On exchangeable multinomial distributions.
We derive an expression for the joint distribution of exchangeable multinomial random variables, which generalizes the multinomial distribution based on independent trials while retaining some of its important properties. Unlike de Finneti's representation theorem for a binary sequence, the exchangeable multinomial distribution derived here does not require that the finite set of random variables under consideration be a subset of an infinite sequence. Using expressions for higher moments and correlations, we show that the covariance matrix for exchangeable multinomial data has a different form from that usually assumed in the literature, and we analyse data from developmental toxicology studies. The proposed analyses have been implemented in R and are available on CRAN in the CorrBin package.
Department of Mathematical Sciences, The University of Memphis, Memphis, Tennessee 38152, U.S.A.
E Olusegun
EO
George
Biometrics Research, Merck, 770 Sumneytown Pike, West Point, Pennsylvania 19486, U.S.A. , katie.cheon@gmail.com.
Kyeongmi
K
Cheon
Advanced Analytics, IMS Health, One IMS Drive, Plymouth Meeting, Pennsylvania 19462, U.S.A. , yyuan@us.imshealth.com.
Yilian
Y
Yuan
Division of Biostatistics, Institute for Health and Society, Medical College of Wisconsin, Milwaukee, Wisconsin 53226, U.S.A. , aszabo@mcw.edu.
Aniko
A
Szabo
Clustered multinomial data; Finite exchangeable set; Marginal compatibility; Overdispersion