General Growth Mixture Analysis of Adolescents' Developmental Trajectories of Anxiety: The Impact of Untested Invariance Assumptions on Substantive Interpretations

Abstract

Substantively, this study investigates potential heterogeneity in the developmental trajectories of anxiety in adolescence. Methodologically, this study demonstrates the usefulness of general growth mixture analysis (GGMA) in addressing these issues and illustrates the impact of untested invariance assumptions on substantive interpretations. This study relied on data from the Montreal Adolescent Depression Development Project (MADDP), a 4-year follow-up of more than 1,000 adolescents who completed the Beck Anxiety Inventory each year. GGMA models relying on different invariance assumptions were empirically compared. Each of these models converged on a 5-class solution, but yielded different substantive results. The model with class-varying variance–covariance matrices was retained as providing a better fit to the data. These results showed that although elevated levels of anxiety might fluctuate over time, they clearly do not represent a transient phenomenon. This model was then validated in relation to multiple predictors (mostly related to school violence) and outcomes (grade-point average, school dropout, depression, loneliness, and drug-related problems).

Keywords:

• adolescence
• anxiety
• growth mixture analysis
• invariance
• latent class growth analysis

Notes

Alexandre J. S. Morin and Christophe Maïano contributed equally to this article and their order was determined at random. Both should be considered first authors.

¹This study relies on data collected in Quebec (Canada), where children start school around the age of 6 and usually remain in the same elementary school until Grade 6, after which they experience the secondary school transition (close to the age of 12), where they remain for 5 years (Grades 7–11).

²Models were estimated with manifest time-specific indicators, as is common in GGMA. Still, longitudinal models based on manifest indicators could present problems, as they rely on the (often-untested) assumption of strict longitudinal measurement invariance and might confound unstable reliability with stability or instability of the construct (Marsh, Muthén, et al., 2009; Meredith, 1993). Preliminary analyses confirmed that this assumption was reasonably met in this study.

³When participants differ in age, relying on uniform time codes versus individual-specific codes might result in estimation bias (Metha & West, 2000). In this study, this limitation is partly offset because all participants are quite close in age and of the same grade level. Moreover, uniform time coding could still be appropriate when (Metha & West, 2000) (a) the regression of the intercept of the LCM on participants' age at Time 1 is equal to the slope factor, and (b) the regression of the slope on age at Time 1 is equal to zero. Both conditions were reasonably met in this study.

⁴Classical LRTs cannot be used to compare GGMA models with differing numbers of classes. However, they can be used to compare models based on the same variables and number of latent classes, differing on the pattern of free versus constrained parameters (e.g., Petras & Masyn, 2010). LRTs are computed as minus two times the difference in the log likelihood of the nested models and are interpreted as chi-square with degrees of freedom equal to the difference in free parameters between both models. As this study relied on MLR, the LRT needs to be divided by its scaling correction composite, cd, where (a) cd = (p0 * co – p1 * c1)/(p0 – p1); (b) p0 and p1 are the number of free parameters in the nested and comparison models; and (c) c0 and c1 are the scaling correction factors for the nested and comparison models (L. K. Muthén & Muthén, 2008; Satorra & Bentler, 1999).

*p ≤ .05.

**p ≤ .01.

⁵To verify that the clustering of students within schools did not influence the results, conditional models were also estimated with four dummy variables representing the five schools added to the predictors. These predictors were nonsignificant and their presence did not modify the results.

*p ≤ .05.

**p ≤ .01.

*p ≤ .05.

**p ≤ .01.