The variance-covariance matrix, or sometimes just covariance matrix, is the matrix whose $(i,j)$ element is the covariance between the $i^\text{th}$ and $j^\text{th}$ variable (or the $i^\text{th}$ and $j^\text{th}$ parameter).

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Variance-Covariance matrix interpretation

Assume we have a linear model Model1 and vcov(Model1) gives the following matrix: ...
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Significant box's test equality covariance matrices, How bad it is?

Having equal number of cases across two groups (60 total cases), if one wants to perform a split-plot Anova and finds out that the Box's Test of Equality of Covariance Metrices is less than 0.001 then ...
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How to draw estimates based on variance covariance matrix?

Suppose I fitted a logistic model and get the estimates as well as their vcov matrix. I would realize this: draw length($\beta_s$) independent $\mathcal N(0,1)$ ...
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17 views

Condition number of covariance matrix

I am interested in generating a covariance matrix of dimension say 100. I managed to get a correlation matrix with finite condition number. To construct a covariance matrix I need to have standard ...
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52 views

Plotting error ellipsoid from 3x3 covariance matrix in R?

I'm hoping to be able to take a 3x3 covariance matrix and turn this into an error ellipsoid but so far I haven't been able to achieve this. I'm very new to R (in fact turned to it to attempt to solve ...
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83 views

Gradient of Gaussian log-likelihood

I'm trying to find the MAP estimate for a model by gradient descent. My prior is multivariate Gaussian with a known covariance matrix. On a conceptual level, I think I know how to do this, but I was ...
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55 views

Alternative to visualize hyper-ellipsoid defined by variance-covariance matrix

Let say at the beginning I have two variables $a_{1}$ and $a_{2}$ of the same type then I would have the variance-covariance matrix defined as: $\sum = \begin{bmatrix} \sigma^{2}_{a_{1}} & ...
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28 views

Regression Puzzle GLS var/covar matrix of B given summary statistics

There is a problem posted back in 2009 that I found that has me puzzled. I believe the estimates are from a generalized linear regression because after some thought it seems $X'X$ is impossible to ...
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19 views

Finding parameter bias under omitted variable, with variance covariance notation

Dear CrossValidated community, Can anyone help me to prove the bias in a given parameter of a regression when there is omitted variable? I know to do it using matrices and matrix algebra. For ...
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32 views

Error Calculating MVN Likelihood of Time Series with AR(1) Errors in R

I'm having trouble calculating the likelihood of a time series with AR(1) errors. I am generating my covariance matrix according to page 2 of (http://cran.r-project.org/doc/contri...regression.pdf), ...
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9 views

Regression factors and covariance matrix

I am trying to follow someone else's notes. They have two matrices. One is called comfact (company factors). This is a 580 x 5 matrix. The 580 rows represent 580 ...
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62 views

If x = y*y, and you know var(y), var(z), and cov(y,z), do I know cov(x,z)?

If I know that x = y*y, and I know a whole of statistics pertaining to y, such as the variance and its covariance with other variables, can I analytically solve for the variance and covariance of x? ...
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Finding the covariance matrix to find the best linear predictor (AR(1) model)?

I need to find the covariance matrix of two given estimates of an AR(1) model $$X_t = \phi X_{t-1} + Z_t$$ to find its best linear predictor of $X_2$, given $X_1$ and $X_3$. Let W = ($X_1, X_3$)' ...
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78 views

Variance-covariance structure for random-effects in glmer

What is the default variance-covariance structure for random-effects in glmer in lme4 package? How does one specify other ...
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42 views

How to constrain covariance parameters in sas proc mixed?

I would like to test whether 3 dependent variables (measured with the same participants) differ in variance. My plan is to fit one model in which the 3 variables have the same variance, and one model ...
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20 views

Distance from bivariate Gaussian mean in terms of variance

Not sure if my question is a valid one but I will just put it out here. Consider a bivariate data set $(x_i, y_i)$ $[i=1,...,n]$ to which a bivariate Gaussian Distribution is fitted. Now, consider ...
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1answer
62 views

Heteroskedasticly Consistent Estimators for Var-Cov Matrix, Large Sample OLS Regression

I have a cross-sectional data sample of nearly 40,000 observations and tests for heteroskedasticity fail to reject the assumption of homoskedasticity. However, it seems common practice to report ...
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57 views

Variance Inequality for Random Vectors

I know that if X and Y are random scalar variables, then: \begin{align*} \mathrm{Var}(X+Y) & = \mathrm{Var}(X) + \mathrm{Var}(Y) + 2\mathrm{Corr}(X,Y)\sqrt{\mathrm{Var}(X)\mathrm{Var}(Y)} \\ ...
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56 views

Appropriate measure to find smallest covariance matrix

In the textbook I am reading they use positive definiteness (semi-positive definiteness) to compare two covariance matrices. The idea being that is A-B is pd then B is smaller than A. But I'm ...
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62 views

Proposal distributions for covariance matrices in MCMC implementation of hierarchical models [duplicate]

In a MCMC implementation of hierarchical models, with normal random effects and a Wishart prior for their covariance matrix, Gibbs sampling is typically used. However, if we change the distribution ...
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1answer
76 views

Contingency table analysis to rank preferences of birds per feature

I have a dataset that contains observations of objects that female blackbirds carry to their nests. The birds have id tags and the objects are grouped categorically with respect to their ...
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27 views

nearPD function in Matrix package

Does anyone know how the eigenvalues are adjusted to make a non-positive definite matrix into a positive definite matrix in Matrix package? I mean in nearPD function.
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124 views

Export variance-covariance matrix using PROC GLM

I have a ordinary linear regression model like this y = b0 + b1*x + b2*z + b3*x*z I used PROC GLM in ...
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23 views

Did anyone know how to fit factor analytic covriance struture either in R or SAS?

I would like to make meaningful interpretation from a two-way interaction data using factor analytic covariance structure. I have a genotype x environment matrix and I would like to know which ...
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1answer
80 views

Would the group means of PC scores differ from the PC scores of group means?

I have $2$ $n\times p$ matrices, where $n$ are the rows (samples), and $p$ the columns (measurements). Each matrix has samples and measurements from different groups. I call these the "raw" data. ...
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51 views

what's the pdf and covariance for this distribution?

I am stuck on a problem and wonder if anyone can give me some suggestions. $X_1, X_2, X_3$ all follow a $\text{Uniform}[0,1]$ distribution and are subject to the constraint $X_1+X_2+X_3\leq 1$. ...
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121 views

Measures of multidimensional spread or variance

What's a good measure of spread in a multidimensional space? In a single dimension variance would be the measure I need, but in a multidimensional space I need more than just variances. Note that in ...
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97 views

Hard thresholding a covariance matrix

I am new to the concept of thresholding a variance-covariance matrix and am having trouble understanding the exact process. I am following Bickel and Levina (2008) in choosing a hard threshold. What ...
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89 views

Variance covariance matrix of regression coefficients with a probit link

Suppose we are performing ordinal regression using a probit link function. The data are doses (log transformed) and responses. The responses are ordinal and can be from 0 to 4. Suppose that some of ...
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44 views

Fitting FA0(1) covariance models in SAS

I want to fit the following covariance model with SAS but I do not know how to do it. Can anyone help to me? FA0(1)>=0 FA0(1)=<0 The general factor-analytic structure with q ≤ s factors[FA(q)] ...
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Why does correlation matrix need to be positive semi-definite and what does it mean to be or not to be positive semi-definite?

I have been researching the meaning of positive semi-definite property of correlation or covariance matrix. Any information on Definition of positive semi-definiteness Its Important properties, ...
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The vcov function cannot be applied?

I originally asked a question about the delta-method in the context of the hyperbolic distribution. I got an answer there, which is useful, except that it says I should apply the ...
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Variance-covariance matrix of the parameter estimates wrongly calculated?

I fitted an hyperbolic distribution to my data with the hyperbFit(mydata,hessian=TRUE) command (package HyperbolicDist). The hessian looks like: ...
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194 views

Factor Analysis: calculate maximum likelihood factor loadings from only the correlation (R) matrix and/or covariance (S) matrix?

Does anybody know how to calculate the maximum likelihood factor loadings from only the correlation (R) matrix and/or covariance (S) matrix in Factor Analysis "by hand" (i.e., by Excel)? Or, even ...
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604 views

How to normalize data prior to computation of covariance matrix

In all my self-study, I have come across many different ways in which people seem to normalize their data, prior to the computation of the covariance matrix. I am confused as to what ways are ...
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114 views

Using the covariance matrix to calculate correlations

I'm a bit lost here. I have a matrix of response variables, $y$, and I fit a model to account for a number of predictor variables, say $x_1$, $x_2$ and $x_3$: ...
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Hausman test: the larger the sample the more significant the Hausman test statistic?

Hausman test statistic formula: $$ H=(\beta_{f}-\beta_{r})' \left[\mathrm{Cov}(\beta_{f})-\mathrm{Cov}(\beta_{r})\right]^{-1}(\beta_{f}-\beta_{r} ) $$ where $\beta_{f}$ is the beta of fixed effects ...
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How to calculate weighted covariance?

I have two variables X and Y with weights a and b ...
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Variance-covariance matrix of the errors in linear regression

How is the var/cov error matrix calculated by statistical analysis packages in practice? This idea is clear to me in theory. But not in practice. I mean, if I have a vector of random variables ...
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106 views

How do I create a random variance matrix (x'x)/N with confidence that it will be invertible?

I see some similar threads, but no answer that I know how to apply to this question. I wish to create a variance matrix for a (pseudo)random matrix $X$ with dimensions $K \times N$, where each row $k$ ...
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How can I compute covariances between parameters in WinBUGS?

I am wondering if there is an easy way to compute the covariances between parameters in WinBUGS/OpenBUGS. It is easy to obtain the variances, but for subsequent analysis, I need the covariances. ...
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Is every covariance matrix positive definite?

I guess the answer should be yes, but I still feel something is not right. There should be some general results in the literature, could anyone help me?
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332 views

Covariance matrix explanation

I try to understand and visualize myself covariance matrix. Supposing I have a matrix A = [ 2 3 4; 5 5 6 ], how do I calculate its covariance matrix, and what is ...
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341 views

Is the square root of a positive semi-definite matrix a unique result?

I am trying to decompose a time series of $n$ observations $\bf{\mathrm{v_c}}$ into the $n \times n$ variance-covariance structure $\sum$ and a random series $\bf{\mathrm{v}}$. So, I can derive the ...
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181 views

Variance of a series of correlated variables

I have started with a time series of 5000 random numbers drawn from uniform distribution with mean 0 and variance of 1. I then construct a Variance-Covariance matrix and use this to induce ...
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1answer
218 views

A measure of overall variance from multivariate Gaussian

I am performing some regression task, where I try to discover the underlying multivariate Gaussians from a set of $n$, $p$-dimensional vectors. For example, given a split of the set into $S_i$ and ...
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How to avoid 0 determinant when sample covariance matrix has very small values

I have $n$, $p$-dimensional vectors and I am constructing the $p \times p$ covariance matrix using the following formula: $$\mathrm{Cov}(j,k) = \frac{1}{n-1} {\sum^n_{i=1}} (x_i(j) - ...
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Ways to measure distance from multivariate Gaussian (Mahalanobis distance)

I have a cluster of p-dimensional points and given a new p-dimensional point $x$ I want to determine whether or not it is likely to belong to this cluster. The cluster is made up of $n$ ...
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What to do when sample covariance matrix is not invertible?

I am working on some clustering techniques, where for a given cluster of d-dimension vectors I assume a multivariate normal distribution and calculate the sample d-dimensional mean vector and the ...
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Variance-covariance matrix in lmer

I know that one of the advantages of mixed models is that they allow to specify variance-covariance matrix for the data (compound symmetry, autoregressive, unstructured, etc.) However, ...