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Log‐linear Models for Polytomous Data
Author(s) -
Formann Anton K.
Publication year - 1981
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.4710230405
Subject(s) - polytomous rasch model , goodness of fit , statistics , mathematics , confidence interval , econometrics , score test , test (biology) , statistical hypothesis testing , item response theory , psychometrics , paleontology , biology
The present study discusses two variants of linear logistic models for polytomous variables for „unordered” and for „ordered” categories (polydimensional and one‐dimensional model). The ML‐estimation equations and the possibilities to test the validity of the model are given for both. A test for goodness‐of‐fit (external validity) and a test for equality of the parameter estimates for split data (interval validity) are suggested. In addition, statistical tests for the significance of individual parameters on the basis of the information matrix and likelihood ratio tests for one or more parameters are described. The presentation is completed by an empirical example from the area of audiology.