A Note on the Identifiability of Generalized Linear Mixed Models

I present here a simple proof that, under general regularity conditions, the standard parametrization of generalized linear mixed model is identifiable. The proof is based on the assumptions of generalized linear mixed models on the first and second order moments and some general mild regularity conditions, and, therefore, is extensible to quasi-likelihood based generalized linear models. In particular, binomial and Poisson mixed models with dispersion parameter are identifiable when equipped with the standard parametrization.Comment: 9 pages, no figure

On the Bias of the Score Function of Finite Mixture Models

We characterize the unbiasedness of the score function, viewed as an inference function, for a class of finite mixture models. The models studied represent the situation where there is a stratification of the observations in a finite number of groups. We show that if the observations belonging to the same group follow the same distribution and the K distributions associated with each group are distinct elements of a sufficiently regular parametric family of probability measures, then the score function for estimating the parameters identifying the distribution of each group is unbiased. However, if one introduces a mixture in the scenario described above, so that for some observations it is only known that they belong to some of the groups with a given probability (not all in { 0, 1}), then the score function becomes biased. We argue then that under further mild regularity conditions, the maximum likelihood estimate is not consistent.Comment: 9 page

Multivariate Survival Mixed Models for Genetic Analysis of Longevity Traits

A class of multivariate mixed survival models for continuous and discrete time with a complex covariance structure is introduced in a context of quantitative genetic applications. The methods introduced can be used in many applications in quantitative genetics although the discussion presented concentrates on longevity studies. The framework presented allows to combine models based on continuous time with models based on discrete time in a joint analysis. The continuous time models are approximations of the frailty model in which the hazard function will be assumed to be piece-wise constant. The discrete time models used are multivariate variants of the discrete relative risk models. These models allow for regular parametric likelihood-based inference by exploring a coincidence of their likelihood functions and the likelihood functions of suitably defined multivariate generalized linear mixed models. The models include a dispersion parameter, which is essential for obtaining a decomposition of the variance of the trait of interest as a sum of parcels representing the additive genetic effects, environmental effects and unspecified sources of variability; as required in quantitative genetic applications. The methods presented are implemented in such a way that large and complex quantitative genetic data can be analyzed.Comment: 36 pages, 2 figures, 3 table

High-Dimensional Graphical Model Search with the gRapHD R Package

This paper presents the R package gRapHD for efficient selection of high-dimensional undirected graphical models. The package provides tools for selecting trees, forests, and decomposable models minimizing information criteria such as AIC or BIC, and for displaying the independence graphs of the models. It has also some useful tools for analysing graphical structures. It supports the use of discrete, continuous, or both types of variables.