Distributional Assumptions of Growth Mixture Models: Implications for Overextraction of Latent Trajectory Classes.

Abstract

Growth mixture models are often used to determine if subgroups exist within the population that follow qualitatively distinct developmental trajectories. However, statistical theory developed for finite normal mixture models suggests that latent trajectory classes can be estimated even in the absence of population heterogeneity if the distribution of the repeated measures is nonnormal. By drawing on this theory, this article demonstrates that multiple trajectory classes can be estimated and appear optimal for nonnormal data even when only 1 group exists in the population. Further, the within-class parameter estimates obtained from these models are largely uninterpretable. Significant predictive relationships may be obscured or spurious relationships identified. The implications of these results for applied research are highlighted, and future directions for quantitative developments are suggested.

Investigating population heterogeneity with factor mixture models.

“…Determining the number of classes is the subject of a stillgrowing body of research and has led to interesting discussions (Bauer & Curran, 2003a;Bauer & Curran, 2003b;Cudeck & Henly, 2003;B. O. Muthén, 2003;Rindskopf, 2003).…”

“…Condi-tional normality is relevant in the context of using test statistics such as the adjusted likelihood ratio statistic (aLRT) for model comparisons (see Step-by-Step Analysis of LSAY Data at a Single Time Point below), which assume within-class normality. Note that violations of conditional normality can have implications for the number of classes that are extracted (Bauer & Curran, 2003a). Conditional normality is also relevant in the context of missing data.…”

Conduct problems trajectories and psychosocial outcomes: a systematic review and meta-analysis

“…Though trajectories were comparable across studies, we acknowledge that the methods used to derive these trajectories differed, with some studies using two time points and others applying general growth mixture models. In addition, we acknowledge that growth mixture models have limitations, which include over-fitting the number of trajectories [48] which can lead to biased estimates of covariate effects (i.e., outcomes of trajectories) [7]. Furthermore, the measures used to construct these trajectories differed across studies (i.e., different versions of the SDQ or CBCL, or other teacher-reported measures) resulting in some degree of measurement inconsistency.…”

Nonnormality and divergence in posttreatment alcohol use: Reexamining the Project MATCH data "another way."

“…Shown in Table 4, the three-class models provided a good fit to the observed data in the u-and y-part models on the basis of BIC, the entropy statistic, and significant LRT. In both models, the estimation of a fourth class did not add substantial information to the three-class models, and the frequency of class membership for the fourth class was less than 5%; thus, to avoid overextraction (Bauer & Curran, 2003), a three-class model was retained for all remaining analyses.The u-part was specified to have random intercept and linear slope parameters, and the variance of the intercept was also estimated. For model identification the variance of the u-part slope was constrained to zero; this constraint is often needed in two-part modeling (K. Masyn, personal communication, July 11, 2006).…”