Latent class analysis (LCA; Lazarsfeld & Henry, 1968; Rost, 2003) can be understood as an alternative explanatory approach to item response analyses. Whereas the Rasch model assumes a distribution of a quantitative person characteristic on a continuous latent dimension, LCA postulates that persons differ from each other with regard to their response pattern and, according to their pat tern, belong to different latent classes. The classes are called latent because they are not observable, but constructed from the test data, just as the latent traits of the Rasch model.
The aim of LCA is the identification of groups of subjects who show different response patterns. Latent class models cannot be characterized by their ICCs because there is no latent dimension that the response probabilities could depend on. However, the response probabilities are specific for and constant within latent classes so that the meaning of a latent class is well represented by its item profile (see Figure 18.2). These profiles show the class-specific response probabilities. Because response probabilities are constant among the subjects within each class, the model parameters are simply defined as conditional response probabilities, given that person v belongs to class c.
Equation (3) defines the response probability p(X^ = 1) of a subject v that belongs to class c (6y = c) to be a constant parameter 7tic. There is another type of parameter in LCA that represents the unconditional response probabilities, n. These parameters define the subject's probability to belong to class c and can be interpreted as class size parameters.
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