# Questions tagged [covariance-matrix]

A $k\times k$ matrix of covariances between all pairs of $k$ random variables. It is also called variance-covariance matrix or simply the covariance matrix.

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### Does invariance of PCA under orthogonal transformation hold for data that is not centered?

I read the proof in the top answer to this question, but that page assumes that $\overline{A} = 0$. If the data instead has some nonzero mean $\mu$, I'm not sure if the same logic applies: ...
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### Covariance matrix of multivariate normal when negative values are made zero

Let $x$ be $n$ dimensionally multivariate normally distributed with mean $\mu$ and covariance matrix $\Sigma$. Now let $y$ be random variables defined by \begin{equation} y_i= \begin{cases} 0, ...
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### Interpret Coefficient of Determination in matrix form

In matrix form, a linear regression can be represented in the following form: $$Y \sim \mathbf{X} \beta + \epsilon; \\ \epsilon \sim N(0, \sigma^2 \mathbf{I})$$ The definition of $R^2$ is the ...
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### How to interpret the endogenous factor matrix in the General Structural Equation Model?

Bollen (1989) introduces a general structural equation model of the (matrix) form: $$\eta = \beta \eta + \gamma \xi + \zeta$$ $$y = \lambda \eta + \epsilon$$ Most textbooks (e.g. Depaili 2021) ...
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### Creating a random sparse precision matrix?

In my current project, I want to create a random sparse precision matrix $\boldsymbol{P}=\boldsymbol{\Sigma}^{-1}$ (the inverse of a covariance matrix $\boldsymbol{\Sigma}$). My current procedure ...
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### Interpretation of the elements of the error matrix as inverse of hessian matrix [duplicate]

In a report I am reading at work, the error matrix is calculated as the inverse of the hessian matrix and used to calculate the error ellipse angle and axes with a not theoretically correct formula. ...
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### Is it possible to know the actual covariance matrix, but fail to take-down heteroscedasticity and autocorrelation?

Is it possible to know the actual covariance matrix and estimate betas using $\Sigma$, but fail to defeat the problems caused by heteroscedasticity and autocorrelation and have biased or high-...
1 vote
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### Addition of Covariate Matrices in Multi Normal Gaussian Addition

I want to merge two different distance functions for one set of observations $(x, y)$ to use in a gaussian process regression. I have the covariance matrix $\Sigma_1$ from distance function number 1 ...
1 vote
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### Understanding the Covariance and Loading Matrices in Confirmatory Factor Analysis

I am currently stuck on how to correctly formulate the model for Confirmatory Factor Analysis(CFA). The general formula is $Y = \Lambda \xi + \epsilon$. According to Wikipedia $Y$ is a $p \times 1$ ...
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### Why is "design matrix of correlation parameters" a proxy for the "actual covariance matrix/working correlation matrix?

The example shows that knowing the design matrix of correlation parameters is sufficient to specify the working correlation. ...
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### How to obtain "normalized" model residuals for Generalized Estimating Equations?

How does one compute the "normalized" model residuals based via geepack's geeglm/gee in R? The nlme package in R allows one to compute the normalized model residuals: (standardized ...
1 vote
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### Covariance matrix of beta coefficients for constrained multiple regression

I have a linear least-squares problem with constraints that two of the coefficients must be non-negative. For a typical (unconstrained) least squares estimation, I know that the variance-covariance ...
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### Why do some poeple claim, that choice of the working correlation in GEE doesn't affect the marginal coefficients?

I found this discussion: GEE: choosing proper working correlation structure Cite: Correlation structure in GEE, unlike mixed models, does not affect the marginal parameter estimates (which you are ...
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