Work

An Innovation to Test Treatment X Pretest Interactions within Difference-in-Differences

Year: 2025

Type: article

Abstract: We introduce a way to test Treatment X Pretest interactions within difference-in-differences (DID). Mathematically adding a Treatment X Pretest interaction to DID transforms the treatment estimate to an ANCOVA-type estimate, which differs from DID's estimate and is often biased against at-risk cases. Dual-centered ANCOVA duplicates DID's treatment estimate and can test whether that estimate varies by pretest scores. To illustrate, we test a Treatment X Pretest interaction for the effects of therapy for depression using the Fragile Families and Child Wellbeing longitudinal dataset. After centering posttest and pretest outcome data on pretest group means, DID and ANCOVA estimates are both equivalent to the original DID treatment estimate. ANCOVA of these dual-centered data can then test a Treatment X Pretest interaction.

Source: Journal of Behavioral Data Science

DOI: 10.35566/jbds/larzelere

Authors: Robert Larzelere, Hua Lin

Institution: Oklahoma State University

Language: English

Topic: Advanced Causal Inference Techniques

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

SDG: Good health and well-being

Open Access status: diamond

Funders: Oklahoma State University, National Institute of Child Health and Human Development