Page 337 - Contributed Paper Session (CPS) - Volume 2

CPS1878 Zakir H. et al.

Modelling randomization with misspecification
of the correlation structure and distribution of
random effects in a poisson mixed model
1
3
2
Zakir Hossain , Heiko Grossmann , Steven Gilmour
1 Department of Statistics, University of Dhaka, Bangladesh
2 School of Mathematical Sciences, University of Magdeburg, Germany
3 School of Mathematical Sciences, Kings College London, UK

Abstract
We consider the generalized linear mixed model (GLMM) for the randomized
complete block design (RCBD) with random block effects. The variance-
covariance matrices for the random effects are derived from the
randomization. The randomization of blocks and units within each block has
been modelled by using the wreath product of two symmetric groups.
Typically, the random effects in a GLMM are uncorrelated and assumed to
follow a normal distribution. However, in our case, the random effects are
found to be correlated due to randomization. The impact of misspecification
of the correlation structure and distribution of the random effects upon the
estimation of fixed effects and variance components in a Poisson mixed model
has been investigated via simulation studies. The simulation results show that
misspecification of both the correlation structure and the random effects
distribution has hardly any effect on the estimates of the fixed effects
parameters. However, the estimated variance components are frequently
severely biased and standard errors of these estimates are found to be
substantially higher.

Keywords
Generalized linear mixed model; Randomized complete block design;
Symmetric group; Wreath product

1. Introduction
The random effects in a GLMM are usually assumed to have a normal
distribution. However, inferences that are based on the normality assumption
may be incorrect if the actual distribution of the random effects is not normal.
Recently it has been investigated how misspecification of the random effects
distribution affects the estimates of the model parameters. To this end,
simulation studies have been performed which have lead to conflicting
conclusions. Some studies report that misspecification has a strong effect
[Heagerty and Kurland (2001), Agresti et al. (2004), Litière et al. (2007, 2008),
Hernández and Giampaoli (2018)] while others claim the contrary [Neuhaus et
al. (2011), McCulloch and Neuhaus (2011), Neuhaus et al. (2011), Neuhaus et
al. (2013)].

326 | I S I W S C 2 0 1 9