Latent class CUB models

Authors:
Leonardo Grilli;Maria Iannario;Domenico Piccolo;Carla Rampichini
Affiliations:
DiSIA, Department of Statistics, Informatics, Applications, "G. Parenti" University of Florence, Florence, Italy;Department TEOMESUS, University of Naples Federico II, Naples, Italy;Department TEOMESUS, University of Naples Federico II, Naples, Italy;DiSIA, Department of Statistics, Informatics, Applications, "G. Parenti" University of Florence, Florence, Italy
Venue:
Advances in Data Analysis and Classification
Year:
2014

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Abstract

The paper proposes a latent class version of Combination of Uniform and (shifted) Binomial random variables ( CUB ) models for ordinal data to account for unobserved heterogeneity. The extension, called LC-CUB , is useful when the heterogeneity is originated by clusters of respondents not identified by covariates: this may generate a multimodal response distribution, which cannot be adequately described by a standard CUB model. The LC-CUB model is a finite mixture of CUB models yielding a multimodal theoretical distribution. Model identification is achieved by constraining the uncertainty parameters to be constant across latent classes. A simulation experiment shows the performance of the maximum likelihood estimator, whereas the usefulness of the approach is illustrated by means of a case study on political self-placement measured on an ordinal scale.