Abstract
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.
Item Type: | Paper |
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Keywords: | Ordinal data, cumulative model, sequential model, repeated measurements, isotonic ordinal regression, random effects models |
Faculties: | Mathematics, Computer Science and Statistics > Statistics > Collaborative Research Center 386 Special Research Fields > Special Research Field 386 |
Subjects: | 500 Science > 510 Mathematics |
URN: | urn:nbn:de:bvb:19-epub-1676-9 |
Language: | English |
Item ID: | 1676 |
Date Deposited: | 05. Apr 2007 |
Last Modified: | 04. Nov 2020, 12:45 |