Interpreting effects in generalized linear modeling

With nonlinear link functions in generalized linear models, it can be difficult for nonstatisticians to understand how to interpret the estimated effects. For this purpose, it can be helpful to report approximate effects based on differences and ratios for the mean response. We illustrate with effect measures for models for categorical data. We mainly focus on binary response variables, showing how such measures can be simpler to interpret than logistic and probit regression model parameters and their corresponding effect measures, such as odds ratios. For describing the effect of an explanatory variable on a binary response 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 from standard models such as logistic regression. We also summarize recent literature on such effect measures for models for ordinal response variables. We illustrate the measures for two examples and show how to implement them with R software.