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.