Leon Jay Gleser

A meta-analytic evaluation of couples weight-loss programs.

Applied Hedges and Olkins (1985) statistical meta-analytic procedures to summary data from all published studies that compared behavioral weight-control programs that formally involved partners in treatment (couples programs) to similar programs in which subjects participated alone (subject-alone programs). Based on tests of effect sizes, couples programs are significantly superior to subject-alone programs at posttreatment (p less than .05). A nearly significant (p = .06) statistical superiority for couples programs versus subject-alone programs is also found at 2- to 3-month follow-up, but not thereafter. The couples programs differed in the kinds of social support provided by partners, and the most productive kinds of partner support remain to be identified. In particular, the use of partners in providing social support to subjects after formal therapy has ended is still an area of largely unexplored potential.

Models for estimating the number of unpublished studies.

The possible existence of unreported studies can cast doubt on the conclusions of a meta-analytic summary of the literature, particularly if there is reason to believe that there is a publication bias against non-significant results. The present article proposes two general models that describe how the preponderance of published studies could report significant p-values even when testing a null hypothesis that is, in fact, true. Each such model allows one to estimate the number, N, of unpublished studies using the p-values reported in the published studies; the meta-analyst can then evaluate the plausibility of this estimated value of N, or related confidence bounds. Use of models of the kind suggested here allows meta-analysts to assess the problem of unpublished studies from various perspectives and thus can lead to greater understanding of, and confidence in, meta-analytic conclusions.

The Gamma Distribution as a Mixture of Exponential Distributions

Abstract A gamma distribution with arbitrary scale parameter θ and shape parameter r < 1 can be represented as a scale mixture of exponential distributions.

The Importance of Assessing Measurement Reliability in Multivariate Regression

Abstract In many contexts involving multivariate linear regression models, some or all of the independent (predictor) variables are measured with error. It is argued that if the goal is to assess the relationship of the dependent variables to the true predictor variables, then it is important to determine the reliability matrix Λ of the measurement X of the vector of true predictors. If Λ is singular, then the slope matrix B is not identifiable. If Λ is nearly singular, then B cannot be accurately estimated. A two-step estimation procedure is proposed in which Λ is estimated from data on the measured predictors X and on prior information from reliability studies on these predictors and the parameters of the (latent) linear relationship are estimated by classical linear regression methods. This approach not only allows the use of available software but also lends itself to traditional diagnostic methods. Large-sample properties of the estimators resulting from this approach are derived. It is shown how a c...

Estimating the Mean of a Normal Distribution with Known Coefficient of Variation

Abstract Estimation of the mean θ of a normal distribution N(θ, aθ2) with known coefficient of variation a 1/2 is treated as a decision problem with squared-error loss. It is shown that all estimators linear in the sample mean and sample standard deviation s, as well as the maximum likelihood estimator (MLE), are dominated in risk by the admissible, minimum risk, scale equivariant estimator . A class of Bayes estimators against inverted-gamma priors is constructed, and shown to include within its closure. All members of this latter class, as well as , can be easily computed using continued fractions.

Comparison of Least Squares and Errors-in-Variables Regression, with Special Reference to Randomized Analysis of Covariance

Abstract In an errors-in-variables regression model, the least squares estimate is generally inconsistent for the complete regression parameter but can be consistent for certain linear combinations of this parameter. We explore the conjecture that, when the least squares estimate is consistent for a linear combination of the regression parameter, it will be preferred to an errors-in-variables estimate, at least asymptotically. The conjecture is false, in general, but it is true for some important classes of problems. One such problem is a randomized two-group analysis of covariance, upon which we focus.

Exact Power of Goodness-of-Fit Tests of Kolmogorov Type for Discontinuous Distributions

Abstract Goodness-of-fit tests of Kolmogorov type reject a null hypothesis H 0 : F(x) = F*(x) whenever the graph of the sample cumulative distribution function crosses one of two boundary functions, G 1(x), G 2(x). The best-known example of a test of this type is the Kolmogorov—Smirnov test D. When the true cumulative distribution function F(x) is continuous, a number of algorithms are available for calculating the exact powers of such tests. In this article it is shown that such algorithms can also be used to calculate the exact power and level of significance of Kolmogorov-type goodness-of-fit tests when F(x) is discontinuous.

A Canonical Representation for the Noncentral Wishart Distribution Useful for Simulation

Abstract This article provides a simple distributional representation for the noncentral Wishart distribution most useful when the noncentrality matrix is of less than full rank. It is shown that the representation leads to a method for simulating a noncentral Wishart matrix that has advantages over a procedure currently used.

Simex approaches to measurement error in roc studies

This paper explores the estimation of the area under the ROC curve when test scores are subject to errors. The naive approach that ignores measurement errors generally yields inconsistent estimates. Finding the asymptotic bias of the naive estimator, Coffin and Sukhatme (1995, 1997) proposed bias-corrected estimators for parametric and nonparametric cases. However, the asymptotic distributions of these estimators have not been developed because of their complexity. We propose several alternative approaches, including the SIMEX procedure of Cook and Stefanski (1994). We also provide the asymptotic distributions of the SIMEX estimators for use in statistical inference. Small simulation studies illustrate that the SIMEX estimators perform reasonably well when compared to the bias-corrected estimators.

Inference about comparative precision in linear structural relationships

Abstract We study point and confidence region estimators of the precisions of instruments, and of the ratios of such precisions to the precision of a standard instrument, in situations where a nonreplicated linear structural model describes the measurements simultaneously obtained from several instruments. Some drawbacks of maximum likelihood estimators of the precision ratios are noted. A union-intersection test for the null hypothesis H0 that the standard instrument is at least as precise as the other instruments is proposed for situations where the relative precision of the standard instrument is known.