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Mixture of latent trait analyzers for model-based clustering of categorical data


Isabella Gollini, Brendan Murphy

Publication Type: 
Refereed Original Article
Model-based clustering methods for continuous data are well established and commonly used in a wide range of applications. However, model-based clustering methods for categorical data are less standard. Latent class analysis is a commonly used method for model-based clustering of binary data and/or categorical data, but due to an assumed local independence structure there may not be a correspon- dence between the estimated latent classes and groups in the population of interest. The mixture of latent trait analyzers model extends latent class analysis by assuming a model for the categorical response variables that depends on both a categorical latent class and a continuous latent trait vari- able; the discrete latent class accommodates group structure and the continuous latent trait accommodates dependence within these groups. Fitting the mixture of latent trait ana- lyzers model is potentially difficult because the likelihood function involves an integral that cannot be evaluated ana- lytically. We develop a variational approach for fitting the mixture of latent trait models and this provides an efficient model fitting strategy. The mixture of latent trait analyzers model is demonstrated on the analysis of data from the Na- tional Long Term Care Survey (NLTCS) and voting in the U.S. Congress. The model is shown to yield intuitive clus-tering results and it gives a much better fit than either latent class analysis or latent trait analysis alone.
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Statistics and Computing
National University of Ireland, Dublin (UCD)
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