Understanding the Performance of Random Intercept Latent Transition Analysis Under Varied Conditions and Competing Models

• In Event: Interrogating Mixture Models in Pursuit of True Population Heterogeneity

Abstract

Recently, random intercept latent transition analysis (RI-LTA; Muthén & Asparouhov, 2020) has emerged as a possible extension and improvement to the latent transition analysis (LTA) model. RI-LTA differs from LTA in that it uses a random effect to partition between subjects' variation through a random intercept latent variable, resulting in a more accurate estimate of within-subject variation. Muthén & Asparouhov, (2020) claim that this leads to more precise estimates of the transition probabilities, the parameter of interest in LTA. Since transition probability results in the parameters that describe changes, it is important to better understand the utility of RI-LTA in practice.

Initial simulation studies of the RI-LTA model conducted in the seminal paper support the benefit of the model, but the number of conditions in those initial simulations was limited. The Muthén and Asparouhov (2020) paper provided support for models that included 2 and 3 timepoints, varied sample size, a single factor loading on the random intercept (RI) factor of 2 logits (i.e., probability of .881), and considered one set of transition probabilities (i.e., a probability of staying in class 1 at time two of .622 and the probability of staying in class 2 at time 2 of .500).

When loadings on the RI factor are zero, the addition of the RI on the LTA model is not necessary (Muthén & Asparouhov, 2020), which was supported by recent studies (Carter et al, 2021). For example, Nylund-Gibson et al. (2022) found in their model that fit statistics did not fully support the RI-LTA model when compared to the more traditional LTA; however, there was only one significant loading on the RI factor. Carter and colleagues (2022) provided additional evidence of this finding with a simulation study that supported the use of RI-LTA in all conditions, except when loadings on the RI factor were less than .40. In this simulation, all other conditions tested supported the use of RI-LTA, including varied loading size (i.e., from 0 to 2.5 logits for most conditions), varied sample size (N = 500 - 4000), and varied transition probability of staying in class 1 at time two from .200 to .800.

The current study
In this paper, we use Monte Carlo simulation studies to extend the previous work in two important areas, (a) expand and vary conditions that reflect real-world scenarios in applied research and (b) test RI-LTA against theoretical competing models (e.g., see Imai, 2011; Maydeu-Olivares, 2006; Mueller & Hancock, 2008). First, we will simulate data and test the RI-LTA model across several conditions including an increased number of classes (i.e., 3 and 4 classes) and varied loadings across RI items in addition to varied transition probabilities, sample sizes, and time points. Competing models will include the RI-LTA model and the local item dependence model. Initial results of the simulation show that RI-LTA is accurate across all conditions when loadings on the RI are .4 and higher. Also, RI-LTA exhibited superior parameter recovery and fit when compared to the local item dependence (LID) model.

Authors

• Delwin Carter, University of California - Santa Barbara
  Presenting Author

• Karen L. Nylund-Gibson, University of California - Santa Barbara
  Presenting Author