A Unified Framework for Specification Tests of Continuous Treatment Effect Models

Abstract

Ex-post harmonisation is one of many data preprocessing processes used to combine the increasingly vast and diverse sources of data available for research and analysis. Documenting provenance and ensuring the quality of multi-source datasets is vital for ensuring trustworthy scientific research and encouraging reuse of existing harmonisation efforts. However, capturing and communicating statistically relevant properties of harmonised datasets is difficult without a universal standard for describing harmonisation operations. Our paper combines mathematical and computer science perspectives to address this need. The Crossmaps Framework defines a new approach for transforming existing variables collected under a specific measurement or classification standard to an imputed counterfactual variable indexed by some target standard. It uses computational graphs to separate intended transformation logic from actual data transformations, and avoid the risk of syntactically valid data manipulation scripts resulting in statistically questionable data. In this paper, we introduce the Crossmaps Framework through the example of ex-post harmonisation of aggregated statistics in the social sciences. We define a new provenance task abstraction, the crossmap transform, and formalise two associated objects, the shared mass array and the crossmap. We further define graph, matrix and list encodings of crossmaps and discuss resulting implications for understanding statistical properties of ex-post harmonisation and designing error minimising workflows.

Nonparametric Estimation of Mediation Effects with A General Treatment

“…Estimation of continuous treatment effects has drawn considerable attention (see Hirano & Imbens (2004), Imai & van Dyk (2004), Galvao & Wang (2015), Kennedy et al (2017), Fong et al (2018), Dong et al (2019), Colangelo & Lee (2020), Ai, Linton, Motegi & Zhang (2021), Huang et al (2021) among others). However, all of the above studies focus on the total treatment effect, rather than analyzing the causal mediation effects.…”

“…t )}. This can help conduct statistical inference, as we can approximate the limiting distribution of our estimator by adopting the exchangeable bootstrap method(Chernozhukov et al 2013, Donald & Hsu 2014, Huang et al 2021. Using Theorem 1, the asymptotic results of the estimated direct and indirect effects can be easily obtained.…”

Nonparametric Estimation of the Continuous Treatment Effect with Measurement Error

“…Rosenbaum andRubin, 1983, 1984;Hahn, 1998;Hirano et al, 2003). More recently, as opposed to such binary treatments, researchers have been investigating the causal effect of a continuously valued treatment, where the effect depends not only on the introduction of the treatment but also on the intensity; see Hirano and Imbens (2004); Galvao and Wang (2015); Kennedy et al (2017); Fong et al (2018); Huber et al (2020); Dong et al (2021); Ai et al (2021Ai et al ( , 2022, and Huang et al (2021), among others. However, all these methods require the treatment data to be measured without errors.…”