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.

The most commonly used method to test an indirect effect is to divide the estimate of the indirect effect by its standard error and compare the resulting z statistic with a critical value from the standard normal distribution. Confidence limits for the indirect effect are also typically based on critical values from the standard normal distribution. This article uses a simulation study to demonstrate that confidence limits are imbalanced because the distribution of the indirect effect is normal only in special cases. Two alternatives for improving the performance of confidence limits for the indirect effect are evaluated: (a) a method based on the distribution of the product of two normal random variables, and (b) resampling methods. In Study 1, confidence limits based on the distribution of the product are more accurate than methods based on an assumed normal distribution but confidence limits are still imbalanced. Study 2 demonstrates that more accurate confidence limits are obtained using resampling methods, with the bias-corrected bootstrap the best method overall.

/pdf/confidence-limits-for-the-indirect-effect-distribution-of-2yv44tb6it.pdf

Confidence Limits for the Indirect Effect: Distribution of the Product and Resampling Methods.

nities and the individuals who live in them, and may be especially beneficial in poor neighborhoods. In contrast, a social isolation perspective proposes that neighborhood stability has negative effects on residents'psychological well-being in economically disadvantaged neighborhoods. This analysis of multilevel data-data in which survey information from a representative sample of Illinois residents is linked to census-tract information about poverty and stability in their neighborhoodsupports a social isolation perspective. In affluent neighborhoods, stability is associated with low levels of distress; under conditions of poverty the opposite is true. In part this occurs because residents of poor, stable neighborhoods face high levels of disorder in their neighborhoods. Stability does not reduce perceived disorder under conditions of poverty, as it does in more affluent neighborhoods, which leaves residents feeling powerless to leave a dangerous place. Finally, the negative effects of poor, stable neighborhoods on residents'psychological well-being do not stem from a lack of social ties among neighbors. N EIGHBORHOOD stability traditionally has been heralded as a boon to quality of life, but stability's influence may not always be positive. We extend the research on neighborhood stability by showing how the benefits of stability for individual psychological well-being depend on the local economic context. We make three contributions. First, we directly assess residents' psychological distress, measured as depression and anxiety. We depart from the tradition of considering crime as the ultimate outcome and instead examine the effects of neighborhood stability and poverty on the psychological well-being of residents. Second, we examine the effects of residential stability across different types of neighborhoods because the effect of neighborhood stability on psychological well-being may depend on economic context. Third, we investigate whether physical and social disorder in the neighborhood mediates the joint effect of neighborhood stability and poverty on distress because disorder influences residents' perceptions that they are powerless to leave a threatening and dangerous environment.

https://www.jstor.org/stable/pdfplus/2657384.pdf

The contingent meaning of neighborhood stability for residents' psychological well-being

Past research has indicated an association between parents' beliefs and adolescent children's self-perceptions of ability and has shown the importance of accounting for parents' gender-stereotyped beliefs when examining boys' and girls' self-perceptions of math-science ability. The current study extends these findings by examining the longitudinal relations between mothers' earlier gender stereotypes and perceptions and adolescents' later math-science achievement beliefs and career choices. As predicted, mothers' earlier perceptions of their adolescents' abilities were related to adolescents' math-science self-efficacy 2 years after high school, with adolescents' self-perceptions of math ability during 10th grade mediating the relation with mothers' perceptions. Moreover, mothers' earlier predictions of their children's abilities to succeed in math careers were significantly related to later career choices.

Achievement in Math and Science: Do Mothers' Beliefs Matter 12 Years Later?.

Testing Stereotype Threat: Does Anxiety Explain Race and Sex Differences in Achievement?

Binkley, James K., and Philip C. Abbot. 1987. \"The Fixed X Assumption in Econometrics: Can the Textbooks be Trusted?\" American Statistician 41:206-14. Breiman, Leo, and Philip Spector. 1992. \"Submodel Selection and Evaluation in Regression: The X-Random Case.\" International Statistical Review 60:291-319. Clogg, Clifford C., Eva Petkova, and Adamantios Haritou. 1995. \"Statistical Methods for Comparing Regression Coefficients between Models.\" American Journal of Sociology. In this issue. Cox, D. R., and D. V. Hinkley. 1974. Theoretical Statistics. Cambridge: Chapman & Hall. Goldberger, Arthur S. 1991. A Course in Econometrics. Cambridge, Mass.: Harvard University Press. J6reskog, Karl G., and Dag S6rbom. 1993. New Features in LISREL 8. Chicago: Scientific Software. Sobel, Michael E. 1982. \"Asymptotic Confidence Intervals for Indirect Effects in Structural Equation Models.\" Pp. 290-312 in Sociological Methodology 1982, edited by Samuel Leinhardt. San Francisco: Jossey-Bass. White, Halbert. 1980. \"A Heteroscedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroscedasticity.\" Econometrica 48:817-38.

Reply to Allison: More on Comparing Regression Coefficients

A model is considered for the regression analysis of multivariate binary data such as repeated-measures data (for example, panel data) or multiple-indicators with measures of some underlying characteristic such as attitude or ability (for example, surveys or tests). The model is related to the usual Rasch model, the usual latent-class model, and other familiar models such as logistic regression. In addition to a regression specification, the model includes parameters that describe heterogeneity not accounted for by the predictors. In contrast to most other approaches, a nonparametric specification of the latent mixing distribution is used, leading to a formulation based on scaled latent classes. We examine the relationship between this model and several other models, give a tractable formulation of the likelihood function and likelihood equations, present an algorithm for maximum-likelihood estimation, and analyze marginal and conditional latent structures. The approach is illustrated with longitudinal data from the German Socioeconomic Panel.

Tzuwei Cheng

Papers

Reply to Allison: More on Comparing Regression Coefficients

Regression Analysis of Multivariate Binary Response Variables Using Rasch‐Type Models and Finite‐Mixture Methods