A Tutorial on Testing the Equality of Standardized Regression Coefficients in Structural Equation Models using Wald Tests with lavaan

Abstract

Comparing the effects of two or more explanatory variables on a dependent variable in structural equation models, with either manifest or latent variables, may be hampered by the arbitrary metrics which are common in social sciences and psychology. A possible way to compare the effects is the comparison of standardized regression coefficients by means of the Wald test. In this tutorial, we show how the Wald test can be used to compare standardized regression coefficients. Moreover, we demonstrate how this can be implemented in R using the lavaan package. Additionally, we provide a convenience function that allows doing a Wald test by only setting up equality constraints. The Wald test, its application and the implementation in R are illustrated by means of worked-examples. We also discuss theoretical aspects and implications when hypotheses about the equality of standardized regression parameters in structural equation models are tested. Keywords comparing standardized regression coefficients, Wald test, structural equation modeling. Tools lavaan.

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“…To compare the indirect effects by groups, we performed a multiple mediator model with multiple groups by gender, using the Wald test for testing the group difference in the indirect path effects (Ryu and Cheong, 2017 ; Klopp, 2019 ). In the group of women, the frequency of coping activities was significantly associated with the increase in negative emotional states among women; however, in men, no significant relationship was observed between coping activities and emotional states.…”

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“…We used a modified Wald test to compare the magnitude of standardized regression coefficients (Klopp, 2020). Wald’s test indicated that the effects of Phonemic Proficiency on Real Word and Pseudo Word factors were not equivalent for ages 8–11 W (1, 480) = 15.475, p < .001, 12–19 W (1, 720) = 18.991, p < .001, or 20–50 W (1, 152) = 5.04, p =.02.…”

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