Questions tagged [covariance]
Covariance is a quantity used to measure the strength and direction of the linear relationship between two variables. The covariance is unscaled, & thus often difficult to interpret; when scaled by the variables' SDs, it becomes Pearson's correlation coefficient.
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Covariances among the five box-plot statistics for a sample from a normal population
For $X_1,\ldots,X_n\sim\operatorname N(\mu,\sigma^2),$ how much is known about the $5\times5$ matrix of covariances among the box-plot summary statistics: the minimum, the three quartiles, and the ...
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How to define a correlation structure for relational data in glmmTMB?
I have relational data, i.e. observations for pairs of objects. More specifically these are migration rates between plant populations, which I would like to explain by a predictor. The migration rates ...
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How to estimate covariance matrix for stocks with different lengths of data
Suppose I have 10 stocks, for which i have 10 year data for 9 stocks and 5 year data for 1 stock. How should I proceed with the covariance estimation? I am asking this question because if we proceed ...
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Modeling fixed effect, time variable, and errors for dyadic daily diary study using MPlus
I'm trying to analyse dyadic daily diary data using a multilevel model on MPlus. The dyads are distinguishable (women and men).
I would like to see whether attachment (trait level, measured only once ...
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Correcting bias in covariance between a random variable and linear regression slopes from a finite sample
Note that I am performing a linear regression of a predictor variable $x_{i}$ with $i \in (1, 2 ..,m)$ on a response variable $y$ in a finite population of size $N_{t}$. Since the linear regression is ...
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Uncertainty ellipse on (x, y) location using azimuthal measurements from network of points [closed]
I am working on a problem relating to the 'distinguishability' of a source, that is, given a network of points in space where measurements of the azimuth to the source can be made, I would like make a ...
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Bootstrap for calculation of effective number of parameters
In regression, the effective number of parameters (closely related to the concept of degrees of freedom)
$k_{\mathrm{eff}}=\sum\limits_{i=1}^{n}\mathrm{Cov}(\hat{y}_i, y_i)$
is given as a sum over the ...
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Why are the point estimates of estimated marginal means from a Bayesian binomial GLMM so different in the presence of residual covariance?
As the question title says, I am confused why the estimated marginal means (obtained using emmeans()) for a Bayesian binomial generalized linear mixed model are so ...
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Lavaan serial mediation model - covariance between mediators and adding covariates
I'm trying to set up a serial mediation in lavaan with two mediators, and have a couple of questions about setting up the model that I haven't been able to find the answer to so far.
I had initially ...
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Use bigger sample for predictors in regression
I need to regress continuous y on multi-dimensional X (for prediction mostly, not inference, but do I need the betas to make ...
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Mixed effect model or linear model- isSingular problem
so I have 10 levels for genótipo (plant genotype) and 5 levels for Local (sample locals, they are located far apart geographically). I'm interested, in the current model, in the overall effect of ...
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For reducing aggregate standard error, better to sample n items measured one time or n/k items measured k times?
I have a measurement system where we need to measure an item using an instrument with unknown noise.
Our metric of interest is average quality per item.
We have a lot of items that have been produced. ...
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Covariance matrix construction problem for multivariate normal sampling
I have encountered a problem when trying to simulate from a multivariate normal distribution with a covariance matrix built to encode specific correlations. Most of my parameters are estimated from ...
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Relating omitted-variable bias to the re-arrangement of a multilinear regression
Note that
\begin{equation} \tag{Eq. 1}
y=a\sum_{i}^{m}X_{q,k}^{2} + a\sum_{i}^{m}X_{q,k}^{2}\sum_{j= i + 1}^{m} \frac{X_{q,j}}{X_{q,i}}
\end{equation}
which could be re-arranged as:
\begin{equation} \...
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Covariance of a summation of a squared random variable with a double summation of two random variables
I would like to know how to expand the covariance between a summation and a double summation. Here there is an example:
$$
\text{Cov}\big(\sum_{i}^{m}{X_{q,i}^2},\sum_{i}^{m}\sum_{j\neq i}^{m}{X_{q,i}...
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