A Monte Carlo study compared 14 methods to test the statistical significance of the intervening variable effect. An intervening variable (mediator) transmits the effect of an independent variable to a dependent variable. The commonly used R. M. Baron and D. A. Kenny (1986) approach has low statistical power. Two methods based on the distribution of the product and 2 difference-in-coefficients methods have the most accurate Type I error rates and greatest statistical power except in 1 important case in which Type I error rates are too high. The best balance of Type I error and statistical power across all cases is the test of the joint significance of the two effects comprising the intervening variable effect.

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A comparison of methods to test mediation and other intervening variable effects.

Mediation models are widely used, and there are many tests of the mediated effect. One of the most common questions that researchers have when planning mediation studies is, "How many subjects do I need to achieve adequate power when testing for mediation?" This article presents the necessary sample sizes for six of the most common and the most recommended tests of mediation for various combinations of parameters, to provide a guide for researchers when designing studies or applying for grants.

/pdf/required-sample-size-to-detect-the-mediated-effect-gv4evnzl6h.pdf

Required Sample Size to Detect the Mediated Effect

This is an invited expository article for The American Statistician. It reviews the nonparametric estimation of statistical error, mainly the bias and standard error of an estimator, or the error rate of a prediction rule. The presentation is written at a relaxed mathematical level, omitting most proofs, regularity conditions, and technical details.

/pdf/a-leisurely-look-at-the-bootstrap-the-jackknife-and-cross-5b6li2d91n.pdf

A Leisurely Look at the Bootstrap, the Jackknife, and Cross-Validation

On introduit une nouvelle classe de fonctions de densite dependant du parametre de forme λ, telles que λ=0 corresponde a la densite normale standard

A class of distributions which includes the normal ones

This paper proposes a simple modification of a conventional method of moments estimator for a discrete response model, replacing response probabilities that require numerical integration with estimators obtained by Monte Carlo simulation. This method of simulated moments (MSM) does not require precise estimates of these probabilities for consistency and asymptotic normality, relying instead on the law of large numbers operating across observations to control simulation error, and hence can use simulations of practical size. The method is useful for models such as high-dimensional multinomial probit (MNP), where computation has restricted applications.

A method of simulated moments for estimation of discrete response models without numerical integration

/pdf/tables-for-computing-bivariate-normal-probabilities-4f0vsrf8gb.pdf

Tables for Computing Bivariate Normal Probabilities

Integrals of functions of the univariate, bivariate, trivariate and multivariate normal densities are given. Both indefinite and definite integrals are included.

A table of normal integrals

The exact distributions of the estimated process capability indices are presented and their means, variances, and mean-squared errors are given. The basic assumption is that the process measurements are taken from a normal distribution. Theresults in this article are useful in evaluating process capability.

On the distributions of the estimated process capability indices

Lower confidence limits are derived for the common measures of process capability, usually indicated by Cp, CPU, CPL, and Cpk. The measures are estimated based on a random sample of observations from the process when the process is assumed to be normall..

Lower confidence limits on process capability indices.

A general procedure for reducing the bias of point estimators is introduced. The technique includes the “jackknife” as a special case. The existing notion of reapplication is shown to lack a desirable bias removal property for which it was originally designed. Proper reapplication is proposed to conform to the general notion of higher order bias elimination and an interesting algorithm for the correct method is defined. Illustrative examples are drawn from ratio estimation, reliability and truncated distributions. The reduced mean square error which attracted some attention to the jackknife is present in the generalization for some applications.

Donald B. Owen

Papers

Tables for Computing Bivariate Normal Probabilities

A table of normal integrals

On the distributions of the estimated process capability indices

Lower confidence limits on process capability indices.

On Bias Reduction in Estimation