Simple ways to interpret effects in modeling binary data

Traditional methods for the analysis of binary response data are generalized linear models that employ logistic or probit link functions. Unfortunately, effect measures for these type of models do not have a straightforward interpretation. Hence, in this paper we survey probability-based effect measures that can be simpler to understand than logistic and probit regression model parameters and their corresponding effect measures, such as odds ratios. For describing the effect of an explanatory variable while adjusting for others, it is sometimes possible to employ the identity and log link functions to generate simple effect measures. When such link functions are inappropriate, one can still construct analogous effect measures. For comparing groups that are levels of categorical explanatory variables or relevant values for quantitative explanatory variables, such measures can be based on average differences or log-ratios of the probability modeled. For quantitative explanatory variables, they can also be based on average instantaneous rates of change for the probability. We also propose analogous measures for interpreting effects in models with nonlinear predictors, such as generalized additive models. We illustrate the measures for two examples and show how to implement them with R software.