How to Compare Cross-Lagged Associations in a Multilevel Autoregressive Model

By modeling variables over time it is possible to investigate the Granger-causal cross-lagged associations between variables. By comparing the standardized cross-lagged coefficients, the relative strength of these associations can be evaluated in order to determine important driving forces in the dynamic system. The aim of this study was twofold: first, to illustrate the added value of a multilevel multivariate autoregressive modeling approach for investigating these associations over more traditional techniques; and second, to discuss how the coefficients of the multilevel autoregressive model should be standardized for comparing the strength of the cross-lagged associations. The hierarchical structure of multilevel multivariate autoregressive models complicates standardization, because subject-based statistics or group-based statistics can be used to standardize the coefficients, and each method may result in different conclusions. We argue that in order to make a meaningful comparison of the strength of the cross-lagged associations, the coefficients should be standardized within persons. We further illustrate the bivariate multilevel autoregressive model and the standardization of the coefficients, and we show that disregarding individual differences in dynamics can prove misleading, by means of an empirical example on experienced competence and exhaustion in persons diagnosed with burnout.