A latent variable model for a derived ordinal response accounting for sampling weights, missing values and covariates

We consider a latent class model especially tailored for an ordinal response derived by comparing two continuous variables. We propose a general method to estimate the model parameters with survey data when there are missing responses and survey weights. First, we estimate the model with the missing responses without covariates with a weighted likelihood function maximised through the Expectation-Maximization algorithm. In order to determine the suitable number of latent classes we rely on the Akaike Information Criterion. Second, by fixing the parameters of the measurement model we estimate the remaining parameters by adding the full set of covariates. We make predictions on the basis of the maximum a posteriori probability. In the application, we consider Japanese survey data collected at four waves covering 40 years with the aim to study changes on couples' breadwinning patterns.