Linear Logistic Latent Class Analysis

TLDR: In this article, the linear logistic extension of latent class analysis is described and the basic equations of the model state the decomposition of the log-odds of the item latent probabilities and of the class sizes into weighted sums of basic parameters representing the effects of the predictor variables.

Abstract: In the present paper the linear logistic extension of latent class analysis is described. Thereby it is assumed that the item latent probabilities as well as the class sizes can be attributed to some explanatory variables. The basic equations of the model state the decomposition of the log-odds of the item latent probabilities and of the class sizes into weighted sums of basic parameters representing the effects of the predictor variables. Further, the maximum likelihood equations for these effect parameters and statistical tests for goodness-of-fit are given. Finally, an example illustrates the practical application of the model and the interpretation of the model parameters.