Thomas J. Tomberlin

Empirical Bayes Small-Area Estimation Using Logistic Regression Models and Summary Statistics

Many available methods for estimating small area parameters are model-based, where auxiliary variables are used to predict the variable of interest. For nonlinear models, prediction is not straightforward. MacGibbon and Tomberlin (1989) and Farrell, MacGibbon, and Tomberlin (1994) have proposed methods which require micro-data for each individual in a small area. Here, the authors use a second-order Taylor series expansion to obtain model-based predictions which only require local area summary statistics in the case of either continuous or categorical auxiliary variables. The methodology is evaluated using U.S. census data.

Predicting Accident Frequencies for Drivers Classified by Two Factors

Abstract For predicting accident frequencies, a succession of log-linear models for Poisson data, some of which include nested random effects, is introduced. By applying maximum likelihood and empirical Bayes estimation techniques to these models, one can incorporate the actuarial notions of risk classification, model-based smoothing, credibility theory, and experience rating under a unified statistical approach to loss prediction. The performance of these methods is evaluated by using accident data from California.

Outlier detection for a hierarchical Bayes model in a study of hospital variation in surgical procedures

One of the most important aspects of profiling healthcare providers or services is constructing a model that is flexible enough to allow for random variation. At the same time, we wish to identify those institutions that clearly deviate from the usual standard of care. Here, we propose a hierarchical Bayes model to study the choice of surgical procedure for rectal cancer using data previously analysed by Simons et al.1 Using hospitals as random effects, we construct a computationally simple graphical method for determining hospitals that are outliers; that is, they differ significantly from other hospitals of the same type in terms of surgical choice.

Statistical Evidence in Employment Discrimination Cases

Statistical methods in general, and multiple regression analysis in particular, are being used increasingly to provide evidence in employment discrimination cases. While the technical issues involved in using statistical methods to detect discrimination are straightforward, the conceptual issues are much less clearly understood. This article provides a framework to help clarify the conditions under which an estimated effect can be properly attributed to discrimination. Several interrelated issues have caused particular confusion, including the distinction between disparate impact and disparate treatment, the definition of test bias, the use of “reverse regression,” proxy variables for true productivity, and measurement error. A simple mathematical model is developed to analyze the precise nature of these issues. It is concluded that although employment discrimination cases involve all the usual problems involved in causal inference from observational data, certain aspects of the legal context may facilitate the valid application of statistical techniques.

A Focus on Engagement: Defining, Measuring, and Nurturing a Key Pillar of AACSB Standards

ABSTRACT The 2013 Association to Advance Collegiate Schools of Business (AACSB) Standards emphasize three “pillars” upon which schools accredited by the association must regularly demonstrate quality improvement, namely, impact, innovation, and engagement. Focusing on the last of these, our article examines the concept of engagement through both a content analysis of the 2013 AACSB Standards and an empirical study exploring different types of course-level engagement within an undergraduate business course (measured using the Student Course Engagement Questionnaire; Handelsman, Briggs, Sullivan, & Towler, 2005). The results of our content analysis of the 2013 AACSB Standards underscore the focus placed on engagement within the AACSB documentation. However, it is also noted that the definition of engagement within the AACSB Standards is somewhat vague. The findings of our empirical study (N = 142) suggest that students were engaged in the course and that three of the four types of engagement measured (skills, participation/interaction, and performance engagement) were positively correlated with final performance in the course.