Bayesian estimation and case influence diagnostics for the zero-inflated negative binomial regression model

In recent years, there has been considerable interest in regression models based on zero-inflated distributions. These models are commonly encountered in many disciplines, such as medicine, public health, and environmental sciences, among others. The zero-inflated Poisson (ZIP) model has been typically considered for these types of problems. However, the ZIP model can fail if the non-zero counts are overdispersed in relation to the Poisson distribution, hence the zero-inflated negative binomial (ZINB) model may be more appropriate. In this paper, we present a Bayesian approach for fitting the ZINB regression model. This model considers that an observed zero may come from a point mass distribution at zero or from the negative binomial model. The likelihood function is utilized to compute not only some Bayesian model selection measures, but also to develop Bayesian case-deletion influence diagnostics based on q-divergence measures. The approach can be easily implemented using standard Bayesian software, such as WinBUGS. The performance of the proposed method is evaluated with a simulation study. Further, a real data set is analyzed, where we show that ZINB regression models seems to fit the data better than the Poisson counterpart.     

Toward a Culturally Informed Rehabilitation Treatment Model for American Indian/Alaska Native Veterans

American Indians and Alaska Natives (AI/AN) have a long tradition of military service, allying with Western forces in North America since the 1700s. It is hardly surprising, therefore, that AI/AN veterans experience higher rates of overall disability and service-related disability than veterans of other races and ethnicities. It is not clear, however, that AI/AN veterans with disabilities are receiving effective, culturally informed rehabilitation services. This article examines the incidence of disability among contemporary AI/AN veterans, considers barriers to effective treatment, and points out model programs tailored to the particular needs of this population, with attention to the historical and cultural context of AI/AN military service.     

Likelihood analysis for a class of beta mixed models

Beta regression is a suitable choice for modelling continuous response variables taking values on the unit interval. Data structures such as hierarchical, repeated measures and longitudinal typically induce extra variability and/or dependence and can be accounted for by the inclusion of random effects. In this sense, Statistical inference typically requires numerical methods, possibly combined with sampling algorithms. A class of Beta mixed models is adopted for the analysis of two real problems with grouped data structures. We focus on likelihood inference and describe the implemented algorithms. The first is a study on the life quality index of industry workers with data collected according to an hierarchical sampling scheme. The second is a study assessing the impact of hydroelectric power plants upon measures of water quality indexes up, downstream and at the reservoirs of the dammed rivers, with a nested and longitudinal data structure. Results from different algorithms are reported for comparison including from data-cloning, an alternative to numerical approximations which also allows assessing identifiability. Confidence intervals based on profiled likelihoods are compared with those obtained by asymptotic quadratic approximations, showing relevant differences for parameters related to the random effects. In both cases, the scientific hypothesis of interest was investigated by comparing alternative models, leading to relevant interpretations of the results within each context.     

Dynamic Bayesian analysis of generalized odds ratios assuming multivariate skew-normal distribution for the error terms in the system equation

In this paper, we develop a methodology for the dynamic Bayesian analysis of generalized odds ratios in contingency tables. It is a standard practice to assume a normal distribution for the random effects in the dynamic system equations. Nevertheless, the normality assumption may be unrealistic in some applications and hence the validity of inferences can be dubious. Therefore, we assume a multivariate skew-normal distribution for the error terms in the system equation at each step. Moreover, we introduce a moving average approach to elicit the hyperparameters. Both simulated data and real data are analyzed to illustrate the application of this methodology.     

Expanded renal transplantation: a competing risk model approach

Multi-state models (MSMs) are useful to analyze survival data when, besides the event of main interest, one or more intermediate states of the individual are identified. These models take the several existing states and the possible transitions among them into account. At the same time, covariate effects on each transition intensity may be investigated separately and, therefore, MSMs are more flexible than the standard Cox proportional hazards model. In this work, we use MSMs to investigate the impact of the quality of a transplanted kidney for a group of patients at the Hospital Universitario Central de Asturias. Specifically, we use an illness-death model to study the evolution of patients with kidney disease who received a renal transplant after a dialysis period. The intermediate state is defined as the failure of the received organ, while the terminating state is the death of the patient. In order to increase the potential number of organs available for transplant, the standards of quality for the transplanted kidneys were relaxed (the new criteria are labeled expanded criteria), and these ‘expanded kidneys’ were transplanted in appropriate candidates (older patients, with higher prevalence of diabetes mellitus). Results suggest that the expanded kidneys have a minor effect on survival, while both the kidney mortality and the risk of death increase with the patient's age and the serum creatinine and serum hemoglobin levels.     

Smooth-Threshold GEE Variable Selection in High-Dimensional Partially Linear Models with Longitudinal Data

We consider the problem of variable selection in high-dimensional partially linear models with longitudinal data. A variable selection procedure is proposed based on the smooth-threshold generalized estimating equation (SGEE). The proposed procedure automatically eliminates inactive predictors by setting the corresponding parameters to be zero, and simultaneously estimates the nonzero regression coefficients by solving the SGEE. We establish the asymptotic properties in a high-dimensional framework where the number of covariates p_n increases as the number of clusters n increases. Extensive Monte Carlo simulation studies are conducted to examine the finite sample performance of the proposed variable selection procedure.     

Dummy Endogenous Variables in Weakly Separable Models

In this paper, we consider the nonparametric identification and estimation of the average effect of a dummy endogenous regressor in models where the regressors are weakly but not additively separable from the error term. The model is not required to be strictly increasing in the error term, and the class of models considered includes limited dependent variable models such as discrete choice models. Conditions are established conditions under which it is possible to identify the average effect of the dummy endogenous regressor in a weakly separable model without relying on parametric functional form or distributional assumptions and without the use of large support conditions.     

Nonparametric Matching and Efficient Estimators of Homothetically Separable Functions

For vectors z and w and scalar v, let r(v, z, w) be a function that can be nonparametrically estimated consistently and asymptotically normally, such as a distribution, density, or conditional mean regression function. We provide consistent, asymptotically normal nonparametric estimators for the functions G and H, where r(v, z, w) = H[vG(z), w], and some related models. This framework encompasses homothetic and homothetically separable functions, and transformed partly additive models r(v, z, w) = h[v + g(z), w] for unknown functions gand h Such models reduce the curse of dimensionality, provide a natural generalization of linear index models, and are widely used in utility, production, and cost function applications. We also provide an estimator of Gthat is oracle efficient, achieving the same performance as an estimator based on local least squares when H is known.     

Asymptotics for Statistical Treatment Rules

This paper develops asymptotic optimality theory for statistical treatment rules in smooth parametric and semiparametric models. Manski (2000, 2002, 2004) and Dehejia (2005) have argued that the problem of choosing treatments to maximize social welfare is distinct from the point estimation and hypothesis testing problems usually considered in the treatment effects literature, and advocate formal analysis of decision procedures that map empirical data into treatment choices. We develop large‐sample approximations to statistical treatment assignment problems using the limits of experiments framework. We then consider some different loss functions and derive treatment assignment rules that are asymptotically optimal under average and minmax risk criteria.     

Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity

This paper uses control variables to identify and estimate models with nonseparable, multidimensional disturbances. Triangular simultaneous equations models are considered, with instruments and disturbances that are independent and a reduced form that is strictly monotonic in a scalar disturbance. Here it is shown that the conditional cumulative distribution function of the endogenous variable given the instruments is a control variable. Also, for any control variable, identification results are given for quantile, average, and policy effects. Bounds are given when a common support assumption is not satisfied. Estimators of identified objects and bounds are provided, and a demand analysis empirical example is given.