Copula regression spline models for binary outcome

Authors: Rosalba Radice Giampiero Marra Małgorzata Wojtyś

Publish Date: 2015/06/18

Volume: 26, Issue: 5, Pages: 981-995

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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 nonlinear impact on the treatment and outcome variables The problem of unobserved confounding is addressed using a twoequation 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 Nonlinear dependence between treatment and outcome is dealt using copula functions whereas covariateresponse relationships are flexibly modeled using a spline approach Related model fitting and inferential procedures are developed and asymptotic arguments presented

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