Quality & Quantity 34: 323–330, 2000.
© 2000 Kluwer Academic Publishers. Printed in the Netherlands.
Discrete Response Multilevel Models for Repeated
Measures: An Application to Voting Intentions Data
MARIA FERRAO BARBOSA
and HARVEY GOLDSTEIN
Pontiﬁcia Universidade Catolica do Rio de Janeiro;
Institute of Education, University of London
Abstract. Repeated measures data can be modelled as a two-level model where occasions (level
one units) are grouped by individuals (level two units). Goldstein et al. (1994) proposed a multilevel
time series model when the response variable follows a Normal distribution and the measurements are
taken with unequal time intervals. This paper extends the methodology to discrete response variables.
The models are applied to British Election Study data consisting of repeated measures of voting
Key words: discrete response, longitudinal data, multilevel model, repeated measures, time series,
underdispersion, voting intentions.
Repeated measures data can be modelled as a two-level structure where meas-
urement occasions are level one units and individual subjects are level two units.
Consider a data set consisting of repeated measurements of the heights of a random
sample of children. Thus, for linear growth we can write a simple model as
This model assumes that height (Y ) is linearly related to age (X) with each subject
having their own intercept and slope so that, assuming Normality, we have
There is no restriction on the number or spacing of ages, so that we can ﬁt a single
model to subjects who may have one or several measurements. We can clearly
extend Equation (1) to include further explanatory variables, measured either at
the occasion level, such as time of year or state of health, or at the subject level
such as birthweight or gender.