plogLik: Gaussian Pseudo-Loglikelihood

In mcglm: Multivariate Covariance Generalized Linear Models

Gaussian Pseudo-Loglikelihood

Description

Computes the Gaussian pseudo-loglikelihood for fitted multivariate covariance generalized linear models. The pseudo-loglikelihood is obtained by assuming a multivariate normal distribution for the stacked response vector, using the estimated mean vector and covariance matrix from the fitted mcglm object.

Usage

plogLik(object, verbose = TRUE)

Arguments

object	An object of class mcglm or a list of such objects. When a list is supplied, the pseudo-loglikelihood is computed for the joint model obtained by stacking the responses, fitted values and covariance matrices of all elements in the list.
verbose	Logical indicating whether the pseudo-loglikelihood value should be printed to the console. Defaults to TRUE.

Details

The Gaussian pseudo-loglikelihood is computed as

\ell_p = -\frac{n}{2}\log(2\pi) - \frac{1}{2}\log|\Sigma| - \frac{1}{2}(y - \mu)^\top \Sigma^{-1} (y - \mu),

where y is the stacked vector of observed responses, \mu is the stacked vector of fitted means, and \Sigma is the estimated covariance matrix. For a list of mcglm objects, block-diagonal covariance matrices are constructed internally.

This quantity is used mainly for model comparison purposes and as a building block for pseudo-information criteria such as pAIC and pBIC. It is not a true likelihood unless the Gaussian assumption holds.

Value

An invisible list with the following components:

plogLik

A numeric value giving the Gaussian pseudo-loglikelihood.

df

An integer giving the total number of estimated parameters (degrees of freedom) used in the model.

Author(s)

Wagner Hugo Bonat, [e-mail]

See Also

pAIC, pBIC, ESS, pKLIC, GOSHO, RJC

mcglm documentation built on Jan. 9, 2026, 1:07 a.m.