Bayesian quantile regression for single-index models

Using an asymmetric Laplace distribution, which provides a mechanism for Bayesian inference of quantile regression models, we develop a fully Bayesian approach to fitting single-index models in conditional quantile regression. In this work, we use a Gaussian process prior for the unknown nonparametric link function and a Laplace distribution on the index vector, with the latter motivated by the recent popularity of the Bayesian lasso idea. We design a Markov chain Monte Carlo algorithm for posterior inference. Careful consideration of the singularity of the kernel matrix, and tractability of some of the full conditional distributions leads to a partially collapsed approach where the nonparametric link function is integrated out in some of the sampling steps. Our simulations demonstrate the superior performance of the Bayesian method versus the frequentist approach. The method is further illustrated by an application to the hurricane data.     

The classification accuracy of four problem gambling assessment instruments in population research

Improved methodology was used to re-examine the weak correspondence between problem and pathological gamblers identified in population surveys and subsequent classification of these individuals in clinical interviews. The SOGS-R, the CPGI, the NODS and the Problem and Pathological Gambling Measure (PPGM), as well as questions about gambling participation and expenditures, were administered to a total of 7272 adults. Two clinicians then assessed each person's status, based on comprehensive written profiles derived from these questionnaire responses. Instrument classification was then compared to clinical classification. All four instruments correctly classified most non-problem gamblers (i.e. had good to excellent sensitivity, specificity and negative predictive power). However, the PPGM was the only instrument with good classification of problem gamblers (i.e. excellent sensitivity and positive predictive power). The CPGI and SOGS-R had weak positive predictive power and the NODS had only adequate sensitivity and positive predictive power. Improvement in the classification accuracy of the CPGI occurred when a 5+ cut-off was used and when a 4+ cut-off was used with the SOGS. In general, the classification accuracy of the NODS, SOGS and CPGI is better than prior research suggested but overall accuracy is still modest. With adjusted cut-offs, all three instruments are reasonably congruent with clinical ratings.     

Slope Estimation for Bivariate Longitudinal Outcomes Adjusting for Informative Right Censoring Using Discrete Survival Model: Application to the Renal Transplant Cohort

Patients undergoing renal transplantation are prone to graft failure which causes lost of follow-up measures on their blood urea nitrogen and serum creatinine levels. These two outcomes are measured repeatedly over time to assess renal function following transplantation. Loss of follow-up on these bivariate measures results in informative right censoring, a common problem in longitudinal data that should be adjusted for so that valid estimates are obtained. In this study, we propose a bivariate model that jointly models these two longitudinal correlated outcomes and generates population and individual slopes adjusting for informative right censoring using a discrete survival approach. The proposed approach is applied to the clinical dataset of patients who had undergone renal transplantation. A simulation study validates the effectiveness of the approach.     

Strong laws of large numbers for dependent heterogeneous processes: a synthesis of recent and new results

This paper surveys recent developments in the strong law of large numbers for dependent heterogeneous processes. We prove a generalised version of a recent strong law for Lz-mixingales, and also a new strong law for Lpmixingales. These results greatly relax the dependence and heterogeneity conditions relative to those currently cited, and introduce explicit trade-offs between dependence and heterogeneity. The results are applied to proving strong laws for near-epoch dependent functions of mixing processes. We contrast several methods for obtaining these results, including mapping directly to the mixingale properties, and applying a truncation argument.     

Cointegration modeling of fertility in the United States

This paper presents estimates of a multiple time series model of fertility, female labor force participation, women's wages, and the relative cohort size of younger to older adult males. Cointegration methods permit modeling of these nonstationary variables, yielding estimates of the long-run relation among the variables, and the dynamic response of each variable to displacements from the steady state. The estimated steady state relation between fertility and the other variables is consistent with economic models of fertility, with fertility negatively related to female wages and male relative cohort size. Fertility responds to cohort size in a manner that is consistent with Easterlin's relative income model of household behavior. Finally, both female labor market variables adjust significantly to departures from the steady state relation, implying that they cannot be treated as exogenous in time series models of fertility.     

Moment expressions and summary statistics for the complete and truncated weibull distribution

Traditionally, the moments of the Weibull distribution have been calculated using the standard Weibull (Johnson and Kotz, 1970) . This article will expand on that idea and cover the truncated cases for the standard Weibull distributions. Also, the same techniques used for the standard form will be used to derive the moment expressions for the three-parameter complete and truncated Weibull distributions. The summary statistics are then calculated from the moment expressions. Weibull moments involve the gamma and incomplete gamma functions.     

Shy but Getting By? An Examination of the Complex Links Among Shyness,Coping, and Socioemotional Functioning in Childhood

The purpose of the current study was to test a conceptual model of the mediated and moderated associations among shyness, coping strategies, and socioemotional functioning in middle childhood. Participants were 358 children (177 boys) aged 9–13 years (M = 10.16 years, SD =.95). Children completed self‐report assessments of shyness, coping style in response to a social stressor, internalizing problems, and peer difficulties. Among the results, shyness was positively associated with internalizing symptoms and negatively related to perceptions of peer difficulties. However, both of these associations were partially mediated by internalizing coping styles. Moreover, problem‐solving coping moderated these mediated pathways: among children who reported higher levels of problem‐solving coping, the associations between internalizing coping and outcomes were attenuated. Several gender differences also emerged, suggesting that problem‐solving coping may be particularly useful for shy boys. Results are discussed in terms of the complex but potentially critical role of coping in shy children's socioemotional functioning.