Statistics and Its Interface

Volume 15 (2022)

Number 4

Causal measures using generalized difference-in-difference approach with nonlinear models

Pages: 399 – 413



Marcelo M. Taddeo (Institute of Mathematics and Statistics, Federal University of Bahia, Salvador, Bahia, Brazil)

Leila D. Amorim (Center for the Integration of Health Knowledge Data & Institute of Mathematics and Statistics, Federal University of Bahia, Salvador, Bahia, Brazil)

Rosana Aquino (Center for the Integration of Health Knowledge and Data, Public Health School, Federal University of Bahia, Salvador, Bahia, Brazil)


To assess the impact of interventions on observational studies, several approaches have been proposed for identification of causal effects. They include propensity score matching, regression discontinuity, instrumental variables and causal graphs. In this paper, we focus on the Differences-in-Differences. We review the subject, discuss its scope and limitations, and extend it to a class of nonlinear models, inducing more appropriate causal measures in relation to the type of response variable and the corresponding statistical model. More specifically, we extend the usual causal effect identification procedure for more general setups, particularly Generalized Linear Models, presenting the necessary assumptions. We call such methodology Generalized Difference-in-Difference method. To illustrate, we analyze novel data from three relevant health issues in Brazil: the demographic impact of the Zika virus outbreak on birth rates, and the impact of two distinct interventions in primary health care, namely the Family Health Program and the More Doctors Program, on hospitalizations rate. Such analyzes, besides original and referring to important topics, complement and extend previous studies. Finally, we argue, in the methodological and application sections, that the use of the Generalized Difference-in-Difference will help us to avoid errors and fallacies arising from the misapplication of the usual Difference-in-Difference method at different scales.


causal inference, impact evaluation, differences-in-differences, average treatment, generalized linear models, public health

2010 Mathematics Subject Classification

Primary 62Dxx, 62J12. Secondary 97K80.

The research of Dr. Amorim was partially supported by FAPESB (Fundação de Amparo à Pesquisa do Estado da Bahia), grant APP0071/2016, and by CIDACS/FIOTEC, grant IGM-009-FEX-17.

Received 13 August 2020

Accepted 11 September 2021

Published 4 March 2022