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

    Gollini, Isabella and Murphy, T.B. (2014) Mixture of latent trait analyzers for model-based clustering of categorical data. Statistics and Computing 24 (4), pp. 569-588. ISSN 0960-3174.

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    Abstract

    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 correspondence 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 variable; the discrete latent class accommodates group structure and the continuous latent trait accommodates dependence within these groups. Fitting the mixture of latent trait analyzers model is potentially difficult because the likelihood function involves an integral that cannot be evaluated analytically. 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 National Long Term Care Survey (NLTCS) and voting in the U.S. Congress. The model is shown to yield intuitive clustering results and it gives a much better fit than either latent class analysis or latent trait analysis alone.

    Metadata

    Item Type: Article
    Additional Information: The final publication is available at Springer via http://dx.doi.org/10.​1007/​s11222-013-9389-1
    Keyword(s) / Subject(s): Model-based clustering, Mixture models, Latent variables, Categorical data, Variational EM Algorithm
    School: Birkbeck Schools and Departments > School of Business, Economics & Informatics > Economics, Mathematics and Statistics
    Depositing User: Isabella Gollini
    Date Deposited: 04 Nov 2015 09:50
    Last Modified: 04 Nov 2015 09:50
    URI: http://eprints.bbk.ac.uk/id/eprint/13287

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