A count data model with unobserved heterogeneity

Abstract A count data model is defined via the distribution of the durations between successive events. It is assumed that the durations follow independent exponential distributions conditionally to a set of variables. The parameters of these distributions depend not only on observed and unobserved individual specific factors, but also on unobserved spell-specific factors. The count data model is therefore a natural extension of the compound Poisson model. A local version of the count data model is used to analyse the effects of unobserved spell specific factors. In particular, it is shown that spell-specific heterogeneity can induce not only overdispersion, but also underdispersion. The local model is also used to construct a score test for spell-specific heterogeneity in the Poisson model. The results are applied on purchase data of a consumption good.

[1]  Tony Lancaster,et al.  The Econometric Analysis of Transition Data. , 1992 .

[2]  Andrew Chesher,et al.  Testing for Neglected Heterogeneity , 1984 .

[3]  Nicholas M. Kiefer A Simple Test for Heterogeneity in Exponential Models of Duration , 1984, Journal of Labor Economics.

[4]  J. Mullahy Specification and testing of some modified count data models , 1986 .

[5]  A. Cameron,et al.  Regression-based tests for overdispersion in the Poisson model☆ , 1990 .

[6]  Michel Wedel,et al.  A Latent Class Poisson Regression Model for Heterogeneous Count Data , 1993 .

[7]  R. Winkelmann A count data model for gamma waiting times , 1996 .

[8]  L. Gold Generalized poisson distributions , 1957 .

[9]  Tony Lancaster,et al.  Simultaneous equations models in applied search theory , 1985 .

[10]  D. Cox,et al.  Analysis of Survival Data. , 1985 .

[11]  W. Feller,et al.  An Introduction to Probability Theory and Its Application. , 1951 .

[12]  Bruno Crépon,et al.  Research and development, competition and innovation pseudo-maximum likelihood and simulated maximum likelihood methods applied to count data models with heterogeneity☆ , 1997 .

[13]  David R. Cox,et al.  Some remarks on overdispersion , 1983 .

[14]  A. Cameron,et al.  Econometric models based on count data. Comparisons and applications of some estimators and tests , 1986 .

[15]  P. Trivedi,et al.  Overdispersion tests for truncated Poisson regression models , 1992 .

[16]  Lisa M. Ganio,et al.  Diagnostics for Overdispersion , 1992 .

[17]  J. Lawless,et al.  Tests for Detecting Overdispersion in Poisson Regression Models , 1989 .

[18]  J. Robin Econometric Analysis of the Short--run Fluctuations of Households' Purchases , 1993 .

[19]  J. Kalbfleisch,et al.  The Statistical Analysis of Failure Time Data , 1980 .

[20]  Z. Griliches,et al.  Econometric Models for Count Data with an Application to the Patents-R&D Relationship , 1984 .