Categorical data occur in many fields of application like economics, sociology, medicine or education. Examples for categorical variables are sex, highest educational level, industry sector, legal form of a company, or medical treatment. As methods designed for metric data are not appropriate for these data, our focus is on statistical methods designed specifically for the analysis of categorical variables like logistic regression, latent class analysis or cluster analysis. Additionally we are interested in joint models for continuous and categorical response variables and investigate the measurement of a latent metric variable using different categorical scales.