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Abstract:
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Many large-scale surveys collect discrete and continuous variables. Often the investigators are interested in both kinds of variables as well as domain means defined as the mean of the continuous variable for each level of the categorical variable. Our main objective is to introduce a joint mixed model including Gaussian variables and categorical variables, obtained through a conditional model specification. We apply the method to data from the Conservation Effects Assessment project, a survey indented to measure several types of erosion. Because we provide a valid joint distribution, we can calculate empirical Bayes predictors. We find that our joint mixed model provides smaller mean squared errors for all small area parameters compared with univariate model estimators and direct estimators, especially for the domain means. To reduce the computational complexity, we introduce a novel composite likelihood EM algorithm. Additionally, we develop a simple edge selection criterion based on AIC that exploits the model specification through conditional distributions.
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