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

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

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

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 selection models for non-Gaussian responses that are missing not at random

Missing not at random (MNAR) data poses key challenges for statistical inference because the model of interest is typically not identifiable without imposing further (e.g., distributional) assumptions. Sample selection models have been routinely used for handling MNAR by jointly modelling the outcome and selection variables assuming that these follow a bivariate normal distribution. Recent studies have advocated parametric selection model approaches, for example estimated by multiple imputation and maximum likelihood, that are more robust to departures from the normality assumption. However, the proposed methods have been mostly restricted to a specific joint distribution (e.g., bivariate t-distribution). This paper discusses a flexible copula-based selection approach (which accommodates a wide range of non-Gaussian outcome distributions and offers great flexibility in the choice of functional form specifications for both the outcome and selection equations) and proposes a flexible imputation procedure that generates plausible imputed values from the copula selection model. A simulation study characterises the relative performance of the copula model compared with the most commonly used selection models for estimating average treatment effects with MNAR data. We illustrate the methods in the REFLUX study, which evaluates the causal effect of laparoscopic surgery compared to usual medical management on long-term quality of life in patients with reflux disease. We provide software code for implementing the proposed copula framework using the R package GJRM

Neutrino-driven Turbulent Convection and Standing Accretion Shock Instability in Three-Dimensional Core-Collapse Supernovae

We conduct a series of numerical experiments into the nature of three-dimensional (3D) hydrodynamics in the postbounce stalled-shock phase of core-collapse supernovae using 3D general-relativistic hydrodynamic simulations of a $27$-$M_\odot$ progenitor star with a neutrino leakage/heating scheme. We vary the strength of neutrino heating and find three cases of 3D dynamics: (1) neutrino-driven convection, (2) initially neutrino-driven convection and subsequent development of the standing accretion shock instability (SASI), (3) SASI dominated evolution. This confirms previous 3D results of Hanke et al. 2013, ApJ 770, 66 and Couch & Connor 2014, ApJ 785, 123. We carry out simulations with resolutions differing by up to a factor of $\sim$4 and demonstrate that low resolution is artificially favorable for explosion in the 3D convection-dominated case, since it decreases the efficiency of energy transport to small scales. Low resolution results in higher radial convective fluxes of energy and enthalpy, more fully buoyant mass, and stronger neutrino heating. In the SASI-dominated case, lower resolution damps SASI oscillations. In the convection-dominated case, a quasi-stationary angular kinetic energy spectrum $E(\ell)$ develops in the heating layer. Like other 3D studies, we find $E(\ell) \propto \ell^{-1}$ in the "inertial range," while theory and local simulations argue for $E(\ell) \propto \ell^{-5/3}$. We argue that current 3D simulations do not resolve the inertial range of turbulence and are affected by numerical viscosity up to the energy containing scale, creating a "bottleneck" that prevents an efficient turbulent cascade.Comment: 24 pages, 15 figures. Accepted for publication in The Astrophysical Journal. Added one figure and made minor modifications to text according to suggestions from the refere

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

Assessment of Natural Resources Use for Sustainable Development - DPSIR Framework for Case Studies in Portsmouth and Thames Gateway, U.K.

This chapter reports on the uses of the DPSIR framework to assess the sustainability of the intertidal environments within the two UK case study areas, Portsmouth and Thames Gateway. It focuses on statutory conservation areas dominated by intertidal habitats. Two are located in Portsmouth (Portsmouth and Langstone Harbours) and four in the Thames Gateway (Benfleet Marshes, South Thames Estuary, Medway Estuary and the Swale in the Thames Gateway). Based on the reduction of a number of pressures and impacts observed in recent decades and the improvement of overall environmental quality, all six SSSIs are considered to be sustainable in the short and medium term. In the future, it is possible that the impacts of climate change, especially sea-level rise, might result in further reduction in the area and/or quality of intertidal habitats. Further integration between conservation and planning objectives (both for urban development and management of flood risk) at local level is needed to support the long-term sustainability of intertidal habitats

Flexible Causal Inference for Political Science

Measuring the causal impact of state behavior on outcomes is one of the biggest methodological challenges in the field of political science, for two reasons: behavior is generally endogenous, and the threat of unobserved variables that confound the relationship between behavior and outcomes is pervasive. Matching methods, widely considered to be the state of the art in causal inference in political science, are generally ill-suited to inference in the presence of unobserved confounders. Heckman-style multiple-equation models offer a solution to this problem; however, they rely on functional-form assumptions that can produce substantial bias in estimates of average treatment effects. We describe a category of models, flexible joint likelihood models, that account for both features of the data while avoiding reliance on rigid functional-form assumptions. We then assess these models’ performance in a series of neutral simulations, in which they produce substantial (55% to 90%) reduction in bias relative to competing models. Finally, we demonstrate their utility in a reanalysis of Simmons’ (2000) classic study of the impact of Article VIII commitment on compliance with the IMF’s currency-restriction regime