Course Level: Intermediate
Format Requirements: The instructors will use PowerPoint presentation and provide in-class exercises. We will discuss the theoretical and statistical motivation for interaction terms and then illustrate the mathematical derivation of marginal effects in linear and non-linear regression models. Additionally, the ‘marginal effect at the mean’ will be defined and compared with the ‘mean marginal effect’ for continuous and categorical variables for linear and non-linear regression models. In-class exercises will provide participants with the opportunity to calculate and evaluate marginal effect functions. SAS code for estimating these marginal effects and associated confidence intervals also will be provided to the attendees. Familiarity with linear regression models and generalized linear regression models is desirable. Bringing a laptop to the session is helpful but not required.
Background: As payers and insurers identify priorities for improving patient-centered care delivery, there will be an even greater attention paid heterogeneity in the impact of therapeutic and programmatic interventions. Much of the evidence regarding heterogeneity of effect will be generated from observational, real-world studies. Hence, regression models with interaction terms along with associated estimates of marginal effects will facilitate the examination of heterogeneity across groups defined by clinical and/or demographic factors. This course will facilitate the understanding, estimation and interpretation of the marginal effects.
Description and Objectives: Following an overview of the theoretical and statistical motivation for interaction terms, we will illustrate the mathematical derivation of marginal effects for a) linear model, b) logistic model, c) multinomial logit model, d) beta regression model, e) generalized linear models, f) two-stage linear selection models and g) two-stage log-linear Heckman sample selection models. Participants will have the opportunity to derive marginal effect functions based on specific examples. The instructors will present empirical examples of different types of regression models with interaction terms, along with the methods of calculating confidence intervals for the marginal effect estimates. The policy relevance of marginal effect calculations will be discussed. By comparing and contrasting the marginal effects estimated across various regression models, the course participants will be challenged to consider strengths and limitations of the methods employed to estimate and report marginal effect estimates as well as the implications for decision making focused on patient-centered care delivery. After taking this course, participants will be able to:
- Understand the differences between various regression models when conducting tests for statistical significance of interaction terms and interpreting interaction terms;
- Derive the marginal effect function for various model specifications;
- Generate associated confidence intervals on the marginal effect in the presence of statistically significant interactions.