Testing Moderating Hypotheses in Limited Dependent Variable and Other Nonlinear Models

Abstract

The use of limited dependent variable (LDV) models is becoming ubiquitous in empirical management research. When using such models, researchers frequently postulate and test that the relationship between an explanatory variable and the dependent variable is moderated by another variable by including in the model an interaction variable. Although recent papers clarify methods for analyzing a moderating effect in LDV models, it is not widely appreciated that this effect confounds two moderating effects: one associated with including an interaction variable in the model and one associated with the inherent nonlinearity of such models. This article presents a method to separate these two sources of a moderating effect for a general class of nonlinear models that includes all LDV models commonly used in the management literature. For such models, the article demonstrates that the statistically correct method to assess the validity of a moderating hypothesis is not, as currently recommended, to test for significance of the total moderating effect derived from the model that includes the interaction variable but instead to test for significance of the secondary moderating effect, the latter defined as the difference between two moderating effects: the one in the model that includes the interaction variable and the one in the model that excludes this variable. The result that the secondary effect is the correct statistic for testing a moderating hypothesis is very general, and it applies whenever a moderating hypothesis is to be tested by including an interaction variable in any model, whether linear or nonlinear.