Thierno M. O. Diallo

Impact of Misspecifications of the Latent Variance–Covariance and Residual Matrices on the Class Enumeration Accuracy of Growth Mixture Models

This series of simulation studies was designed to assess the impact of misspecifications of the latent variance–covariance matrix (i.e., ) and residual structure (i.e., ) on the accuracy of growth mixture models (GMMs) to identify the true number of latent classes present in the data. Study 1 relied on a homogenous (1-class) population model. Study 2 relied on a population model in which the latent variance–covariance matrix is constrained to be 0 Study 3 relied on a population model in which the latent variance–covariance matrix was specified as invariant across classes Finally, Study 4 relied on a more realistic specification of the latent variance–covariance matrix as different across classes In each of these studies, we assessed the class enumeration accuracy of GMMs as a function of different types of estimated model (6 models corresponding to the 3 types of population models used to simulate the data and involving the free estimation of the residual structure across latent classes or not) and 4 design conditions (within-class residual matrix, sample size, mixing ratio, class separation). Overall, our results show the advantage of relying on models involving the free estimation of the and matrices within all latent classes. However, based on the observation that inadmissible solutions occur more frequently in these models than in more parsimonious models, we propose a more comprehensive sequential strategy to the estimation of GMM.

The impact of total and partial inclusion or exclusion of active and inactive time invariant covariates in growth mixture models

This article evaluates the impact of partial or total covariate inclusion or exclusion on the class enumeration performance of growth mixture models (GMMs). Study 1 examines the effect of including an inactive covariate when the population model is specified without covariates. Study 2 examines the case in which the population model is specified with 2 covariates influencing only the class membership. Study 3 examines a population model including 2 covariates influencing the class membership and the growth factors. In all studies, we contrast the accuracy of various indicators to correctly identify the number of latent classes as a function of different design conditions (sample size, mixing ratio, invariance or noninvariance of the variance-covariance matrix, class separation, and correlations between the covariates in Studies 2 and 3) and covariate specification (exclusion, partial or total inclusion as influencing class membership, partial or total inclusion as influencing class membership, and the growth factors in a class-invariant or class-varying manner). The accuracy of the indicators shows important variation across studies, indicators, design conditions, and specification of the covariates effects. However, the results suggest that the GMM class enumeration process should be conducted without covariates, and should rely mostly on the Bayesian information criterion (BIC) and consistent Akaike information criterion (CAIC) as the most reliable indicators under conditions of high class separation (as indicated by higher entropy), versus the sample size adjusted BIC or CAIC (SBIC, SCAIC) and bootstrapped likelihood ratio test (BLRT) under conditions of low class separation (indicated by lower entropy).

Power of Latent Growth Curve Models to Detect Piecewise Linear Trajectories

Latent curve models (LCMs) have been used extensively to analyze longitudinal data. However, little is known about the power of LCMs to detect nonlinear trends when they are present in the data. This simulation study was designed to investigate the Type I error rates, rates of nonconvergence, and the power of LCMs to detect piecewise linear growth and mean differences in the slopes of the 2 joined longitudinal processes represented by the piecewise model. The impact of 7 design factors was examined: number of time points, growth magnitude (slope mean), interindividual variability, sample size, position of the turning point, and the correlation of the intercept and the second slope as well between the 2 slopes. The results show that previous results based on linear LCMs cannot be fully generalized to a nonlinear model defined by 2 linear slopes. Interestingly, design factors specific to the piecewise context (position of the turning point and correlation between the 2 growth factors) had some effects on the results, but these effects remained minimal and much lower than the effects of other design factors. Similarly, observed rates of inadmissible solutions are comparable to those previously reported for linear LCMs. The major finding of this study is that a moderate sample size (N = 200) is needed to detect piecewise linear trajectories, but that much larger samples (N = 1,500) are required to achieve adequate statistical power to detect slope mean difference of small magnitude.

An internet-supported school physical activity intervention in low socioeconomic status communities: results from the Activity and Motivation in Physical Education (AMPED) cluster randomised controlled trial

Objective Quality physical education (PE) is the cornerstone of comprehensive school physical activity (PA) promotion programmes. We tested the efficacy of a teacher professional learning intervention, delivered partially via the internet, designed to maximise opportunities for students to be active during PE lessons and enhance adolescents’ motivation towards PE and PA. Methods A two-arm cluster randomised controlled trial with teachers and Grade 8 students from secondary schools in low socioeconomic areas of Western Sydney, Australia. The Activity and Motivation in Physical Education (AMPED) intervention for secondary school PE teachers included workshops, online learning, implementation tasks and mentoring sessions. The primary outcome was the proportion of PE lesson time that students spent in moderate-to-vigorous physical activity (MVPA), measured by accelerometers at baseline, postintervention (7–8 months after baseline) and maintenance (14–15 months). Secondary outcomes included observed PE teachers’ behaviour during lessons, students’ leisure-time PA and students’ motivation. Results Students (n=1421) from 14 schools completed baseline assessments and were included in linear mixed model analyses. The intervention had positive effects on students’ MVPA during lessons. At postintervention, the adjusted mean difference in the proportion of lesson time spent in MVPA was 5.58% (p<0.001, approximately 4 min/lesson). During the maintenance phase, this effect was 2.64% (p<0.001, approximately 2 min/lesson). The intervention had positive effects on teachers’ behaviour, but did not impact students’ motivation. Conclusions AMPED produced modest improvements in MVPA and compares favourably with previous interventions delivered exclusively face-to-face. Online teacher training could help facilitate widespread dissemination of professional learning interventions. Trial registration number ACTRN12614000184673.

On the Application of the Three-Step Approach to Growth Mixture Models

This series of simulation studies evaluate, in the context of applied research settings, the impact of the parameterization of the covariance structure of the growth mixture model (GMM) on the regression coefficient and standard error estimates in the 3-step method. The results show that the 1-step approach performs better than the 3-step method across the simulation studies. However, the performance of the 3-step method depends slightly or importantly on the parameterization of the GGM from the first step, on the inclusion or not of the predictor at the first step of the analysis, on the population model, and on the type (i.e., logit vs. linear) and size of the regression coefficient estimates.

Consequences of Misspecifying Across-Cluster Time-Specific Residuals in Multilevel Latent Growth Curve Models

This Monte Carlo study evaluates, in the context of multilevel latent growth curve models, the consequences of under- and overspecifying across-cluster time-specific residuals (i.e., ) on the estimation of the fixed effects, their corresponding standard errors, the variances and covariances of the random effects, Type I error rates, and the statistical power of detecting fixed effects. The results show that underspecifying with all elements of fixed at zero results in a large underestimation of the between- and within-level random effect and standard errors of fixed effect estimates, which, in turn, leads to serious bias in significant testing. Underspecifying with diagonal elements of constrained to equality, or overspecifying with diagonal elements of constrained to equality or freely estimated and residual covariances fixed at zero also leads to bias in the estimation of the between- and within-level random effects. Implications of the compensatory relationship occurring at the covariance level are discussed.