On growth curves and mixture models

Abstract

The multilevel model of change and the latent growth model are flexible means to describe all sorts of population heterogeneity with respect to growth and development, including the presence of sub-populations. The growth mixture model is a natural extension of these models. It comes at hand when information about sub-populations is missing and researchers nevertheless want to retrieve developmental trajectories from sub-populations. We argue that researchers have to make rather strong assumptions about the sub-populations or latent trajectory classes in order to retrieve existing population differences. A simulated example is discussed, showing that a sample of repeated measures drawn from two sub-populations easily leads to the mistaken inference of three sub-populations, when assumptions are not met. The merits of methodological advises on this issue are discussed. It is concluded that growth mixture models should be used with understanding, and offer no free way to growth patterns in unknown sub-populations.

Observations on the Use of Growth Mixture Models in Psychological Research

“…Although the mixture closely approximates the kernel estimator, the latent class structure does not reflect the actual organization of individuals within the population: In this case, the data were generated from a unitary (but non-normal) distribution, not a mixture of normal distributions. Of course, distortions of the latent class structure would also arise if the data had been generated from a mixture of non-normal distributions and then fit by a mixture of normals (Hoeksma & Kelderman, 2006;Tofighi & Enders, 2007). Given the preponderance of non-normal data in psychological research (Micceri, 1989), this problem is particularly vexing.…”

“…The total citation counts for the three papers were, respectively, 200, 105, and 109 citations, and the overall trend shown in Figure 1 points to increasing use of GMMs (Web of Science, Science Citation Index, retrieved 4/8/07). 1 The cautions voiced by myself and others concerning the application and interpretation of these models (e.g., Bauer & Curran, 2003a, 2003b, 2004Hoeksma & Kelderman, 2006;Raudenbush, 2005;Sampson & Laub, 2005; seem to have gone largely unheard. The purpose of this article is to try to convey, more convincingly, my concerns about the use of GMMs in psychological research.…”

A Note on the Use of Mixture Models for Individual Prediction

“…Also included in this latter category is that the distributions of the latent and observed variables are specified correctly (e.g., normal, binomial, Poisson). Within mixture models, both structural and distributional misspecification can compromise class enumeration procedures and lead to inconsistent within-class estimates even when the correct number of classes is selected (Bauer and Curran, 2003; 2004; Hoeksma and Kelderman, 2006; Morin, Maiano, Nagengast, Mars, Morizot, and Janosz, 2011; Van Horn et al, 2012). …”

Analytical methods and issues for symptom cluster research in oncology

“…Growth mixture modeling is a variation of growth modeling where the data are expected to come from unobserved sub-populations and group memberships are unknown [29]. Growth curve analysis in oncology has been used to identify a group of symptoms changing over time in a similar pattern [11 && ] and to examine the patterns of fatigue over time [30].…”