ISSN 1671-3710
CN 11-4766/R

Advances in Psychological Science ›› 2021, Vol. 29 ›› Issue (10): 1773-1782.

• Research Method •

### Random intercept latent transition analysis (RI-LTA): Separating the between-subject variation from the within-subject variation

WEN Congcong1, ZHU Hong2()

1. 1International College, Xiamen University, Xiamen 361102, China
2Institute of Economics of Education, Peking University, Beijing 100871, China
• Received:2020-10-12 Online:2021-10-15 Published:2021-08-23
• Contact: ZHU Hong E-mail:hongzhu@pku.edu.cn

Abstract:

Traditional latent transition analysis (LTA) is usually done using single-level modeling, but can also be viewed as a two-level modeling from a multi-level perspective. In 2020, Muthén and Asparouhov proposed a so-called random intercept latent transition analysis (RI-LTA) model which separates between-subject variation from within-subject variation. By integrating a random intercept factor, latent class transitions are represented on the within level, whereas the between level captures the variability across subjects.

The random intercept factor f is the most important. If the factor loadings on the random intercept factor are large, this indicates that the item probabilities are large and thus the cases have large differences on these items. From this perspective, RI-LTA can be viewed as absorbing the measurement non-invariance of the model. Due to large item differences, the different latent classes are easy to distinguish. These differences are absorbed by the random intercept factor but are not set to influence the latent class variables. Therefore, the off-diagonal values of the transition probability matrix are larger. In traditional LTA, large differences across classes are not absorbed by the random intercept factor, which leads to smaller off-diagonal but larger diagonal values of the transition probability matrix.

Performing RI-LTA in Mplus software can be done in three to four steps. First, implementing LCA across different time points; second, implementing traditional LTA and RI-LTA; third, saving the parameter estimates obtained in the second step and using them as population values to do a Monte Carlo simulation study; fourth, in the event of previous knowledge or existing applications, one may include covariates or distal outcomes in the model. Researchers can also perform multiple-group analysis, Markov chain mover-stayer analysis, multi-level RI-LTA, or longitudinal factor analysis to have deeper insight into the data.

In the current study, a two-wave longitudinal data collection from undergraduates attending in the year 2016 at a research-oriented university was used to demonstrate how to implement RI-LTA in Mplus. The first three steps used were as described in the previous paragraph. For the fourth step, we performed a multiple-group analysis and investigated the interaction effects by including a “type of university enrolment” covariate. Results showed that students of the class labeled “strong intrinsic and extrinsic motivation” class tended to switch to “strong intrinsic motivation but low extrinsic motivation” class and “low intrinsic and extrinsic motivation” class at a 33.0% transition probability of staying in the original class with RI-LTA analysis, while these students tended to stay in the original class at a 68.9% staying transition probability with traditional LTA analysis. This indicated that RI-LTA avoided overestimation on the transition probabilities of students staying in the original class and allowed for clearer interpretation of the data. The RI-LTA model was shown to be better than the traditional LTA model in this situation. By including a “type of university enrolment” covariate, the multiple-group analysis indicated that measurement invariance should be established. Most of the regression coefficients of latent classes on covariate were not significant except c1#1 on dummy2, which was significant at a value of -2.364. This indicated that students who were enrolled via the independent admission examinations and endorsed the “low intrinsic and extrinsic motivation” class were fewer than the recommended students We also found that the interaction effects of the covariate and c1 on c2 were not significant. Thus, a more parsimonious measurement invariant multiple-group analysis including a covariate but without interaction effect model should be chosen. Future research could use Monte Carlo simulation studies to investigate the applicability of RI-LTA, for example by manipulating sample sizes, numbers of indicators, latent classes, and time points. Inspired by multi-level modeling, the implementation of multi-level RI-LTA in statistical software should also be explored further.

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