Abstract
This paper considers the role of covariates when using predicted probabilities to interpret main effects and interactions in logit models. While predicted probabilities are very intuitive for interpreting main effects and interactions, the pattern of results depends on the contribution of covariates. We introduce a concept called the covariate contribution, which reflects the aggregate contribution of all of the remaining predictors (covariates) in the model and a family of tools to help visualize the relationship between predictors and the predicted probabilities across a variety of covariate contributions. We believe this strategy and the accompanying tools can help researchers who wish to use predicted probabilities as an interpretive framework for logit models acquire and present a more comprehensive interpretation of their results. These visualization tools could be extended to other models (such as binary probit, multinomial logistic, ordinal logistic models, and other nonlinear models).