Multivariate methods in rehabilitation

The complexity of relationships between variables in a variety of rehabilitation settings can be appropriately addressed by the use of multivariate methods of statistical analysis. The purpose of this article is to describe (a) some basic concepts and principles of multivariate methods as well as (b) common misconceptions in the application of such methods. Specifically, the authors focus on the use of multivariate analysis of variance (MANOVA) in rehabilitation research and some pitfalls that rehabilitation researchers face when choosing between MANOVA for a set of outcome variables versus separate analyses of variance (ANOVAs) for each outcome variable. Examples of the use of MANOVA in rehabilitation research, as well as references to other multivariate methods, are also provided.     

Using and interpreting analogue designs

Researchers in rehabilitation counseling and disability studies sometimes use analogue research, which involves materials that approximate or describe reality (e.g., written vignettes, videotaped exemplars) rather than investigating phenomena in real-world settings. Analogue research often utilizes experimental designs, and it thereby frequently possesses a high degree of internal validity. Analogue research allows investigators to exercise tight control over the implementation of the independent or treatment variable and over potentially confounding variables, which enables them to isolate the effects of those treatment variables on selected outcome measures. However, the simulated nature of analogue research presents an important threat to external validity. As such, the generalizability of analogue research to real-life settings and situations may be problematic. These and other issues germane to analogue research in vocational rehabilitation are discussed in this article, illustrated with examples from the contemporary literature.     

Evaluating the Effective Degrees of Freedom of the Delete-a-Group Jackknife

The delete-a-group jackknife is sometimes used when estimating the variances of statistics based on a large sample. We investigate heavily poststratified estimators for a population mean and a simple regression coefficient, where both full-sample and domain estimates are of interest. The delete-a-group (DAG) jackknife employing 30, 60, and 100 replicates is found to be highly unstable, even for large sample sizes. The empirical degrees of freedom of these DAG jackknives are usually much less than their nominal degrees of freedom. This analysis calls into question whether coverage intervals derived from replication-based variance estimators can be trusted for highly calibrated estimates.     

THE GREAT OVERESTIMATION: TAX DATA AND INEQUALITY MEASUREMENTS IN THE UNITED STATES, 1913–1943

Historical measures of income inequality in the United States must grapple with the challenge of data quality. We examine one such problem affecting the well-known estimates of income inequality produced by Piketty and Saez (2003) using the records of the Internal Revenue Service (IRS). Prior to 1943, incomes were self-reported. Combined with lax enforcement on the part of the IRS, self-reporting of incomes could provide a misleading portrait of the income distribution. To test the accuracy of IRS records, we compare them to independently tabulated state income tax returns between 1919 and 1945 from states with more comprehensive and rigorously enforced tax collection procedures. State income tax records show lower overall levels of income inequality than IRS records. However, we still find that top income concentrations declined across the period between 1929 and World War II. These findings attest to the sensitivity of distributional estimation to the reporting selectivity and economic quality of underlying tax data, suggesting that the existing IRS-derived series systematically overstates top-income concentration in the interwar period. (JEL H2, N32, D31, E01)     

Economic Evaluation of Scale Dependent Technology Investments

We study the effect of financial risk on the economic evaluation of a project with capacity decisions. Capacity decisions have an important effect on the project̂s value through the up‐front investment, the associated operating cost, and constraints on output. However, increased scale also affects the financial risk of the project through its effect on the operating leverage of the investment. Although it has long been recognized in the finance literature that operating leverage affects project risk, this result has not been incorporated in the operations management literature when evaluating projects. We study the decision problem of a firm that must choose project scale. Future cash flow uncertainty is introduced by uncertain future market prices. The firm's capacity decision affects the firm's potential sales, its expected price for output, and its costs. We study the firm's profit maximizing scale decision using the CAPM model for risk adjustment. Our results include that project risk, as measured by the required rate of return, is related to the inverse of the expected profit per unit sold. We also show that project risk is related to the scale choice. In contrast, in traditional discounted cash flow analysis (DCF), a fixed prescribed rate is used to evaluate the project and choose its scale. When a fixed rate is used with DCF, a manager will ignore the effect of scale on risk and choose suboptimal capacity that reduces project value. S/he will also misestimate project value. Use of DCF for choosing scale is studied for two special cases. It is shown that if the manager is directed to use a prescribed discount rate that induces the optimal scale decision, then the manager will greatly undervalue the project. In contrast, if the discount rate is set to the risk of the optimally‐scaled project, the manager will undersize the project by a small amount, and slightly undervalue the project with the economic impact of the error being small. These results underline the importance of understanding the source of financial risk in projects where risk is endogenous to the project design.     

More social than capital: Social capital accumulation through social network exchange among legal and unauthorized Mexican migrants

Social capital is frequently used to explain many policy related outcomes, but research has not adequately explained how it is accumulated. It is unclear whether the economic or social characteristics of others in a social network motivate social capital accumulation. This lack of understanding has called some to question social capital's efficacy. Employing data from a survey of randomly selected foreign-born Mexicans in Los Angeles County, the influence of social and economic characteristics of a migrant's social network members are estimated. Results suggest a negative association with social capital accumulation for Mexican migrants with a social network member outside their neighborhood. Having married social network members is positively associated for legal Mexicans, while having network members who work in occupations requiring more social skills is positively associated for unauthorized Mexicans accumulating social capital. Measures of human and financial capital are not associated with the probability of developing social capital.