The analysis of ordinal time-series data via a transition (Markov) model |
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Authors: | Kathryn Bartimote-Aufflick Peter C Thomson |
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Institution: | 1. Institute for Teaching and Learning, Carslaw F07 , University of Sydney , NSW, 2006, Australia;2. Faculty of Veterinary Science , University of Sydney , Private Bag 4003, Narellan, NSW, 2567, Australia |
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Abstract: | While standard techniques are available for the analysis of time-series (longitudinal) data, and for ordinal (rating) data, not much is available for the combination of the two, at least in a readily-usable form. However, this data type is common place in the natural and health sciences where repeated ratings are recorded on the same subject. To analyse these data, this paper considers a transition (Markov) model where the rating of a subject at one time depends explicitly on the observed rating at the previous point of time by incorporating the previous rating as a predictor variable. Complications arise with adequate handling of data at the first observation (t=1), as there is no prior observation to use as a predictor. To overcome this, it is postulated the existence of a rating at time t=0; however it is treated as ‘missing data’ and the expectation–maximisation algorithm used to accommodate this. The particular benefits of this method are shown for shorter time series. |
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Keywords: | E–M algorithm ordinal repeated measures transition model longitudinal categorical |
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