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Unformatted text preview: Journal of Applied Statistics, Vol. 28, No. 5, 2001, 623-632 Markov zero-in ated Poisson regression models for a time series of counts with excess zeros PEIMING WANG, Nanyang Business School, Nanyang Technological University, Singapore abstract This paper discusses a class of Markov zero-in ated Poisson regression models for a time series of counts with the presence of excess zero relative to a Poisson distribution, in which the frequency distribution changes according to an underlying two-state Markov chain. Features of the proposed model, estimation method based on the EM and quasi- Newton algorithms, and other implementation issues are discussed. A Monte Carlo study shows that the estimation method is accurate and reliable as long as the sample size is reasonably large, and the choice of starting probabilities for the Markov process has little impact on the parameter estimates. The methodology is illustrated using daily numbers of phone calls reporting faults for a mainframe computer system. 1 Introduction This paper proposes a model for a time series of counts with the presence of excess zeros relative to a Poisson distribution, which allows for the frequency distribution to change according to the states of a two-state discrete time Markov chain with the transition probabilities associated with covariates. The model is developed assuming that the frequency distribution conditional on one of the two states is a Poisson distribution with its mean associated with covariates through an exponential link function, and the frequency distribution conditional on the other state has the only value of zero, and that the transition probabilities between the two states are associated with covariates through a logit link function. The proposed model allows for overdispersion relative to a Poisson distribution and for correlation between observations. Correspondence : Peiming Wang, Nanyang Business School, S3-B1A-33, Nanyang Technological Univer- sity, Nanyang Avenue, Singapore 639798. ISSN 0266-4763 print; 1360-0532 online/01/050623-10 2001 Taylor & Francis Ltd DOI: 10.1080/02664760120047951 624 P. Wang For count data of independent observations with excess zeros relative to a Poisson distribution, the zero-in ated Poisson (ZIP) regression models have been discussed extensively as a possible mechanism for handling this type of count data (e.g. Heilbron, 1989; Lambert, 1992; Bo hning et al ., 1999). The main assumptions of the ZIP models can be interpreted as the following: (1) there are two underlying states: perfect and imperfect; (2) conditional on the perfect state the only observa- tion is zero, and conditional on the imperfect state a Poisson random variable is observed with the mean associated with covariates; and (3) the probabilities of being in the perfect and imperfect states are p and (1 2 p ) respectively, where p may be also associated with covariates. The ZIP models may not be suitable for time series of count data with excess zeros relative to Poisson distribution as there...
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