  This paper develops computationally feasible methods for estimating random
effects models in the context of regression modelling of multiple independent
time series of discrete valued counts in which there is serial dependence.
Given covariates, random effects and process history, the observed responses at
each time in each series are independent and have an exponential family
distribution. We develop maximum likelihood estimation of the mixed effects
model using an observation driven generalized linear autoregressive moving
average specification for the serial dependence in each series. The paper
presents an easily implementable approach which uses existing single time
series methods to handle the serial dependence structure in combination with
adaptive Gaussian quadrature to approximate the integrals over the regression
random effects required for the likelihood and its derivatives. The models and
methods presented allow extension of existing mixed model procedures for count
data by incorporating serial dependence which can differ in form and strength
across the individual series. The structure of the model has some similarities
to longitudinal data transition models with random effects. However, in
contrast to that setting, where there are many cases and few to moderate
observations per case, the time series setting has many observations per series
and a few to moderate number of cross sectional time series. The method is
illustrated on time series of binary responses to musical features obtained
from a panel of listeners.
