Conditional Inference for Multivariate Generalised Linear Mixed Models

07/25/2021
by   Jeanett S. Pelck, et al.
0

We propose a method for inference in generalised linear mixed models (GLMMs) and several extensions of these models. First, we extend the GLMM by allowing the distribution of the random components to be non-Gaussian, that is, assuming an absolutely continuous distribution with respect to the Lebesgue measure that is symmetric around zero, unimodal and with finite moments up to fourth-order. Second, we allow the conditional distribution to follow a dispersion model instead of exponential dispersion models. Finally, we extend these models to a multivariate framework where multiple responses are combined by imposing a multivariate absolute continuous distribution on the random components representing common clusters of observations in all the marginal models. Maximum likelihood inference in these models involves evaluating an integral that often cannot be computed in closed form. We suggest an inference method that predicts values of random components and does not involve the integration of conditional likelihood quantities. The multivariate GLMMs that we studied can be constructed with marginal GLMMs of different statistical nature, and at the same time, represent complex dependence structure providing a rather flexible tool for applications.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
07/30/2021

Multivariate Generalised Linear Mixed Models With Graphical Latent Covariance Structure

This paper introduces a method for studying the correlation structure of...
research
09/22/2022

Standardisation overcomes counter-examples of conditional extremes

A key aspect where extreme values methods differ from standard statistic...
research
06/14/2022

Minimum information dependence modeling

We propose a method of dependence modeling for a broad class of multivar...
research
12/06/2013

A sequential reduction method for inference in generalized linear mixed models

The likelihood for the parameters of a generalized linear mixed model in...
research
03/04/2021

Approximate Bayesian Conditional Copulas

Copula models are flexible tools to represent complex structures of depe...
research
06/22/2019

Relative variation indexes for multivariate continuous distributions on [0,∞)^k and extensions

We introduce some new indexes to measure the departure of any multivaria...

Please sign up or login with your details

Forgot password? Click here to reset