title: Log-linear modeling with the negative multinomial distribution.
abstract: We develop a negative multinomial sampling plan in which observed cell counts are positively correlated. We show that maximum likelihood estimates of cell means are the same as those found under independent Poisson sampling. There is no maximum likelihood estimate for the shape parameter in general. We propose an estimate of the shape parameter based on the mean and quantiles of Pearson's chi-squared statistic. These techniques are applied to models of cancer incidence for three cities in Ohio and longitudinal health care utilization by a group of senior citizens.
authors.affiliation: Division of Biostatistics, University of Minnesota, Minneapolis 55455-0378, USA.
authors.forename: L A
authors.initials: LA
authors.lastname: Waller
authors.forename: D
authors.initials: D
authors.lastname: Zelterman
mesh_terms: D000368:Aged; D001699:Biometry / Q000379:methods; D016009:Chi-Square Distribution; D006299:Health Services for the Aged / Q000706:statistics & numerical data; D006801:Humans; D008137:Longitudinal Studies; D015233:Models, Statistical; D009820:Ohio; D016012:Poisson Distribution; D011336:Probability