  We propose a multivariate probability distribution for categorical and
ordinal random variables. To this end, we use the Grassmann distribution in
conjunction with dummy encoding of categorical and ordinal variables. To
realize the co-occurrence probabilities of dummy variables required for
categorical and ordinal variables, we propose a parsimonious parameterization
for the Grassmann distribution that ensures the positivity of probability
distribution. As an application of the proposed distribution, we develop a
factor analysis for categorical and ordinal variables and show the validity of
the model using a real dataset.
