Modelling of repeated ordered measurements by isotonic sequential regression

The paper introduces a simple model for repeated observations of an
ordered categorical response variable which is isotonic over time.
It is assumed that the measurements represent an irreversible
process such that the response at time t is never lower than the
response observed at the previous time point t-1. Observations of
this type occur for example in treatment studies when improvement
is measured on an ordinal scale. Since the response at time t
depends on the previous outcome, the number of ordered response
categories depends on the previous outcome leading to severe
problems when simple threshold models for ordered data are used. In
order to avoid these problems the isotonic sequential model is
introduced. It accounts for the irreversible process by considering
the binary transitions to higher scores and allows a parsimonious
parameterization. It is shown how the model may easily be estimated
by using existing software. Moreover, the model is extended to a
random effects version which explicitly takes heterogeneity of
individuals and potential correlations into account.