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Copula regression spline models for binary outcomes

Radice, R. ORCID: 0000-0002-6316-3961, Marra, G. & Wojtys, M. (2016). Copula regression spline models for binary outcomes. Statistics and Computing, 26(5), pp. 981-995. doi: 10.1007/s11222-015-9581-6


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.

Publication Type: Article
Additional Information: This is a post-peer-review, pre-copyedit version of an article published in Statistics and Computing. The final authenticated version is available online at:
Publisher Keywords: Bivariate binary outcomes, Copula, Endogeneity, Penalized regression spline, Simultaneous equation estimation, Unobserved confounding
Subjects: H Social Sciences > HA Statistics
Q Science > QA Mathematics
R Medicine
Departments: Bayes Business School > Actuarial Science & Insurance
SWORD Depositor:
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