| Abstract: | This paper presents an extended threshold model for analyzing ordered categorical data. The model admits interactions between the position of the thresholds and the levels of the effective factors. These interactions are described according to the approach of Milliken and Graybill (1970). Especially important for practical application is the special assumption that there is a linear relation between interactions and thresholds, and that the slopes of the concerning regression lines may be different for samples. This means that the latent variables are distributed according to the same type of distributions, but may have different expectations and variances. Underlying this submodel, the estimation of parameters and the testing of hypotheses according to the maximum likelihood method is described. The procedure is illustrated by a numerical example, and an outline is given about a cluster analysis using model parameters. |
