On the null distribution of distance between two groups,using mixed continuous and categorical variables

The location model is a useful tool in parametric analysis of mixed continuous and categorical variables. In this model, the continuous variables are assumed to follow different multivariate normal distributions for each possible combination of categorical variable values. Using this model, a distance between two populations involving mixed variables can be defined. To date, however, no distributional results have been available, against which to assess the outcomes of practical applications of this distance. The null distribution of estimated distance is therefore considered in this paper, for a range of possible situations. No explicit analytical expressions are derived for this distribution, but easily implementable Monte Carlo schemes are described. These are then applied to previously cited examples.