" rel="nofollow">this post</a> the best way to do post hoc analysis in ANOVA in R is t-test + ptukey. Because lme + glht "essentially assumes the sphericity assumption holds".</p>
<p>How are t-test + ptukey "concerned about the sphericity"? What are the disadvantages of this method?</p> | 73,726 | [
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<p>I have a problem with this exercise in probability and statistics:
Calculate the probability density function (PDF) of
$$Z=X+Y$$
where $Y$ is discrete random variable which is equal to $-1$ and $1$ with equal probability;
$X$ is a standard gaussian random variable independent of $Y$.</p>
<p>I know that the PDF of the sum of two continuous independent variables is given by the convolution of the marginal PDFs
$$f_z(z)=f_x*f_y,$$
but if one of the two variables is discrete what should I do?</p> | 73,727 | [
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<p>I am having trouble understanding the plot below (taken from <a href="http://blog.echen.me/2012/03/20/infinite-mixture-models-with-nonparametric-bayes-and-the-dirichlet-process/" rel="nofollow">Edwin Chen's blog</a>). </p>
<ul>
<li>What is the <strong>x-axis</strong> supposed to represent? Shouldn't color be a categorical variable? Does the <strong>x-axis</strong> have to be on the real line for the Polya urn model?</li>
<li>Are we supposed to see significant changes across runs for the same alpha?</li>
</ul>
<p><img src="http://i.stack.imgur.com/7G5hD.png" alt="enter image description here"></p> | 73,728 | [
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<p><a href="http://en.wikipedia.org/wiki/Factorial_experiment" rel="nofollow">Factorial experiments</a> have several advantages when one wants to examine the effect of several independent variables (factors) on an outcome. Perhaps most importantly, they often allow additional factors without major increases in sample size.</p>
<p>However, sampling is often the most difficult thing to begin with, and in some cases, even a 2x2 factorial design can require a sample that is practically impossible to obtain. It is not necessarily the sample size that is the problem, but the feasibility of obtaining a <em>random</em> sample.</p>
<p>I'm considering a case where, for practical and ethical reasons, I have no options but to compare a preselected group of people to another group which I can select randomly from a larger population. The purpose is to examine whether a certain treatment has an effect on a behaviour which everyone in the population (including the preselected group) will carry out continuously in collaboration with each other. Everyone in the population has gone through an integration process in which they have learned, one way or the other, the behaviour. The question is whether the treatment is effective for quickly learning the desired behaviour in the preselected group – is the behaviour learned in a shorter time and with more accuracy than what previous newcomers have been able to learn without the treatment. There will also be other factors in the design except the treatment.</p>
<p>In an ideal case, I could randomly select two groups that are part of the population, and give the treatment to one of them. However, it is impossible in this case, because I cannot give the treatment to anyone but the preselected group. In addition, due to ethical reasons, I cannot randomly split the preselected group in half and give the treatment only to one half: everyone in the group must get the treatment. Thus I am forced to give the treatment to everyone in the preselected group and use a random sample of the existing population as a proxy for the non-treatment group.</p>
<p>Are there any valid ways of conducting a factorial experiment under these conditions where I have to deal with a non-random sample? If not, are there any other ways to assess the effect of the treatment under these conditions?</p> | 73,729 | [
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<p>If you're training a model using cross validation on one set of data, and then you're scoring that model on a separate set of data, is it advised to score, say, 1000 times on subsets of your data? </p>
<p>I'm thinking taking bootstrap samples or something, and then scoring the model, then another boot strap, etc. It seems like this way you'd get an idea of the stability of model performance, but I'm not sure if that's legit or not...</p> | 73,730 | [
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<p>Suppose $U, W, V, S$ are four independent normal random variables with mean $0$ and variance $1$. Let $X=W+U$, $Y=2W+S$, $Z=3W+V$. What is $f(X, Y, Z)$?</p>
<p>Thanks!</p> | 47,733 | [
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<p>I was wondering if any of you could help me understand the response I got from this clustering algorithm (Metis). As you probably can see, I'm trying to cluster IP addresses based on common records accessed. The graph file contains one node per IP, and weighted edges, where the weight is equal to the number of common accesses. A couple of specific questions:</p>
<ul>
<li><p>This algorithm requires a pre-defined number of clusters. How should I, based on this response, decide on the optimal number? (The algorithm is really fast, so repeated runs is possible).</p></li>
<li><p>How should I go about evaluating this clustering? I don't have a training/test set as of now. Should I create one? How would I do that with a binary access log?</p></li>
</ul>
<p>If you have any other tips regarding this algorithm, they are more than welcome!</p>
<p>Thanks for taking a look! Here comes the response:</p>
<pre><code>******************************************************************************
METIS 5.0 Copyright 1998-13, Regents of the University of Minnesota
(HEAD: , Built on: Jul 1 2014, 14:23:44)
size of idx_t: 32bits, real_t: 32bits, idx_t *: 64bits
Graph Information -----------------------------------------------------------
Name: gt2rec_gt2ip_b_rec_sorted_nobots_pdf_full.graph, #Vertices: 103924, #Edges: 34678560, #Parts: 10
Options ---------------------------------------------------------------------
ptype=kway, objtype=cut, ctype=shem, rtype=greedy, iptype=metisrb
dbglvl=0, ufactor=1.030, no2hop=NO, minconn=NO, contig=NO, nooutput=NO
seed=-1, niter=10, ncuts=1
Direct k-way Partitioning ---------------------------------------------------
- Edgecut: 16083558, communication volume: 662037.
- Balance: constraint #0: 1.030 out of 0.000
- Most overweight partition:
pid: 4, actual: 10704, desired: 10392, ratio: 1.03.
- Subdomain connectivity: max: 9, min: 9, avg: 9.00
- The original graph had 1243 connected components and the resulting
partitioning after removing the cut edges has 2362 components.
Timing Information ----------------------------------------------------------
I/O: 7.162 sec
Partitioning: 10.511 sec (METIS time)
Reporting: 2.118 sec
Memory Information ----------------------------------------------------------
Max memory used: 1021.427 MB
******************************************************************************
</code></pre> | 73,731 | [
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<p>I am analyzing data from an experiment in which treatment levels increase quadratically, e.g. the treatment levels are $0, 1, 4, 9$.</p>
<p>When analyzing the response using regression, would it make sense to use the square root of the treatment level as a predictor? </p>
<p>If so, how would this affect interpretation?</p> | 36,188 | [
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<p>I really enjoy this resource -- its been super helpful to learn and read along as I explore some concepts for a new venture. But now I need real help -- in the short term contract, and in the long term statistical pros. What are the best sites were folks look for side projects and gigs? What is the best advice you have for someone hiring stats folks?</p> | 73,732 | [
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<p>I am exploring different classification methods for a project I am working on, and am interested in trying Random Forests. I am trying to educate myself as I go along, and would appreciate any help provided by the CV community.</p>
<p>I have split my data into training/test sets. From experimentation with random forests in R (using the randomForest package), I have been having trouble with a high misclassification rate for my smaller class. I have read <a href="http://www.stat.berkeley.edu/tech-reports/666.pdf">this paper</a> concerning the performance of random forests on imbalanced data, and the authors presented two methods with dealing with class imbalance when using random forests.</p>
<p><strong>1. Weighted Random Forests</strong></p>
<p><strong>2. Balanced Random Forests</strong></p>
<p>The R package does not allow weighting of the classes (from the R help forums, I have read the classwt parameter is not performing properly and is scheduled as a future bug fix), so I am left with option 2. I am able to specify the number of objects sampled from each class for each iteration of the random forest. </p>
<p>I feel uneasy about setting equal sample sizes for random forests, as I feel like I would be losing too much information about the larger class leading to poor performance with future data. The misclassification rates when downsampling the larger class has shown to improve, but I was wondering if there were other ways to deal with imbalanced class sizes in random forests?</p> | 73,733 | [
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<p>(Apologies if the notations are "unusual", I'm not sure what the correct notations should be. I'm putting an example at the end of the question.)</p>
<p>Let's assume there was an initial dataset of an n by m matrix $M=(x_{ij})$ with $1<=i<=n$ and $1<=j<=m$, from which the following two vectors have been calculated:</p>
<ul>
<li>the vector of the column-wise means, that is, a vector of length $n$ where each element of index $j$ is the mean of the $m$ elements in column $j$ of the matrix: $(\bar{x}_{*j})$ with $1<=i<=n$, where $\bar{x}_{*j} = \frac{1}{m}\sum_{i=1}^m{x_{ij}}$.</li>
<li>the corresponding vector of the columns-wise standard deviations ($s_{*j}$).</li>
</ul>
<p>I'd like to get the mean and standard deviation of the row-wise vector of means, that is, the column vector made of the mean of each row: $(\bar{x}_{i*})$ with $1<=j<=m$, where $\bar{x}_{i*} = \frac{1}{n}\sum_{j=1}^n{x_{ij}}$, assuming that the initial matrix has been lost.</p>
<p>The mean of the elements in the row-wise vector is also the mean of the elements in the column-wise vector (which is also the mean of all the elements in the matrix, with equal weight): $\frac{1}{m}\sum_{i=1}^m{\bar{x}_{i*}} = \frac{1}{m}\sum_{i=1}^m({\frac{1}{n}\sum_{j=1}^n{x_{ij}}}) = \frac{1}{n\times m}\sum_{i=1}^m\sum_{j=1}^n{x_{ij}}$</p>
<p>Is there any way to get the standard deviation within the row-wise vector of means without having the original matrix?</p>
<p>For example:</p>
<p>$$
M = \left(\begin{matrix}
1 & 2 & 3\\
7 & 5 & 4\\
8 & 2 & 3\\
5 & 2 & 4
\end{matrix}\right)
$$</p>
<p>$$
(\bar{x}_{*j}) = \left(\begin{matrix}5.25 & 2.75 & 3.5\end{matrix}\right)
$$</p>
<p>$$
(s_{*j}) = \left(\begin{matrix} 2.68 & 1.29 & 0.5\end{matrix}\right)
$$</p>
<p>$$
(\bar{x}_{i*}) = \left(\begin{matrix} 2\\ 5.33 \\ 4.33 \\ 3.66\end{matrix}\right)
$$</p>
<p>The mean of $\{2, 5.33, 4.33, 3.66\}$ is $3.83$ (also the mean of ${5.25, 2.75, 3.5}$).
The standard deviation of $\{2, 5.33, 4.33, 3.66\}$ is $1.21$. Would there be any way of calculating this standard deviation, knowing $(\bar{x}_{*j})$, $(s_{*j})$, but without knowing $M$ nor $(\bar{x}_{i*})$?</p>
<p>Is there anything else that could have been calculated "column-wise" (that is, independently for each column, thus excluding the "row-wise" means themselves) that would help find out the (preferably sample) standard deviation of the "row-wise" means?</p>
<p>Thank you.</p> | 73,734 | [
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<p>I'm having problems understanding the concept of a random variable as a function. I understand the mechanics (I think) but I do not understand the motivation...</p>
<p>Say $(\Omega, B, P) $ is a probability triple, where $\Omega = [0,1]$, $B$ is the borel-$\sigma$-algebra on that interval and $P$ is the regular lebesgue measure. Let $X$ be a random variable from $B$ to $\{1,2,3,4,5,6\}$ such that $X([0,1/6)) = 1$, $X([1/6,2/6)) = 2$, ..., $X([5/6,1]) = 6$, so $X$ has a discrete uniform distribution on the values 1 through 6. </p>
<p>That's all good, but I do not understand the necessity of the original probability triple... we could have directly constructed something equivalent as $(\{1,2,3,4,5,6\}, S, P_x)$ where $S$ is all the appropriate $\sigma$-algebra of the space, and $P_x$ is a measure that assigns to each subset the measure (# of elements)/6. Also, the choice of $\Omega=[0,1]$ was arbitrary-- it could've been $[0,2]$, or any other set.</p>
<p>So my question is, why bother constructing an arbitrary $\Omega$ with a $\sigma$-algebra and a measure, and define a random variable as a map from the $\sigma$-algebra to the real line? </p> | 36,192 | [
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<p>I was wondering if you can share your experiences on what you feel is the best method to test lead / lag relationships between I(1) time series variables (i.e stock prices) and advantages and disadvantages of your proposed method(s). Also if you have links to academic papers that further describe these methods I would greatly appreciate them.</p>
<p>I have read several papers that speak of VECMs, IRSUR, simple OLS, threshold regression etc.. but I'm not sure which to use for my study. I am trying to establish lead/lag relationships in intraday stock data returns (using 1 minute price time series) between stock prices of ~50 companies in one particular sector. </p>
<p>Appreciate the help.</p> | 73,735 | [
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<p>I am sitting on a pile of data concerning wages at a local company and other information, such as the gender, whether the person in question belongs to a minority group etc. What I would like to investigate is whether an additional year of education gives the same relative increase in wages for lower and higher education. For this purpose, I have divided the original data into two subcategories; one group with at most 12 years of education and the other with 13 or more years of education. What I would like to perform is a Chow test of structural change of the form</p>
<p>\begin{equation}
F=\frac{\frac{(RSS-(RSS_{\text{lower}}+RSS_{\text{higher}}))}{2}}{\frac{RSS_{\text{lower}}+RSS_{\text{higher}}}{n-2k}}=\frac{(n-2k)((RSS-(RSS_{\text{lower}}+RSS_{\text{higher}}))}{2(RSS_{\text{lower}}+RSS_{\text{higher}})} \sim F(k,n-2k)
\end{equation}
where $n$ is the total number of observations and $k$ is the number of explanatory variables.</p>
<p>Clearly, I could simply calculate the $RSS:$s directly and then construct $F$ explicitly.</p>
<pre><code> total<-lm(SALARY~EDUC+GENDER+MINORITY)
lower<-lm(SALARY1~EDUC1+GENDER1+MINORITY1)
higher<-lm(SALARY2~EDUC2+GENDER2+MINORITY2)
RSStot<-sum(residuals(total)^2)
RSSlow<-sum(residuals(lower)^2)
RSShig<-sum(residuals(higher)^2)
((576-6)((RSStot-(RSSlow+RSShig)))/(2(RSSlow+RSShig))
</code></pre>
<blockquote>
<p>Nevertheless, I am sure there must be a way to do this directly in R. How exactly would that be? I would truly appreciate any enlightenment from any kindhearted spirit. Cheers to all!</p>
</blockquote> | 36,193 | [
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<p>I would like to calculate the value of bacteria on 4 surfaces $i=\{1..4\}$. A person touches some of those 4 surfaces at random and a count is made on their finger after each surface contact ($x_i$). </p>
<p>Someone lost the bacteria count ($x_i$) after each surface but I do know the total count (X) on a persons's finger after they've touched a number of surfaces. I also know which ones and in which order.</p>
<p>What I know:</p>
<ol>
<li>Final bacteria count on a person's finger: $X$</li>
<li>Transfer efficiency from surface to finger: $PT_i=\displaystyle \frac{\text{Finger contact area}}{\text{Area of surface}_i}\frac{1}{\gamma_i}$ where $\gamma$ is a surface dependent constant.</li>
<li>The number of times the person touched a particular surface: $h_i$.</li>
</ol>
<p>If I had surface counts $C_i$, the summation of bacteria is linear:
ie
$\begin{eqnarray}
h_1C_1PT_1&=&x_1\\
h_2C_2PT_2&=&x_2\\
\vdots\quad &=& \quad \vdots\\
h_iC_iPT_i&=&x_i
\end{eqnarray}$</p>
<p>such that summing over all surfaces $i$ the total count x is: $\displaystyle \sum_i h_iC_iPT_i=\sum_i x_i=X$.</p>
<p>Can I back calculate $C_i$, without $x_i$ even statistically or probabilistically?<br>
Best regards.</p> | 36,194 | [
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<p>I have set of 16 questions that have been answered on a numerical scale, from 1 to 7. They are answered by 200 couples, and I want to show there is a difference in the answers on gender. On a casual glance at the data, I see there is little difference between the genders for 6 of the questions, but is for the other. </p>
<p>If I run a series of t-tests for each, and show significant differences for 10 of them; I should be able to conclude that on the set as a whole, there are differences.
Is there a better way to show that for this series, answers differ based on gender? Mu</p> | 73,736 | [
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<p>We have a potential biomarker for predicting whether a patient has cancer or not. The biomarker test result is binary being positive or negative. We want to get some sense of the amount of patients that need to be tested to determine whether this biomarker is a good predictor or not.</p>
<p>From reading on the internet it seems that the way to go is to look at the sensitivity (for the number of cases) and specificity (for the number of controls). It is suggested that you should treat this situation as a one-sample proportion test, but it remains unclear how you should go about estimating what the sensitivity is and the range you are prepared to except. If say I consider any biomarker with a sensitivity of greater than 0.8 to be "good", how would you set the two variables up? I would like my null hypothesis to be the biomarker is no better than a random assignment i.e. a sensitivity of 0.5. Could anyone give an example of the best way to do this (especially if it is in R).</p> | 36,196 | [
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