Fitting an Latent Growth effect within a CLPM (RS-CLPM)

CLPM has been used to identify the cross-lagged effects with more than 3 time points in areas of social and behavioral sciences. To clarify the effects of between- and within-person variances within the CLPM, a CLPM with random intercepts was proposed and it resolved several issues in model specifications related to longer time span. This paper focuses more on growth patterns within the CLPM, naming random-slope CLPM (RS-CLPM). Applying a simulation study with variables of between- and within-person effects and cross-lagged effects with and without random slopes, we found the lower accuracy of RI-CLPM for both cases of with and without random slopes, which proves the flexibility and accuracy of the RS-CLPM. Based on the simulation result, we also fit the RS-CLPM into empirical data of ECLS-K:2011. Two variables of science achievement and cognitive flexibility were considered in the RS-CLPM. The result shows that the RS-CLPM would reduce the potential bias in parameter estimates of the CLPM, which extends the flexibility of the CLPM.