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.

The Theory of Planned Behavior during the COVID-19 pandemic: A comparison of health behaviors between Belgian and French residents

“…Additionally, we tested the equality of correlations and standardized regression coefficients between Belgian and French residents using a series of Wald Chi-Squared Tests [ 32 ]. Specifically, we assessed constraints on statistical parameters (i.e., correlations and regressions paths individually and independently) based on the weighted distance between the unrestricted estimate and its hypothesized value under the null hypothesis, where the weight is the precision of the estimate [ 33 , 34 ].…”

“…Following the recommendations for analyzing the TPB model using path analysis [31], we first analyzed a saturated model including all possible paths in the model to calculate direct effects of each predictor. Then, based on theory, we deleted the two direct paths from attitudes to behavior and social norms to behavior to avoid saturated model, retaining only the expected direct effect of perceived control on health behavior.…”

Emotional Reactions and Adaptation to COVID-19 Lockdown (or Confinement) by Spanish Competitive Athletes: Some Lesson for the Future

“…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.…”

Der Einfluss der Arbeit auf das Wohlbefinden unter Berücksichtigung verschiedener Berufsprofile

“…In der betrieblichen Gesundheitsförderung wird ein großes Augenmerk auf die Früherkennung und Prävention gelegt. Aus der klinischen Forschung ist bekannt, dass bestimmte individuelle Faktoren, insbesondere Persönlichkeitsstile und -störungen [5,19], das Risiko für stressbedingte Erkrankungen im Arbeitskontext erhöhen. Auch gibt es Untersuchungen, die auf besonders gefährdete Berufsfelder fokussieren (z.…”

“…Die unstandardisierten Regressionskoeffizienten werden als klar signifikanten Prediktor für die Zielvariable betrachtet, wenn der p-Wert < 0,01 beträgt und als leicht signifikant für p < 0,05. Um zu prüfen, ob die Effektstärke für verschiedene Faktoren signifikant verschieden ist, wird ein Wald-Test auf die standardisierten Regressionskoeffizienten angewendet [19].…”