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Fuzzy clusterwise quasi-likelihood generalized linear models

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Abstract

The quasi-likelihood method has emerged as a useful approach to the parameter estimation of generalized linear models (GLM) in circumstances where there is insufficient distributional information to construct a likelihood function. Despite its flexibility, the quasi-likelihood approach to GLM is currently designed for an aggregate-sample analysis based on the assumption that the entire sample of observations is taken from a single homogenous population. Thus, this approach may not be suitable when heterogeneous subgroups exist in the population, which involve qualitatively distinct effects of covariates on the response variable. In this paper, the quasi-likelihood GLM approach is generalized to a fuzzy clustering framework which explicitly accounts for such cluster-level heterogeneity. A simple iterative estimation algorithm is presented to optimize the regularized fuzzy clustering criterion of the proposed method. The performance of the proposed method in recovering parameters is investigated based on a Monte Carlo analysis involving synthetic data. Finally, the empirical usefulness of the proposed method is illustrated through an application to actual data on the coupon usage behaviour of a sample of consumers.

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Authors and Affiliations

  1. Department of Psychology, McGill University, 1205 Dr. Penfield Avenue, Montreal, QC, H3A 1B1, Canada

    Heungsun Hwang

  2. Department of Marketing, HEC Montreal, 3000 chemin de la Côte-Sainte-Catherine, Montreal, QC, H3T 2A7, Canada

    Marc A. Tomiuk

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  1. Heungsun Hwang
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  2. Marc A. Tomiuk
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Correspondence to Heungsun Hwang.

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Hwang, H., Tomiuk, M.A. Fuzzy clusterwise quasi-likelihood generalized linear models. Adv Data Anal Classif 4, 255–270 (2010). https://doi.org/10.1007/s11634-010-0069-0

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  • DOI: https://doi.org/10.1007/s11634-010-0069-0

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