Inferring Longitudinal Relationships Between Variables: Model Selection Between the Latent Change Score and Autoregressive Cross-Lagged Factor Models

Abstract

This research focuses on the problem of model selection between the latent change score (LCS) model and the autoregressive cross-lagged (ARCL) model when the goal is to infer the longitudinal relationship between variables. We conducted a large-scale simulation study to (a) investigate the conditions under which these models return statistically (and substantively) different results concerning the presence of bivariate longitudinal relationships, and (b) ascertain the relative performance of an array of model selection procedures when such different results arise. The simulation results show that the primary sources of differences in parameter estimates across models are model parameters related to the slope factor scores in the LCS model (specifically, the correlation between the intercept factor and the slope factor scores) as well as the size of the data (specifically, the number of time points and sample size). Among several model selection procedures, correct selection rates were higher when using model fit indexes (i.e., comparative fit index, root mean square error of approximation) than when using a likelihood ratio test or any of several information criteria (i.e., Akaike’s information criterion, Bayesian information criterion, consistent AIC, and sample-size-adjusted BIC).

Keywords:

• autoregressive cross-lagged model
• causal inference
• latent change score model
• longitudinal data
• model selection

FUNDING

This work was supported by JSPS KAKENHI Grant-in-Aid for Research Activity Start-up Grant Number 26885007.

Notes

¹ Coefficients are usually considered invariant over time (e.g., ergodic; McArdle, 2009). This assumption can be relaxed so that different patterns of longitudinal (or causal) influence can be assumed at different times, although the resulting relationships become more complex and are not so easily interpreted. Likewise, although time-invariant constants and are typically assumed, time-variant factor loadings can also be specified as and . Under this specification, when these values are fixed as for model identification.

² Although difference of chi-square statistic between models does not precisely come from chi-square distribution with 7df due to the violation of regularity conditions, likelihood ratio tests provide more conservative result.

³ Although another index, the standardized root mean square residual (SRMR) can be used (e.g., Wu & West, 2010), we omit this here because the SRMR is widely known to assess the fit of the covariance structure only and display insensitivity to misfit in the mean structure (Preacher et at., 2008).

Additional information

Funding

This work was supported by JSPS KAKENHI Grant-in-Aid for Research Activity Start-up Grant Number 26885007.