%0 Journal Article %1 WZ97 %A Waller, Lance A. %A Zelterman, Daniel %D 1997 %I Wiley, International Biometric Society %J Biometrics %K negative_multinomial_distribution %N 3 %P 971-982 %T Log-Linear Modeling with the Negative Multinomial Distribution %U http://www.jstor.org/stable/2533557 %V 53 %X 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

@article{WZ97, 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}, added-at = {2017-06-16T16:49:15.000+0200}, author = {Waller, Lance A. and Zelterman, Daniel}, biburl = {https://www.bibsonomy.org/bibtex/24189d1567212f9e547ca8586d678f51c/pfernique}, interhash = {ea9cd53d87ca094504d93d5cb42a2bd8}, intrahash = {4189d1567212f9e547ca8586d678f51c}, issn = {0006341X, 15410420}, journal = {Biometrics}, keywords = {negative_multinomial_distribution}, number = 3, pages = {971-982}, publisher = {[Wiley, International Biometric Society]}, timestamp = {2017-06-16T16:49:15.000+0200}, title = {Log-Linear Modeling with the Negative Multinomial Distribution}, url = {http://www.jstor.org/stable/2533557}, volume = 53, year = 1997 }