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Modelling of repeated ordered measurements by isotonic sequential regression
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| Zeitschriftentitel: | Statistical Modelling |
|---|---|
| Personen und Körperschaften: | |
| In: | Statistical Modelling, 5, 2005, 4, S. 269-287 |
| Format: | E-Article |
| Sprache: | Englisch |
| veröffentlicht: |
SAGE Publications
|
| Schlagwörter: |
| author_facet |
Tutz, Gerhard Tutz, Gerhard |
|---|---|
| author |
Tutz, Gerhard |
| spellingShingle |
Tutz, Gerhard Statistical Modelling Modelling of repeated ordered measurements by isotonic sequential regression Statistics, Probability and Uncertainty Statistics and Probability |
| author_sort |
tutz, gerhard |
| spelling |
Tutz, Gerhard 1471-082X 1477-0342 SAGE Publications Statistics, Probability and Uncertainty Statistics and Probability http://dx.doi.org/10.1191/1471082x05st101oa <jats:p> 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. </jats:p> Modelling of repeated ordered measurements by isotonic sequential regression Statistical Modelling |
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SAGE Publications, 2005 |
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| title |
Modelling of repeated ordered measurements by isotonic sequential regression |
| title_unstemmed |
Modelling of repeated ordered measurements by isotonic sequential regression |
| title_full |
Modelling of repeated ordered measurements by isotonic sequential regression |
| title_fullStr |
Modelling of repeated ordered measurements by isotonic sequential regression |
| title_full_unstemmed |
Modelling of repeated ordered measurements by isotonic sequential regression |
| title_short |
Modelling of repeated ordered measurements by isotonic sequential regression |
| title_sort |
modelling of repeated ordered measurements by isotonic sequential regression |
| topic |
Statistics, Probability and Uncertainty Statistics and Probability |
| url |
http://dx.doi.org/10.1191/1471082x05st101oa |
| publishDate |
2005 |
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269-287 |
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<jats:p> 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. </jats:p> |
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| description | <jats:p> 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. </jats:p> |
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| spelling | Tutz, Gerhard 1471-082X 1477-0342 SAGE Publications Statistics, Probability and Uncertainty Statistics and Probability http://dx.doi.org/10.1191/1471082x05st101oa <jats:p> 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. </jats:p> Modelling of repeated ordered measurements by isotonic sequential regression Statistical Modelling |
| spellingShingle | Tutz, Gerhard, Statistical Modelling, Modelling of repeated ordered measurements by isotonic sequential regression, Statistics, Probability and Uncertainty, Statistics and Probability |
| title | Modelling of repeated ordered measurements by isotonic sequential regression |
| title_full | Modelling of repeated ordered measurements by isotonic sequential regression |
| title_fullStr | Modelling of repeated ordered measurements by isotonic sequential regression |
| title_full_unstemmed | Modelling of repeated ordered measurements by isotonic sequential regression |
| title_short | Modelling of repeated ordered measurements by isotonic sequential regression |
| title_sort | modelling of repeated ordered measurements by isotonic sequential regression |
| title_unstemmed | Modelling of repeated ordered measurements by isotonic sequential regression |
| topic | Statistics, Probability and Uncertainty, Statistics and Probability |
| url | http://dx.doi.org/10.1191/1471082x05st101oa |