Daniel A. Relles

Tools for Intuition about Sample Selection Bias and Its Correction

The authors provide mathematical tools to assist intuition about selection bias in concrete empirical analyses. These new tools do not offer a general solution to the selection bias problem; no method now does that. Rather, the techniques they present offer a new decomposition of selection bias. This decomposition permits an analyst to develop intuition and make reasoned judgments about the sources, severity, and direction of sample selection bias in a particular analysis. When combined with simulation results, also presented in this paper, their decomposition of bias also permits a reasoned, empirically-informed judgment of when the well-known two-step estimator of J. Heckman is likely to increase or decrease the accuracy of regression coefficient estimates. The authors also use simulations to confirm mathematical derivations

Theory Testing in a World of Constrained Research Design

Because censored sampling is often unavoidable in much sociological data analysis, computationally simple corrections of censoring bias would be useful. Heckmans correction is simple to compute, widely used, and proven asymptotically correct under certain assumptions, but its limitations in practical situations are not well known in sociology. Here, we overview prior criticisms of Heckmans estimator, and we consider the case in which its normality assumptions are satisfied, censoring rates are high, and sample sizes are small. Results of 14,400 analyses of computer-generated simulation data suggest that Heckmans method performs well under certain circumstances, but that it very frequently worsens estimates, especially under conditions that are likely to be present in sociological data. Thus, the technique is probably not a general cure for censoring bias in sociology, except perhaps where strong theory permits certain strong assumptions. We reconsider censored sampling correction strategies in the context of statistical analysis as a theory-building tool, with emphasis on research strategy in the presence of irremediable censoring bias.

Demand-based assessment of workforce requirements for orthopaedic services.

On the basis of an analysis of the supply of and demand for orthopaedic surgeons, we projected that there will be 21,134 full-time-equivalent orthopaedists in the year 2010 if training continues at current levels. We estimated a demand-based requirement of 17,012 full-time-equivalent orthopaedic surgeons, indicating a surplus of 4122 full-time equivalents. In terms of orthopaedist-to-population ratios, we estimated that there will be 7.5 full-time-equivalent orthopaedists per 100,000 population in 2010 compared with a demand-based requirement of 6.0 full-time equivalents. However, we did not include estimates of the demand for orthopaedic surgeons as assistants in the operating room in our model. If an assistant orthopaedic surgeon is required for all procedures, an additional 3906 full-time-equivalent orthopaedists would be demanded, thus eliminating the surplus. The demand for an assistant orthopaedic surgeon in only half of the procedures would still lead to a sizable reduction in the surplus.

Estimating Eye Care Workforce Supply and Requirements

PURPOSE To estimate the workforce supply and requirements for eye care in the United States. METHODS Three models were constructed for analysis: supply of providers, public health need for eye care, and demand (utilization) for eye care. Ophthalmologists, other physicians, and optometrists were included in the models. Public health need was determined by applying condition-specific prevalence and incidence rates from population-based and other epidemiologic studies. Demand was determined by use of national databases, such as the National Ambulatory Care Survey, National Hospital Discharge Survey, and Medicare Part B. Time requirements for care were obtained through a stratified sample survey of the membership of the American Academy of Ophthalmology. RESULTS Under modeling assumptions that use a work-time ratio of one between optometrists and ophthalmologists and between specialist and generalist ophthalmologists, a significant excess of eye care providers exists relative to both public health need and demand. Changes in the work-time ratio, work-hours per year per provider, care patterns for the same condition, or other factors could significantly reduce or eliminate the surplus relative to need. CONCLUSION If optometrists are the preferred primary eye care provider, ophthalmologists would be in excess under all demand scenarios and all need scenarios where the optometrist to ophthalmologist work-time ratio is greater than 0.6. No excess of ophthalmologists would exist if ophthalmologists are the preferred primary eye care provider. Data on the appropriate work time ratio will help refine estimates of the imbalance between supply and requirements.

Foreign student academic performance in U.S. Graduate schools: Insights from American MBA programs☆

Abstract Foreign citizens are a rapidly growing, important segment of the graduate student population of the United States. Their academic success in American universities has important consequences for them, for the countries which send them here, and for the departments in which they study. However, past research on graduate student academic performance appears to have (1) generally excluded foreign students, perhaps inadvertantly, (2) included factors which are difficult or impossible to measure for most foreign students, and (3) excluded important factors—mostly English fluency and country of origin—which are invariant for native-born American graduate students, but not for foreign graduate students. These shortcomings do not diminish the applicability of previous findings to nonforeign graduate students, but they do imply that previous empirical results may tell us little about educational performance of foreign graduate students in the United States. Our purpose here is to develop testable hypotheses about factors which affect foreign student academic performance and to use data from MBA programs to test those conjectures. Our efforts focus on the impact of English fluency and country of origin, but also include abilities measured by standardized admission tests, which have dominated results of analyses of academic performance by nonforeign graduate students. Findings suggest that country-of-origin effects persist after holding constant academic ability and English language fluency. Other findings, some surprising, are reported and interpreted.

Clustering by Identification with Special Application to Two-Way Tables of Counts

Abstract The formation of a partition of objects, each with an associated random measurement X, is given operational meaning and a figure of merit. The information about X, given each object, is first reduced to information about X, given the cluster in the partition to which that object belongs. The figure of merit for a partition is then the probability of a correct object identification, on the basis of a realization of X, after the information loss. An algorithm is derived for performing the calculations on two-way tables of counts.

The Utility of Empirical Bayes Methods for Comparing Regression Structures in Small Subsamples

Empirical Bayes (EB) techniques have considerable potential for extracting useful information from data in which sample subgroups are small and suspected of having been drawn from population subgroups in which substantively interesting processes are governed by parameters with different values. This paper explicates these methods at a nontechnical level illustrates their use in an application to graduate school academic performance of foreign students in US graduate schools of business and compares results obtained with EB methods to results obtained with more common least squares techniques. This paper reviews the basic principles of EB analysis as well as certain past applications of EB methods to substantive questions which bear some similarity to those commonly addressed by sociologists. The next section explicates the procedures used to estimate the posterior distribution of Bi the vector of regression coefficients for the ith group. 2 basic methodological conclusions are drawn from the EB and the ordinary least squares analyses. 1st though the absence of convenient computer software for EB regression analysis is a nuisance the authors are much impressed with the power of EB to estimate population parameters from small sample data which tend to overwhelm ordinary least squares with random fluctuation. Secondly the average within-group EB and ordinary least squares estimates are about the same although much more computation and effort is required to calculate that average with EB than with ordinary least squares. Thus if the substantive questions one poses can be answered with the average within-group effect then one may just as well use the simpler ordinary least squares methods to approximate that average. But when the specific within-group effects are important then the advantages of EB seem to be considerable and well worth the additional effort required.