A semiparametric regression model for paired longitudinal outcomes with application in childhood blood pressure development

This research examines the simultaneous influences of height and weight on longitudinally measured systolic and diastolic blood pressure in children. Previous studies have shown that both height and weight are positively associated with blood pressure. In children, however, the concurrent increases of height and weight have made it all but impossible to discern the effect of height from that of weight. To better understand these influences, we propose to examine the joint effect of height and weight on blood pressure. Bivariate thin plate spline surfaces are used to accommodate the potentially nonlinear effects as well as the interaction between height and weight. Moreover, we consider a joint model for paired blood pressure measures, that is, systolic and diastolic blood pressure, to account for the underlying correlation between the two measures within the same individual. The bivariate spline surfaces are allowed to vary across different groups of interest. We have developed related model fitting and inference procedures. The proposed method is used to analyze data from a real clinical investigation.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS567 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

ESTIMATION AND TESTING AN ADDITIVE PARTIALLY LINEAR MODEL IN A SYSTEM OF ENGEL CURVES

The form of the Engel curve has long been a subject of discussion in appliedeconometrics and until now there has no been definitive conclusion about its form. In this paperan additive partially linear model is used to estimate semiparametrically the effect of totalexpenditure in the context of the Engel curves. Additionally, we consider the non-parametricinclusion of some regressors which traditionally have a non linear effect such as age andschooling. To that end we compare an additive partially linear model with the fullynonparametric one using recent popular test statistics. We also provide the p-values computedby bootstrap and subsampling schemes for the proposed test statistics. Empirical analysis basedon data drawn from the Spanish Expenditure Survey 1990-91 shows that modelling the effectsof expenditure, age and schooling on budget share deserves a treatment better than that adoptedin simple semiparametric analysis.Engel curve, expenditure, nonparametric estimation, marginal integration

Mostly Harmless Simulations? Using Monte Carlo Studies for Estimator Selection

We consider two recent suggestions for how to perform an empirically motivated Monte Carlo study to help select a treatment effect estimator under unconfoundedness. We show theoretically that neither is likely to be informative except under restrictive conditions that are unlikely to be satisfied in many contexts. To test empirical relevance, we also apply the approaches to a real-world setting where estimator performance is known. Both approaches are worse than random at selecting estimators which minimise absolute bias. They are better when selecting estimators that minimise mean squared error. However, using a simple bootstrap is at least as good and often better. For now researchers would be best advised to use a range of estimators and compare estimates for robustness

A Robust Estimation of the Effects of Taxation on Charitable Contributions

While many studies find that the tax-price elasticity of giving exceeds unity, several recent studies find the contrary. This is important because it can be shown that if the elasticity exceeds one, then allowing taxpayers to deduct charitable giving from their taxable income is efficient in the sense that the amount donated exceeds the loss to the treasury. Here we use Consumer Expenditure Survey data to estimate the price elasticity of all deductible contributions. Because specification tests reject the consistency of estimators such as Tobit or the two-stage Heckman we use the semiparametric method of Ahn and Powell (1993). Rather than selecting bandwidths through cross-validation we demonstrate that because high and low bandwidths lead to the standard linear model one may use visual inspection for bandwidth selection. We also do not use the covariance matrix estimator of Ahn and Powell, instead bootstrapping a confidence interval. These bootstraps are also used to remove the finite sample bias inherent in nonlinear estimators. In our results we find an elasticity estimate greater than unity for the Tobit and Heckman methods but less than one for the Ahn and Powell method. Because specification tests suggest that the likelihood assumptions ensuring the consistency of the Tobit and Heckman do not hold, our results suggest that previous high tax-price elasticities may be caused by misspecification. However, our estimate of the elasticity of contributions to just social welfare organizations exceeds unity. In this sense the deduction for those types of contributions is efficient.

Functional Regression

Functional data analysis (FDA) involves the analysis of data whose ideal units of observation are functions defined on some continuous domain, and the observed data consist of a sample of functions taken from some population, sampled on a discrete grid. Ramsay and Silverman's 1997 textbook sparked the development of this field, which has accelerated in the past 10 years to become one of the fastest growing areas of statistics, fueled by the growing number of applications yielding this type of data. One unique characteristic of FDA is the need to combine information both across and within functions, which Ramsay and Silverman called replication and regularization, respectively. This article will focus on functional regression, the area of FDA that has received the most attention in applications and methodological development. First will be an introduction to basis functions, key building blocks for regularization in functional regression methods, followed by an overview of functional regression methods, split into three types: [1] functional predictor regression (scalar-on-function), [2] functional response regression (function-on-scalar) and [3] function-on-function regression. For each, the role of replication and regularization will be discussed and the methodological development described in a roughly chronological manner, at times deviating from the historical timeline to group together similar methods. The primary focus is on modeling and methodology, highlighting the modeling structures that have been developed and the various regularization approaches employed. At the end is a brief discussion describing potential areas of future development in this field

Have Econometric Analyses of Happiness Data Been Futile? A Simple Truth About Happiness Scales

Econometric analyses in the happiness literature typically use subjective well-being (SWB) data to compare the mean of observed or latent happiness across samples. Recent critiques show that comparing the mean of ordinal data is only valid under strong assumptions that are usually rejected by SWB data. This leads to an open question whether much of the empirical studies in the economics of happiness literature have been futile. In order to salvage some of the prior results and avoid future issues, we suggest regression analysis of SWB (and other ordinal data) should focus on the median rather than the mean. Median comparisons using parametric models such as the ordered probit and logit can be readily carried out using familiar statistical softwares like STATA. We also show a previously assumed impractical task of estimating a semiparametric median ordered-response model is also possible by using a novel constrained mixed integer optimization technique. We use GSS data to show the famous Easterlin Paradox from the happiness literature holds for the US independent of any parametric assumption

General Semiparametric Shared Frailty Model Estimation and Simulation with frailtySurv

The R package frailtySurv for simulating and fitting semi-parametric shared frailty models is introduced. Package frailtySurv implements semi-parametric consistent estimators for a variety of frailty distributions, including gamma, log-normal, inverse Gaussian and power variance function, and provides consistent estimators of the standard errors of the parameters' estimators. The parameters' estimators are asymptotically normally distributed, and therefore statistical inference based on the results of this package, such as hypothesis testing and confidence intervals, can be performed using the normal distribution. Extensive simulations demonstrate the flexibility and correct implementation of the estimator. Two case studies performed with publicly available datasets demonstrate applicability of the package. In the Diabetic Retinopathy Study, the onset of blindness is clustered by patient, and in a large hard drive failure dataset, failure times are thought to be clustered by the hard drive manufacturer and model