Observations on the Use of Growth Mixture Models in Psychological Research

Abstract

Psychologists are applying growth mixture models at an increasing rate. This article argues that most of these applications are unlikely to reproduce the underlying taxonic structure of the population. At a more fundamental level, in many cases there is probably no taxonic structure to be found. Latent growth classes then categorically approximate the true continuum of individual differences in change. This approximation, although in some cases potentially useful, can also be problematic. The utility of growth mixture models for psychological science thus remains in doubt. Some ways in which these models might be more profitably used are suggested.

ACKNOWLEDGMENTS

This research was supported by the National Science Foundation grant SES-0716555. I thank Patrick Curran, Robert MacCallum, and Sonya Sterba for helpful comments on an earlier draft of this article. I also thank Kenneth Bollen and Patrick Curran for their invaluable advice and guidance during and after my post-doctoral training. Much of the research upon which this article was based would not have been possible without their support and active collaboration.

Notes

¹In comparison, two foundational papers on latent curve modeling, Meredith & Tisak (1990) and McArdle & Epstein (1987), were cited 171 and 119 times, respectively, between 1999 and 2006. A key paper describing how longitudinal data could be analyzed by way of hierarchical linear models (mutlilevel models) published by Bryk & Raudenbush (1987) was cited 283 times over the same period.

²The standard errors of the ML estimates can be biased when the data are not multivariate normal, but robust standard errors can be computed via the method of Satorra & Bentler (1994).

³In contrast to the LCM, this conditional formulation is standard for multilevel growth models.

⁴ For identification, one of the classes is declared as the reference class and the intercept (α _{c k} ) and slopes (γ _{c k} ) of the multinomial regression for this class are set to zero. For example, if the last class were the reference class, then α _{c K} ≡0 and γ _{c K} ≡0. For interpretation, the slope estimates are typically exponentiated to provide odds ratios indicating the increased odds of being in class k relative to the reference class for each unit change in x.

⁵ Across 500 simulated data sets, the two-class GMM was favored over the one-class GMM by the BIC 100% of the time.

⁶ To confirm that this trend was not due simply to the loss of information associated with missing data, the same patterns of missingness were produced via a completely random process. With the MAR assumption in tact, the two-class model was preferred in 94% and 91.2% of the replications given average and extreme amounts of missing data, respectively. Thus, it is nature and not just the extent of missing data that affects the estimated latent class structure.

⁷ Some studies have found that a sample-size adjustment to the BIC proposed by Sclove (1987) improves selection of the number of classes for a GMM (Tofighi & Enders, 2007; see also Lubke & Neale, 2006), whereas others have shown superior performance for the unadjusted BIC (Nylund, Aparouhov, & Muthén, 2007). In the present simulation, the sample-size adjusted BIC was more likely to select too many classes than the BIC, and hence only the more conservative results for the BIC are reported.

⁸ A case can sometimes be made for types even when behaviors are multidetermined, for instance by arguing that only certain developmental pathways represent coherent patterns of adaptation (or maladaptation, as the case may be) or that threshold effects trigger developmental bifurcations.