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An Extended Threshold Model for Analyzing Ordered Categorical Data
Author(s) -
Quednau H. D.
Publication year - 1988
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710300204
Subject(s) - categorical variable , mathematics , relation (database) , statistics , maximum likelihood , position (finance) , regression analysis , econometrics , computer science , data mining , finance , economics
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.