How to Evaluate Causal Dominance Hypotheses in Lagged Effects Models

Abstract

The (Random Intercept) Cross-Lagged Panel Model ((RI-)CLPM) is increasingly used in psychology and related fields to assess the longitudinal relationship of two or more variables on each other. Researchers are interested in the question which of the lagged effects is causally dominant receives considerable attention. However, currently used methods do not allow for the evaluation of causal dominance hypotheses. This paper will show the performance of the Generalized Order-Restricted Information Criterion Approximation (GORICA), an extension of Akaike’s Information Criterion (AIC), in the context of causal dominance hypotheses using a simulation study. The GORICA proves to be an adequate method to evaluate causal dominance in lagged effects models.

Keywords:

• Causal dominance
• informative hypotheses
• model selection
• order restrictions

Acknowledgements

We acknowledge support by The Royal Thai Government.

Notes

¹In case of constraining variances to zero (e.g., the variances of the random intercepts in a RI-CLPM), the test should be adjusted, since variances are nonnegative values. Note that the reference value zero lies on the boundary of the parameter space of a variance. Consequently, the zero variance model should be tested against a model with a positive variance instead of a model with a freely-estimated variance. This can be done by using the Chi-bar-square difference test (Hamaker et al., 2015; Stoel et al., 2006), available in the R package Chibarsq.difftest (Kuiper, 2021a) for which example code can be found on: chi-bar-square test. Notably, the Chi-bar-square difference test cannot compare non-nested models nor can it evaluate inequality constraints other than testing positive variances.

²There is another framework to compare the relative evidence for one model over the other, namely the Bayesian framework based on Bayes Factors (BFs; Kass and Raftery (1995)). The BF quantifies the relative support provided by the data for two competing hypotheses. BFs can be calculated in R, for example, using the bain package (Gu et al., 2019, 2018; Hoijtink et al., 2019). For the comparison of the performance of GORICA and bain, the interested reader is referred to the supplementary material.

³We used the estimates from the first to second wave of the RI-CLPM in Masselink et al. (2018) since they estimate wave-specific ones. Note that, for ease, we use a (RI-)CLPM where the parameters are not wave-specific. In the example section and the supplementary material, we will show how the GORICA can be applied to models with and without wave-specific parameters.

⁴In practice, one will find an equal fit, an equal complexity, and thus GORICA weights of 0.5 (which is the same as the weights based on the complexity/penalty). This then indicates that both hypotheses are equally supported, which reflects support for the border of the hypothesis, that is, support for equal strength of parameters.

⁵Notably, if there is a competing theory stating different orderings (perhaps even the opposite ordering of this one) or no causal dominance (stating that the reciprocal cross-lagged parameters are of equal strength), then this should be added to the set and then the unconstrained hypothesis should be included as safeguard. In this simulation, we thus assume that there is one theory, which is then compared against all other possible theories.

⁶In practice, one will find an equal fit and GORICA weights that equal the weights based on the complexity/penalty. This then indicates that both hypotheses are equally supported, which reflects support for their border.