This Article Full Text (PDF) References Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Add to Saved Citations Download to citation manager Add to My Marked Citations Citing Articles Citing Articles via Google Scholar Citing Articles via Scopus Google Scholar Articles by Booth, J. G Articles by Hobert, J. P Search for Related Content Social Bookmarking                         What's this?

Negative binomial loglinear mixed models

Department of Statistics, University of Florida, Gainesville, FL, USA

George Casella

Department of Statistics, University of Florida, Gainesville, FL, USA

Herwig Friedl

Institute of Statistics, Technical University Graz, Graz, Austria

James P Hobert

Department of Statistics, University of Florida, Gainesville, FL, USA

The Poisson loglinear model is a common choice for explaining variability in counts. However, in many practical circumstances the restriction that the mean and variance are equal is not realistic. Overdispersion with respect to the Poisson distribution can be modeled explicitly by integrating with respect to a mixture distribution, and use of the conjugate gamma mixing distribution leads to a negative binomial loglinear model. This paper extends the negative binomial loglinear model to the case of dependent counts, where dependence among the counts is handled by including linear combinations of random effects in the linear predictor. If we assume that the vector of random effects is multivariate normal, then complex forms of dependence can be modelled by appropriate specification of the covariance structure. Although the likelihood function for the resulting model is not tractable, maximum likelihood estimates (and standard errors) can be found using the NLMIXED procedure in SAS or, in more complicated examples, using a Monte Carlo EM algorithm. An alternate approach is to leave the random effects completely unspecified and attempt to estimate them using nonparametric maximum likelihood. The methodologies are illustrated with several examples.

Key Words: Monte Carlo EM • NLMIXED procedure • nonparametric maximum likelihood • over-dispersion • random effects

Statistical Modelling, Vol. 3, No. 3, 179-191 (2003)
DOI: 10.1191/1471082X03st058oa


CiteULike    Complore    Connotea    Del.icio.us    Digg    Reddit    Technorati    Twitter    What's this?