Local Solutions in the Estimation of Growth Mixture Models

Finite mixture models are well known to have poorly behaved likelihood functions featuring singularities and multiple optima. Growth mixture models may suffer from fewer of these problems, potentially benefiting from the structure imposed on the estimated class means and covariances by the specified...

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Bibliographic Details
Published in:Psychological methods 2006-03, Vol.11 (1), p.36-53
Main Authors: Hipp, John R, Bauer, Daniel J
Format: Article
Language:English
Subjects:
Adolescent
Alcohol Drinking - epidemiology
Alcoholic Intoxication - diagnosis
Alcoholic Intoxication - epidemiology
Analysis of Variance
Biological and medical sciences
Case Studies
Class Means
Computation
Computer Simulation
Computer Software
Female
Fundamental and applied biological sciences. Psychology
Health Surveys
Human
Humans
Likelihood Functions
Longitudinal Studies
Male
Maximum Likelihood
Maximum Likelihood Statistics
Models, Psychological
Models, Statistical
Monte Carlo Method
Monte Carlo Methods
Problem Solving
Psychology. Psychoanalysis. Psychiatry
Psychology. Psychophysiology
Psychometrics
Psychometrics. Statistics. Methodology
Spatial Ability
Statistical Estimation
Statistics. Mathematics
Structural Equation Models
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Summary:Finite mixture models are well known to have poorly behaved likelihood functions featuring singularities and multiple optima. Growth mixture models may suffer from fewer of these problems, potentially benefiting from the structure imposed on the estimated class means and covariances by the specified growth model. As demonstrated here, however, local solutions may still be problematic. Results from an empirical case study and a small Monte Carlo simulation show that failure to thoroughly consider the possible presence of local optima in the estimation of a growth mixture model can sometimes have serious consequences, possibly leading to adoption of an inferior solution that differs in substantively important ways from the actual maximum likelihood solution. Often, the defaults of current software need to be overridden to thoroughly evaluate the parameter space and obtain confidence that the maximum likelihood solution has in fact been obtained.
ISSN:1082-989X
1939-1463
DOI:10.1037/1082-989X.11.1.36