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

Abstract

Growth mixture modeling is often used to identify unobserved heterogeneity in populations. Despite the usefulness of growth mixture modeling in practice, little is known about the performance of this data analysis technique in the presence of time-varying covariates. In the present simulation study, we examined the impacts of five design factors: the proportion of the total variance of the outcome explained by the time-varying covariates, the number of time points, the error structure, the sample size, and the mixing ratio. More precisely, we examined the impact of these factors on the accuracy of parameter and standard error estimates, as well as on the class enumeration accuracy. Our results showed that the consistent Akaike information criterion (CAIC), the sample-size-adjusted CAIC (SCAIC), the Bayesian information criterion (BIC), and the integrated completed likelihood criterion (ICL-BIC) proved to be highly reliable indicators of the true number of latent classes in the data, across design conditions, and that the sample-size-adjusted BIC (SBIC) also proved quite accurate, especially in larger samples. In contrast, the Akaike information criterion (AIC), the entropy, the normalized entropy criterion (NEC), and the classification likelihood criterion (CLC) proved to be unreliable indicators of the true number of latent classes in the data. Our results also showed that substantial biases in the parameter and standard error estimates tended to be associated with growth mixture models that included only four time points.

On the motivational nature of authentic leadership practices: a latent profile analysis based on self-determination theory

“…Significant tests suggest that the target solution can be retained. Simulation studies indicate that the CAIC, BIC, ABIC and BLRT are particularly effective, but that the AIC and LMR should not be used (Diallo et al ., 2016, 2017); these indicators are only reported to ensure a complete disclosure. The entropy will also be reported as an indicator of the quality of the classification of individuals into the extracted profiles, where values closer to 1 indicate better classification.…”

Types of union participators over time: Toward a person‐centered and dynamic model of participation

“…All analyses were conducted using MPlus Version 8.1 (Muthén & Muthén, ). We followed best practices to identify the best fitting model and number of union participator classes (Diallo, Morin, & Lu, , , ). We first examined a two‐class model and increased the number of classes until increases in model fit indicated more classes was no longer parsimonious, which is consistent with other LCA/LPA research (Bennett, Gabriel, Calderwood, Dahling, & Trougakos, ; Gabriel et al., ; Morin et al., ; Woo & Allen, ).…”

“…To identify the best fitting model, we examined five fit indices: loglikelihood (LL), Akaike information criterion (AIC), consistent AIC (C‐AIC; the BIC plus the number of free parameters), Bayesian information criterion (BIC), sample‐size‐adjusted BIC (SSA‐BIC), and the Bootstrap likelihood ratio test (BLRT; Diallo et al., , , ; Tofighi & Enders, ). Entropy—a measure of classification accuracy—provides useful information but should not be used for determining model selection (Lubke & Muthén, ) as it penalizes models with a larger number of classes and heavily penalizes LTA results.…”

“…Instead, best fitting models have smaller LL, AIC, C‐AIC, BIC, and SSA‐BIC values compared to other models and BLRT should be statistically significant. We focused primarily on the C‐AIC, BIC, SSA‐BIC, and BLRT indices for selecting the final model, as they are the most accurate indicators for class selection (Diallo et al., , , ).…”

Segmenting anti-Muslim sentiment in Australia: Insights for the diverse project of countering Islamophobia

“…In this study, we followed common practice, relying on the most widely used fit and test statistics: the Akaike's Information Criterion (AIC; Akaike, 1987), Bayesian Information Criterion (BIC, Schwarz, 1978), sample size adjusted BIC (SBIC; Sclove, 1987), Lo-Mendell-Rubin likelihood ratio test (LMR; Lo et al, 2001). Recent simulation studies have, however, indicated that the BIC, SBIC, and LRT are more effective for identifying the correct number of classes (Diallo et al, 2016a(Diallo et al, , 2016b(Diallo et al, , 2017Peugh and Fan, 2013). Therefore, we relied more heavily on these indices to determine the optimal number of classes in our final model.…”