Statistical Modelling 8 (2008), 199218
Model misspecification: finite mixture or homogeneous?
Thaddeus Tarpey
Department of Mathematics and Statistics,
Wright State University,
Dayton, Ohio
U.S.A.
eMail:
thaddeus.tarpey@wright.edu
Dong Yun
Department of Mathematics and Statistics,
Wright State University
U.S.A.
Eva Petkova
School of Medicine,
New York University
U.S.A.
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. 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.
Keywords:
EM algorithm; finite mixture models; placebo response; principal points;
skew normal distribution
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