An INAR(1) negative multinomial regression model for longitudinal count data

Ulf Böckenholt

doi:10.1007/BF02294319

An INAR(1) negative multinomial regression model for longitudinal count data

Ulf Böckenholt^*

^*Corresponding author for this work

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11 Scopus citations

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.

Original language	English (US)
Pages (from-to)	53-67
Number of pages	15
Journal	Psychometrika
Volume	64
Issue number	1
DOIs	https://doi.org/10.1007/BF02294319
State	Published - Mar 1999

Keywords

Binomial thinning
Markov models
Poisson distribution

ASJC Scopus subject areas

Psychology(all)
Applied Mathematics

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10.1007/BF02294319

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title = "An INAR(1) negative multinomial regression model for longitudinal count data",

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 = "Binomial thinning, Markov models, Poisson distribution",

author = "Ulf B{\"o}ckenholt",

note = "Funding Information: 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. Requests for reprints should be sent to Ulf B6ckenholt, University of Illinois at Urbana-Champaign, Department of Psychology, 603 East Daniel Street, Champaign, IL 61820.",

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N1 - Funding Information: 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. Requests for reprints should be sent to Ulf B6ckenholt, University of Illinois at Urbana-Champaign, Department of Psychology, 603 East Daniel Street, Champaign, IL 61820.

PY - 1999/3

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N2 - 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.

AB - 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.

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KW - Markov models

KW - Poisson distribution

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An INAR(1) negative multinomial regression model for longitudinal count data

Abstract

Keywords

ASJC Scopus subject areas

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