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

Does Everyone’s Motivational Beliefs about Physical Science Decline in Secondary School?: Heterogeneity of Adolescents’ Achievement Motivation Trajectories in Physics and Chemistry

“…As Muthén (2001) suggests, the relative strength of LMR and BIC is not sufficiently well-understood though several recent studies do caution that LMR does not always function as a reliable indicator for deciding optimal solution (Diallo, Morin, & Lu, 2016a; 2016b). Accordingly, the decision on the number of classes should not be based solely on statistical measures but also on theoretical justification and interpretability.…”

Parents’ adjustment following the death of their child: Resilience is multidimensional and differs across outcomes examined

“…Besides empirically demonstrating these group differences, our analyses also show that individuals can take different paths towards resilience or recovery. The approach of allowing for the classes to differ in how much they vary between one another is especially critical due to a recent simulation study by Diallo and colleagues (2016) who documented that relaxing the assumptions of homogeneity of variance does in fact improve model fit and leads to better ability to recover distinct sub-groups and protects against over-extraction of distinct sub-groups. More specifically, Diallo and colleagues (2016) found that assuming homogeneity of variance led to over-extraction of classes; data were simulated for one-class underlying the sample, and by applying the aforementioned assumption of homogeneity of variance lead to 4 classes being found in the data.…”

“…The approach of allowing for the classes to differ in how much they vary between one another is especially critical due to a recent simulation study by Diallo and colleagues (2016) who documented that relaxing the assumptions of homogeneity of variance does in fact improve model fit and leads to better ability to recover distinct sub-groups and protects against over-extraction of distinct sub-groups. More specifically, Diallo and colleagues (2016) found that assuming homogeneity of variance led to over-extraction of classes; data were simulated for one-class underlying the sample, and by applying the aforementioned assumption of homogeneity of variance lead to 4 classes being found in the data. Using empirical data, Infurna and Grimm (in press) further demonstrated the importance of the homogeneity of variance of assumption by showing that relaxing this assumption led to improved model fit and better identification of sub-groups in the data.…”

“…However, in our study, we have a smaller sample of individuals who experienced child loss ( n = 461) and it is known that when researchers are limited by sample size, increasing the number of observations increases the statistical power to detect between-person differences in change (see Hertzog et al, 2008; Rast & Hofer, 2014). We acknowledge that these simulation and empirical studies focused on linear and quadratic patterns of change, but these principles of reliability to detect between-person differences in change increasing with observations transfers to other forms of longitudinal model of change, such as multi-phase models and GMM that we implement in this study (see Diallo et al, 2016). The average number of observations were considered in this study was 7.81 for life satisfaction ( SD = 2.36, range 1 – 11), 7.45 for positive affect ( SD = 2.30, range 2 – 11), 7.36 for negative affect ( SD = 2.41, range 2 – 11), 7.20 for general health ( SD = 2.45, range 1 – 11), and 7.33 for physical functioning ( SD = 2.31, range 1 – 11), respectively.…”

Performance of growth mixture models in the presence of time-varying covariates

“…GMMs with TVCs are very complex models and, as such, might benefit from the inclusion of some degree of parsimony, especially in situations in which the sample size and/or number of repeated measures are suboptimal. Referring to the estimation of GMMs more generally, Diallo, Morin, and Lu (2016) suggested that researchers should always start the class enumeration process using a theoretically optimal model, and then slowly incorporate parsimony into the model (i.e., by constraining some parameters to equality across classes or time points) when they encounter convergence problems or inadmissible solutions. Similarly, in the context of GMMs with TICs, Diallo, Morin, and Lu (in press) noted that it might sometimes be preferable to conduct the class enumeration process while excluding covariates, and to include these only once the optimal number of classes has been selected.…”