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Model misspecification

finite mixture or homogeneous?

Thaddeus Tarpey is at Department of Mathematics and Statistics, Wright State University US

Dong Yun

Dong Yun is at Department of Mathematics and Statistics, Wright State University US

Eva Petkova

Eva Petkova is at School of Medicine, New York University, US

A common problem in statistical modelling is to distinguish between finite mixture distribution and a homogeneous non-mixture distribution. Finite mixture models are widely used in practice and often mixtures of normal densities are indistinguishable from homogenous non-normal densities. This paper illustrates what happens when the EM algorithm for normal mixtures is applied to a distribution that is a homogeneous non-mixture distribution. In particular, a population-based EM algorithm for finite mixtures is introduced and applied directly to density functions instead of sample data. This algorithm is used to find finite mixture approximations to common homogeneous distributions. An example regarding the nature of a placebo response in drug treated depressed subjects is used to illustrate ideas.

Key Words: EM algorithm • finite mixture models • placebo response • principal points • skew normal distribution

Statistical Modelling, Vol. 8, No. 2, 199-218 (2008)
DOI: 10.1177/1471082X0800800204


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