Random Intercepts Latent Transition Analysis: Illustration Using the Social Emotional Health Survey

• In Event: The Utility of Mixture Modeling to Understanding Heterogeneous Effects in Educational Studies.

Abstract

Latent Transition Analysis (LTA) is an increasingly useful modeling technique within the mixture modeling family that allows researchers to model group membership and changes among them over time. LTA is widely used in educational research where substantive findings can aid schools, counselors, and practitioners make comprehensive decisions about who may or may not receive interventions. Accordingly, findings should be as accurate as possible to ensure that any decisions are fair and unbiased. Muthén and Asparouhov (2020) have proposed a Random Intercepts (RI-LTA) approach that shows promise in providing more accurate estimates of the transition probabilities.

The key parameters of interest in LTA are the transition probabilities. They describe the probability of a given participant moving from one state to another state over time (VandenBos, 2013) thus, it is of interest to ensure these parameters are estimated accurately. Muthén and Asparouhov (2020) posit that the regular LTA model is vulnerable to overestimation of transition probabilities, especially those who stay within a given class.

RI-LTA has been proposed as a better approach to LTA because it allows researchers to decompose and partition the across subject variance by estimating an overall general factor or factors on the indicators of the categorical latent variable. Thus, the aim is to isolate the between-subject variation with random intercepts, partitioning the within-subject variation to explain the relationships (transition probabilities) between the categorical latent class variables (Muthén & Asparouhov, 2020). Previous studies have shown support for this type of modeling (see Kenny & Zautra, 1995 and Hamaker et al., 2015). Further, in all the simulation examples in Muthén and Asparouhov (2020), the RI-LTA model exhibited superior fit over the traditional LTA. The simulations show great promise and are important in establishing the RI-lTA model as useful, though they do have limitations.

One important topic we will address is if there are conditions when the RI-LTA and LTA model fit equally well, do not impact transition probabilities, and/or if there is signal for the use of RI-LTA. We will generate data with LTA and RI-LTA population models and explore how changing the values of the transition matrices can help us understand when and how the RI-LTA model is useful, and when the LTA model provides overestimates of the transition probabilities.

We also compare the use of the LTA and RI-LTA model in an applied example using 12 sub-scales from the Social Emotional Health Survey (SEHS, Furlong et al., 2014) measured as covitality. Profile enumeration of N = 683 students from Southern California area high schools across two years (10th and 11th grade) resulted in a 3-profile solution for both groups: low covitality (19% and 12.4%), moderate covitality (46.4% and 45%), and high covitality (34.6% and 42.6%) respectively. LTA results indicated invariance of the profiles for each group. The RI-LTA model exhibited superior fit to the LTA model across the BIC, ABIC, AIC, and LL values. Results of the simulation study, a comparison of the transition probabilities derived from the applied example, and implications of the findings will be discussed.

Authors

• Delwin Carter, University of California - Santa Barbara

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

• Michael James Furlong, University of California - Santa Barbara

• Erin Dowdy, University of California - Santa Barbara