ABSTRACT
Categorical random variables have variances that are typically functions of the means. Therefore, the usual model assumptions of normality and constant variance are violated. This chapter discusses a logit regression model for the analysis of categorical data from cross-over designs and considers a logit model for the 2-treatment, 2-period, 2-sequence cross-over design with binary response. It argues that the frequencies within each sequence follow the multinomial distribution. The 2-treatment, 2-period, 2-sequence design is only a single special case of the broader set of cross-over designs. The number of association parameters for each sequence of the 2-treatment, 2-period, 2-sequence cross-over design having a binary response is one. Maximum likelihood estimates for the logit model parameter vector can be computed using a modified Newton-Raphson algorithm. J. J. Gart’s test has been extended from the binary response to the multi-level categorical response, but no simple test statistic exists for this more general cross-over design.
