Testing for Moderating Effects in Limited Dependent Variable Models : Structural versus Secondary Interactions

The use of discrete limited dependent variable (LDV) models such as logit and probit 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. While recent papers clarify the methods for deriving and analyzing a moderating effect in LDV models, it is not widely understood or appreciated that this moderating effect confounds two moderating effects: one that arises from including an interaction variable in the model and one that arises naturally from the inherent nonlinearity of such models. This paper addresses this issue and presents a method to separate these two sources of a moderating effect for a general class of nonlinear models that includes all the LDV models commonly used in the management literature. Given this, the paper demonstrates that the statistically correct method to assess the validity of a moderating hypothesis in such models is not, as currently recommended, to test for significance of the moderating effect derived from the model that includes the interaction variable but is instead to test for significance of the difference between two moderating effects: that arising from the model that includes the interaction variable and arising from the model that excludes the interaction variable; this difference is the secondary moderating effect. The result that the secondary moderating effect is properly the focus of analysis for testing a moderating hypothesis is very general, in that it applies whenever a moderating hypothesis is to be tested by including an interaction variable in any model, whether linear or nonlinear.