PhDIn a generalized linear mixed model (GLMM), the random effects are typically
uncorrelated and assumed to follow a normal distribution. However,
fi ndings from recent studies on how the misspeci cation of the random effects
distribution affects the estimated model parameters are inconclusive. In the
thesis, we extend the randomization approach for deriving linear models to
the GLMM framework. Based on this approach, we develop an algorithm for
estimating the model parameters of the randomization-based GLMM (RBGLMM)
for the completely randomized design (CRD) which does not require
normally distributed random effects. Instead, the discrete uniform distribution
on the symmetric group of permutations is used for the random effects. Our
simulation results suggest that the randomization-based algorithm may be an
alternative when the assumption of normality is violated.
In the second part of the thesis, we consider an RB-GLMM for the randomized
complete block design (RCBD) with random block effects. We investigate the
effect of misspecifi cation of the correlation structure and of the random effects
distribution via simulation studies. In the simulation, we use the variance covariance
matrices derived from the randomization approach. The misspecifi ed model with
uncorrelated random effects is fi tted to data generated from
the model with correlated random effects. We also t the model with normally
distributed random effects to data simulated from models with different random
effects distributions. The simulation results show that misspeci cation
of both the correlation structure and of the random effects distribution has
hardly any effect on the estimates of the fi xed effects parameters. However,
the estimated variance components are frequently severely biased and standard
errors of these estimates are substantially higher
