A joint regression modeling framework for analyzing bivariate binary data in R

We discuss some of the features of the R add-on package GJRM which implements a flexible joint modeling framework for fitting a number of multivariate response regression models under various sampling schemes. In particular,we focus on the case inwhich the user wishes to fit bivariate binary regression models in the presence of several forms of selection bias. The framework allows for Gaussian and non-Gaussian dependencies through the use of copulae, and for the association and mean parameters to depend on flexible functions of covariates. We describe some of the methodological details underpinning the bivariate binary models implemented in the package and illustrate them by fitting interpretable models of different complexity on three data-sets

Flexible Bivariate Binary Models for Estimating the Efficacy of Phototherapy for Newborns with Jaundice

In this work we analyse the efficacy of phototherapy (treatment) on the probability of being hyperbilirubinemic (outcome) in infants. A realistic quantification of the relationship between treatment and outcome can be challenging for various reasons. First, the probability of interest might be too small. Second, confounding unmeasured variables may exist which can bias the efficacy of phototherapy at preventing significant hyperbilirubinemia. Third, relationships between covariates and the outcome variable may exhibit non-linear patterns that, if not accounted for, can bias the relationship of interest. One way of dealing with the second and third issues is to use a semiparametric recursive bivariate probit model. To address the first issue as well, we explore an extension of this model which accounts for the fact that being hyperbilirubinemic can be regarded as a rare event. The proposed approach combines the marginal distributions of treatment and outcome using copulae, and uses asymmetric link functions to deal with rare outcome events. The main features underpinning the use of asymmetric link functions within semiparametric bivariate binary models are discussed

Bivariate copula additive models for location, scale and shape

In generalized additive models for location, scale and shape (GAMLSS), the response distribution is not restricted to belong to the exponential family and all the model’s parameters can be made dependent on additive predictors that allow for several types of covariate effects (such as linear, non-linear, random and spatial effects). In many empirical situations, however, modeling simultaneously two or more responses conditional on some covariates can be of considerable relevance. The scope of GAMLSS is extended by introducing bivariate copula models with continuous margins for the GAMLSS class. The proposed computational tool permits the copula dependence and marginal distribution parameters to be estimated simultaneously, and each parameter to be modeled using an additive predictor. Simultaneous parameter estimation is achieved within a penalized likelihood framework using a trust region algorithm with integrated automatic multiple smoothing parameter selection. The introduced approach allows for straightforward inclusion of potentially any parametric marginal distribution and copula function. The models can be easily used via the copulaReg() function in the R package SemiParBIVProbit. The proposal is illustrated through two case studies and simulated data

Penalized likelihood estimation of a trivariate additive probit model

This article proposes a penalized likelihood method to estimate a trivariate probit model, which accounts for several types of covariate effects (such as linear, nonlinear, random, and spatial effects), as well as error correlations. The proposed approach also addresses the difficulty in estimating accurately the correlation coefficients, which characterize the dependence of binary responses conditional on covariates. The parameters of the model are estimated within a penalized likelihood framework based on a carefully structured trust region algorithm with integrated automatic multiple smoothing parameter selection. The relevant numerical computation can be easily carried out using the SemiParTRIV() function in a freely available R package. The proposed method is illustrated through a case study whose aim is to model jointly adverse birth binary outcomes in North Carolina

Copula regression spline models for binary outcomes

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

Copula Regression Spline Sample Selection Models: The R Package SemiParSampleSel

Sample selection models deal with the situation in which an outcome of interest is observed for a restricted non-randomly selected sample of the population. The estimation of these models is based on a binary equation, which describes the selection process, and an outcome equation, which is used to examine the substantive question of interest. Classic sample selection models assume a priori that continuous covariates have a linear or pre-specified non-linear relationship to the outcome, and that the distribution linking the two equations is bivariate normal. We introduce the R package SemiParSampleSel which implements copula regression spline sample selection models. The proposed implementation can deal with non-random sample selection, non-linear covariate-response relationships, and non-normal bivariate distributions between the model equations. We provide details of the model and algorithm and describe the implementation in SemiParSampleSel. The package is illustrated using simulated and real data examples

Preliminary results from an application of PTV to bed-load grains

River engineeringInnovative field and laboratory instrumentatio

Did the ACA's "guaranteed issue" provision cause adverse selection into nongroup insurance? Analysis using a copula-based hurdle model

Prior to the Affordable Care Act (ACA), insurance companies could charge higher premiums, or outright deny coverage, to people with preexisting health problems. But the ACA's “guaranteed issue” provision forbids such price discrimination and denials of coverage. This paper seeks to determine whether, after implementation of the ACA, nongroup private insurance plans have experienced adverse selection. Our empirical approach employs a copula-based hurdle regression model, with dependence modeled as a function of dimensions along which adverse selection might occur. Our main finding is that, after implementation of the ACA, nongroup insurance enrollees with preexisting health problems do not appear to exhibit adverse selection. This finding suggests that the ACA's mandate that everyone acquire coverage might have attracted enough healthy enrollees to offset any adverse selection

Robust fitting for generalized additive models for location, scale and shape

The validity of estimation and smoothing parameter selection for the wide class of generalized additive models for location, scale and shape (GAMLSS) relies on the correct specification of a likelihood function. Deviations from such assumption are known to mislead any likelihood-based inference and can hinder penalization schemes meant to ensure some degree of smoothness for nonlinear effects. We propose a general approach to achieve robustness in fitting GAMLSSs by limiting the contribution of observations with low log-likelihood values. Robust selection of the smoothing parameters can be carried out either by minimizing information criteria that naturally arise from the robustified likelihood or via an extended Fellner–Schall method. The latter allows for automatic smoothing parameter selection and is particularly advantageous in applications with multiple smoothing parameters. We also address the challenge of tuning robust estimators for models with nonlinear effects by proposing a novel median downweighting proportion criterion. This enables a fair comparison with existing robust estimators for the special case of generalized additive models, where our estimator competes favorably. The overall good performance of our proposal is illustrated by further simulations in the GAMLSS setting and by an application to functional magnetic resonance brain imaging using bivariate smoothing splines