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Latent Structure Models with Direct Effects between Indicators

A basic assumption of latent structure models is that of local independence: given the score on the latent variable, the scores on the manifest variables are independent of each other. This basic assumption is violated when test-retest effects, response consistency effects, correlated response errors, and so forth are present. However, it is possible to reformulate the latent class model in such a way that these direct relations between the indicators (manifest variables) can be accounted for. The reformulation proposed here, takes place within the framework of log-linear modeling.