Statistical Modelling 5 (2005), 269287
Modelling of repeated ordered measurements by
isotonic sequential regression
Gerhard Tutz
Institut für Statistik,
Ludwig-Maximilians-Universität München,
München,
Germany.
eMail: tutz@stat.uni-muenchen.de
Abstract:
This article 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. As 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. 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
using existing software. Moreover,
the model is extended to a random effects version which explicitly
takes heterogeneity of individuals and
potential correlations into account.
Keywords:
cumulative model; isotonic ordinal regression; ordinal data;
random effects models; repeated measurements; sequential model
Downloads:
Data and SAS code
in zipped archive
The author would like to thank Prof C.S. Davies for
making the data available.
The SAS code was developed by Florian Reithinger (LMU Munich).
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