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The latent class analysis of polychotomous data
Author(s) -
Formann Anton K.
Publication year - 1978
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.197800016
Subject(s) - latent class model , mathematics , generalization , uniqueness , class (philosophy) , likelihood function , interpretation (philosophy) , transformation (genetics) , latent variable , statistics , matrix (chemical analysis) , econometrics , maximum likelihood , computer science , artificial intelligence , mathematical analysis , chemistry , materials science , composite material , gene , programming language , biochemistry
The present paper deals with the polychotomous generalization of Lazarsfeld's latent class analysis. First of alla short description of the model is given. To avoid the well‐known problem of uninterpretable latent probabilities, a logistic transformation of the original parameters is proposed. In the following, the estimation equations for the auxiliary parameters are derived according to the maximum likelihood principle. The uniqueness of the solution is proven by investigating the matrix of second order partial derivatives of the log‐likelihood function. Furthermore, statistical tests for the goodness of fit are described and the practical application and interpretation of the results are discussed. The formal presentation ends with an empirical example.