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 a typical textbook display of the Wald test can be used to derive a calculation for 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. We also discuss theoretical aspects and implications when hypotheses about the equality of standardized regression parameters in structural equation models are tested.