Page 36 - Contributed Paper Session (CPS) - Volume 3

CPS1941 Jang S.

A new model selection criterion for finite mixture
models
Jang Schiltz
University of Luxembourg, LSF, Luxembourg

Abstract
We present a generalization of Nagin's finite mixture model that allows non
parallel trajectories for different values of covariates and illustrate its use by
giving typical salary curves for the employees in the private sector in
Luxembourg between 1981 and 2006, as a function of their gender, as well as
of Luxembourg's gross domestic product (GDP). Afterwards, we propose a new
model selection criterion for finite mixture models which is computationally
easy and does not need a correction term for the number of parameters in the
model.

Keywords
Statistical Models; Developmental trajectories; Trajectory Modeling; Model
Selection

1. Introduction
Time series analysis is of the utmost importance for the research on various
subjects in economics, finance, sociology, psychology, criminology and
medicine and a host of statistical techniques have been developed to achieve
it. In the 1990s, the modelization of the evolution of an age or time based
phenomenon gave raise among other methods to latent growth curves
modeling (Muthen 1989) and the nonparametric mixture model (Nagin 1999).
The nonparametric mixed model developed by Nagin (1985) is specifically
designed to detect the presence of distinct subgroups among a set of
trajectories. Compared to subjective classification methods, the nonparametric
mixed model has the advantage of providing a formal framework for testing
the existence of distinct groups of trajectories. This method does not assume
a priori that there is necessarily more than one group in the population. Rather,
an adjustment index is used to determine the number of sub-optimal groups.
While the conceptual aim of the analysis is to identify clusters of individuals
with similar trajectories, the model's estimated parameters are not the result
of a cluster analysis but of maximum likelihood estimation (Nagin, 2005).
The remainder of this article is structured as follows. In section two, we
present the basic version of Nagin's Finite mixture model, as well as one of his
generalizations and we show two drawbacks of the model. In section three, we
present a generalization of the model that overcomes these drawbacks and

25 | I S I W S C 2 0 1 9