Statistics and Computing

, Volume 26, Issue 5, pp 981–995 | Cite as

Copula regression spline models for binary outcomes

  • Rosalba Radice
  • Giampiero Marra
  • Małgorzata Wojtyś
Article

Abstract

We introduce a framework for estimating the effect that a binary treatment has on a binary outcome in the presence of unobserved confounding. The methodology is applied to a case study which uses data from the Medical Expenditure Panel Survey and whose aim is to estimate the effect of private health insurance on health care utilization. Unobserved confounding arises when variables which are associated with both treatment and outcome are not available (in economics this issue is known as endogeneity). Also, treatment and outcome may exhibit a dependence which cannot be modeled using a linear measure of association, and observed confounders may have a non-linear impact on the treatment and outcome variables. The problem of unobserved confounding is addressed using a two-equation structural latent variable framework, where one equation essentially describes a binary outcome as a function of a binary treatment whereas the other equation determines whether the treatment is received. Non-linear dependence between treatment and outcome is dealt using copula functions, whereas covariate-response relationships are flexibly modeled using a spline approach. Related model fitting and inferential procedures are developed, and asymptotic arguments presented.

Keywords

Bivariate binary outcomes Copula  Endogeneity  Penalized regression spline Simultaneous equation estimation Unobserved confounding 

Supplementary material

11222_2015_9581_MOESM1_ESM.pdf (910 kb)
Supplementary material 1 (pdf 910 KB)

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Rosalba Radice
    • 1
  • Giampiero Marra
    • 2
  • Małgorzata Wojtyś
    • 3
    • 4
  1. 1.Department of Economics, Mathematics and StatisticsBirkbeckLondonUK
  2. 2.Department of Statistical ScienceUniversity College LondonLondonUK
  3. 3.Centre for Mathematical SciencesPlymouth UniversityPlymouthUK
  4. 4.Faculty of Mathematics and Information ScienceWarsaw University of TechnologyWarszawaPoland

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