MARKOV-CHAIN MODELS FOR MULTIVARIATE BINARY PANEL-DATA

Multivariate binary responses appear for diseases reported for each me mber of a group of k greater-than-or-equal-to 2 individuals or for eac h of k greater-than-or-equal-to 2 possible sites on a person or an ani mal. The analysis of changes over time of such complex disease measure s in {0, 1}k is considered using Markov chain models. The paper gives a review of various hypotheses on the parameters in the 2k x 2k matrix of transition probabilities. Serial correlations between consecutive observations as well as interactions between individuals are modelled and a hypothesis about the existence of dominating individuals is cons idered. The basic model is an extension of a Rasch model with random e ffects. The use of regression models is suggested. The methods are app lied in an analysis of the occurrence of bacteria in repeated milk sam ples from four teats (k = 4) of cows in production herds.