Regression Models for Ordinal Categorical Time Series Data

  • Brajendra C. SutradharEmail author
  • R. Prabhakar Rao
Part of the Fields Institute Communications book series (FIC, volume 78)


Regression analysis for multinomial/categorical time series is not adequately discussed in the literature. Furthermore, when categories of a multinomial response at a given time are ordinal, the regression analysis for such ordinal categorical time series becomes more complex. In this paper, we first develop a lag 1 transitional logit probabilities based correlation model for the multinomial responses recorded over time. This model is referred to as a multinomial dynamic logits (MDL) model. To accommodate the ordinal nature of the responses we then compute the binary distributions for the cumulative transitional responses with cumulative logits as the binary probabilities. These binary distributions are next used to construct a pseudo likelihood function for inferences for the repeated ordinal multinomial data. More specifically, for the purpose of model fitting, the likelihood estimation is developed for the regression and dynamic dependence parameters involved in the MDL model.


Category transition over time Cumulative logits Marginal multinomial logits Multinomial dynamic logits Pseudo binary likelihood 



The authors are grateful to Bhagawan Sri Sathya Sai Baba for His love and blessings to carry out this research in Sri Sathya Institute of Higher Learning. The authors thank the editorial committee for the invitation to participate in preparing this Festschrift honoring Professor Ian McLeod. It has brought back many pleasant memories of Western in early 80’s experienced by the first author during his PhD study. We have prepared this small contribution as a token of our love and respect to Professor Ian McLeod for his long and sustained contributions to the statistics community through teaching and research in time series analysis, among other areas. The authors thank two referees for their comments and suggestions on the earlier version of the paper.


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© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Memorial UniversitySt. John’sCanada
  2. 2.Sri Sathya Sai Institute of Higher Learning, Prasanthi NilayamAnantapurIndia

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