Cross-Lagged Panel Analysis When Constructs Are Measured Using Ordinal Scales

• In Event: Composite/Factor Scores Analyses With Bias Correction: Good Alternatives to Full Structural Equation Modeling?

Abstract

Cross-lagged panel designs are commonly used in social science studies for investigating causal relations of two variables. For studying the causal relations between time-varying variables, cross-lagged panel models (CLPMs) have been recommended. Three major questions can be studied using CLPMs: (1) whether inter-relations of the two variables exist, (2) what the directions of the relations are, and (3) which variable is causally dominant.

Two forms of CLPMs have been used: one with observed variables (e.g., scale scores; O-CLPM), and the other with latent variables (L-CLPM). O-CLPMs do not account for measurement error whereas L-CLPMs do. Previous studies have found that biased estimates and inaccurate inferences about structural relations can occur when failing to consider measurement error. Therefore, we focus on L-CLPMs. The most common L-CLPM is to use multiple indicators for latent constructs X and Y. Recently, when studying longitudinal mediation (tri-variate relations), Zhang and Yang (in press) recommended L-CLPM with composite scores corrected for measurement error as indicators, which proved to yield accurate estimates and much better controlled type I error rates of model fit test than L-CLPM with multiple indicators. The modeling approach recommended by Zhang and Yang (in press) can be generalized to study bi-variate relations.

When using L-CLPMs, among all the assumptions, longitudinal measurement invariance and correct specification of measurement model need to be satisfied. For L-CLPM with multiple indicators, at least metric invariance is necessary; for L-CLPM with composite scores as indicators, it is sufficient to have equal sums of loadings over time for each latent construct (Zhang & Yang, in press). We assume the measurement model for each construct within each occasion is valid and focus on examining the consequence of omitting correlations among measurement errors across occasions for the same item, or items from different constructs within the same occasion or across occasions. In addition, the constructs X and Y are often measured by scales consisting of ordinal items. Estimation approaches specifically developed for categorical data (e.g., weighted least squares using polychoric correlations; Muthén, 1984) often require a large sample size and fit indexes are sometimes hard to be interpreted (Xia & Yang, 2018). Instead, we focus on continuous estimation strategy. In the study, maximum likelihood estimation with robust standard error (MLR) is used. When using MLR, previous research has shown that having five categories is enough to ensure accurate loading and factor correlation estimates under confirmatory factor analysis models (Rhemtulla et al., 2012). It remains unknown, however, under L-CLPMs whether having five categories is enough and if not, what the minimum number of categories would be.

In sum, with regard to the two forms of L-CLPMs, a simulation study is conducted focusing on the following key factors (1) whether measurement invariance is met and if not the extent of non-invariance, (2) measurement model specification, (3) number of categories per item (5, 6, 7), and (4) ordinal item distributions (symmetric, moderately asymmetric, severely asymmetric). Results are evaluated based on inferences regarding the three research questions under cross-lagged panel designs.

Authors

• Qian Zhang, Florida State University

• Qi Wang, Florida State University