title: Model Misspecification: Finite Mixture or Homogeneous?
abstract: 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. The population-based EM 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.
authors.affiliation: Thaddeus Tarpey is Professor and Dong Yun is a Graduate Research Assistant in the Department of Mathematics and Statistics, Wright State University, Dayton, Ohio. Eva Petkova is Associate Professor, Child Study Center, School of Medicine, New York University, New York, NY 10016-6023.
authors.forename: Thaddeus
authors.initials: T
authors.lastname: Tarpey
authors.forename: Dong
authors.initials: D
authors.lastname: Yun
authors.forename: Eva
authors.initials: E
authors.lastname: Petkova