A Bayesian approach to non-parametric monotone function estimation

Summary.  The paper proposes two Bayesian approaches to non-parametric monotone function estimation. The first approach uses a hierarchical Bayes framework and a characterization of smooth monotone functions given by Ramsay that allows unconstrained estimation. The second approach uses a Bayesian regression spline model of Smith and Kohn with a mixture distribution of constrained normal distributions as the prior for the regression coefficients to ensure the monotonicity of the resulting function estimate. The small sample properties of the two function estimators across a range of functions are provided via simulation and compared with existing methods. Asymptotic results are also given that show that Bayesian methods provide consistent function estimators for a large class of smooth functions. An example is provided involving economic demand functions that illustrates the application of the constrained regression spline estimator in the context of a multiple-regression model where two functions are constrained to be monotone.     

A robust multivariate measurement error model with skew-normal/independent distributions and Bayesian MCMC implementation

Skew-normal/independent distributions are a class of asymmetric thick-tailed distributions that include the skew-normal distribution as a special case. In this paper, we explore the use of Markov Chain Monte Carlo (MCMC) methods to develop a Bayesian analysis in multivariate measurement errors models. We propose the use of skew-normal/independent distributions to model the unobserved value of the covariates (latent variable) and symmetric normal/independent distributions for the random errors term, providing an appealing robust alternative to the usual symmetric process in multivariate measurement errors models. Among the distributions that belong to this class of distributions, we examine univariate and multivariate versions of the skew-normal, skew-t, skew-slash and skew-contaminated normal distributions. The results and methods are applied to a real data set.     

Amplification of Sensitivity Analysis in Matched Observational Studies

A sensitivity analysis displays the increase in uncertainty that attends an inference when a key assumption is relaxed. In matched observational studies of treatment effects, a key assumption in some analyses is that subjects matched for observed covariates are comparable, and this assumption is relaxed by positing a relevant covariate that was not observed and not controlled by matching. What properties would such an unobserved covariate need to have to materially alter the inference about treatment effects? For ease of calculation and reporting, it is convenient that the sensitivity analysis be of low dimension, perhaps indexed by a scalar sensitivity parameter, but for interpretation in specific contexts, a higher dimensional analysis may be of greater relevance. An amplification of a sensitivity analysis is defined as a map from each point in a low dimensional sensitivity analysis to a set of points, perhaps a 'curve,' in a higher dimensional sensitivity analysis such that the possible inferences are the same for all points in the set. Possessing an amplification, an investigator may calculate and report the low dimensional analysis, yet have available the interpretations of the higher dimensional analysis.     

Deletion residuals in the detection of heterogeneity of variances in linear regression

The heterogeneity of error variance often causes a huge interpretive problem in linear regression analysis. Before taking any remedial measures we first need to detect this problem. A large number of diagnostic plots are now available in the literature for detecting heteroscedasticity of error variances. Among them the ‘residuals’ and ‘fits’ (R–F) plot is very popular and commonly used. In the R–F plot residuals are plotted against the fitted responses, where both these components are obtained using the ordinary least squares (OLS) method. It is now evident that the OLS fits and residuals suffer a huge setback in the presence of unusual observations and hence the R–F plot may not exhibit the real scenario. The deletion residuals based on a data set free from all unusual cases should estimate the true errors in a better way than the OLS residuals. In this paper we propose ‘deletion residuals’ and the ‘deletion fits’ (DR–DF) plot for the detection of the heterogeneity of error variances in a linear regression model to get a more convincing and reliable graphical display. Examples show that this plot locates unusual observations more clearly than the R–F plot. The advantage of using deletion residuals in the detection of heteroscedasticity of error variance is investigated through Monte Carlo simulations under a variety of situations.     

Homicide Rates in a Cross‐Section of Countries: Evidence and Interpretations

This study uses a regression analysis to explore the cross‐country variation in homicide rates for a large sample of countries. It starts by identifying seven significant regional variables, to which traditional socioeconomic, cultural, and institutional variables are added and tested. The importance of institutions, culture, and other factors affecting homicide rates is discussed. One unexpected finding is a curious relationship between the level of education and homicide rates: while an increase in male education tends to reduce homicide rates, an increase in female education tends to increase homicides. Several possible interpretations for this phenomenon are proposed. The study points to relatively unexplored areas of research in order to better understand homicide variation around the world.     

Geometric Anisotropic Spatial Point Pattern Analysis and Cox Processes

We consider spatial point processes with a pair correlation function, which depends only on the lag vector between a pair of points. Our interest is in statistical models with a special kind of ‘structured’ anisotropy: the pair correlation function is geometric anisotropic if it is elliptical but not spherical. In particular, we study Cox process models with an elliptical pair correlation function, including shot noise Cox processes and log Gaussian Cox processes, and we develop estimation procedures using summary statistics and Bayesian methods. Our methodology is illustrated on real and synthetic datasets of spatial point patterns.     

Using nursing students to enhance one college's immunization program.

In New York State, all college students who were born on or after January 1, 1957, are required to show proof of immunity against measles, mumps, and rubella (MMR) before the 1st day of classes. Colleges have established immunization programs so that those students who do not have the required proof can be given the necessary injections. Often, our health service office does not have enough staff to administer the MMR shots during the registration period, resulting in long lines of students waiting to be immunized. In this article, the authors describe how one college used nursing students to assist with and enhance its immunization program. The 45 nursing students who participated in this project administered 694 injections over a 5-day period, They received credit from the nursing department for clinical time and all of the participants agree that the project was a success.     

Occupational stress in universities: Staff perceptions of the causes,consequences and moderators of stress

In recent years, the Australian university sector has undergone large-scale organizational change, including restructuring, downsizing and government funding cuts. At the same time, research from across the globe reports an alarming increase in the occupational stress experienced by university staff. We report on the first phase of a longitudinal investigation of occupational stress. A total of 22 focus groups were conducted with a representative sample of 178 academic and general staff from 15 Australian universities. The groups focused on understanding staff 's experience of occupational stress, and perceptions of the sources, consequences and moderators of stress. Both general and academic staff reported a dramatic increase in stress during the previous 5 years. As a group, academic staff reported higher levels of stress than general staff. Five major sources of stress were identified including: insufficient funding and resources; work overload; poor management practice; job insecurity; and insufficient recognition and reward. The majority of groups reported that job-related stress was having a deleterious impact on their professional work and personal welfare. Aspects of the work environment (support from co-workers and management, recognition and achievement, high morale, flexible working conditions), and personal coping strategies (stress management techniques, work/ non-work balance, tight role boundaries and lowering standards), were reported to help staff cope with stress. The findings provide a timely insight into the experience of stress within universities.     

Evaluation in the Social Studies

Online role-playing games such as World Of Warcraft represent new participatory cultures in which today's students engage every day. They are appealing to players largely because of the social aspects of game play. Some features of massively multiplayer online role-playing games (MMORPGs) can be incorporated into classroom culture to create more dynamic interactions between students and improve both content instruction and civic competence.