Classification problems in growth mixture modeling

Abstract

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] Growth mixture modeling can be used for two purposes: 1) to identify mixtures of normal sub-groups, and 2) to approximate oddly shaped distributions by a mixture of normal components. Often in applied research this methodology is applied to both of these situations indistinctly using the same fit statistics and likelihood ratio tests. This can lead to the over extraction of latent classes and the attribution of substantive meaning to these spurious classes. The goals of this study were: 1) to investigate the situations in which spurious classes emerge in finite mixture modeling; 2) to explore how separated two multivariate normal populations need to be before they are distinguishable; and 3) to examine the effects of time invariant covariates in the estimation of the number of latent classes. Four simulation studies were conducted. The first addresses the problem of spurious classes emerging as artifacts of the non-normality of the dependent variables. The second explores the effects of covariates in the estimation of the correct number of latent classes. The third addresses the issue of distinguishing between two classes that overlap. The fourth and last simulation fits one- through four-class solutions to a single non-normal population and compares results. Results show that spurious classes emerge in the data analysis when the population departs from normality even when the non-normality is only present in time invariant covariates, that two populations need to be separated by 2 standard deviations or more to be distinguishable, and that the cat's cradle can be extracted from a single population with skew of 1.6 and kurtosis of 2.