The technique of homogeneity analysis (which is also known as multiple correspondence analysis) is applied to event history data obtained in the National Travel Survey of the Netherlands Central Bureau of Statistics. We introduce the theory of homogeneity analysis by using the idea of optimal quantification or transformation. Optimality is defined in terms of a ratio of quadratic forms, where both quadratic forms are components of the total variance after quantification. This defines a large class of optimal quantification techniques, with the size of the class depending on the number of independent sources of variation in the study design.