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An INAR(1) Negative Multinomial Regression Model for Longitudinal Count Data

Published online by Cambridge University Press:  01 January 2025

Ulf Böckenholt
Ulf Böckenholt*
Affiliation:
University of Illinois at Urbana-Champaign
*
Requests for reprints should be sent to Ulf Böckenholt, University of Illinois at Urbana-Champaign, Department of Psychology, 603 East Daniel Street, Champaign, IL 61820.
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Abstract

This paper discusses a regression model for the analysis of longitudinal count data observed in a panel study. An integer-valued first-order autoregressive [INAR(1)] Poisson process is adapted to represent time-dependent correlations among the counts. By combining the INAR(1)-representation with a random effects approach, a new negative multinomial distribution is derived that includes the bivariate negative binomial distribution proposed by Edwards and Gurland (1961) and Subrahmaniam (1966) as a special case. A detailed analysis of the relationship between personality factors and daily emotion experiences illustrates the approach.

Keywords

Poisson distributionbinomial thinningMarkov models
Type
Original Paper
Information
Psychometrika , Volume 64 , Issue 1 , March 1999 , pp. 53 - 67
Copyright
Copyright © 1999 The Psychometric Society

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Footnotes

This research was partially supported by NSF grant SBR-9409531. The author is grateful to Ulrich Schimmack and Ed Diener for providing the data set used in the application section and for helpful comments on this research.

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