Point and Interval Estimators of an Indirect Effect for a Binary Outcome

Year 2021, Volume: 8 Issue: 2, 279 - 295, 10.06.2021

Hyung Rock Lee , Jaeyun Sung Sunbok Lee

https://doi.org/10.21449/ijate.773659

Cited By: 1

Abstract

Conventional estimators for indirect effects using a difference in coefficients and product of coefficients produce the same results for continuous outcomes. However, for binary outcomes, the difference in coefficient estimator systematically underestimates the indirect effects because of a scaling problem. One solution is to standardize regression coefficients. The residual from a regression of a predictor on a mediator, which we call the residualized variable in this paper, was used to address the scaling problem. In simulation study 1, different point estimators of indirect effects for binary outcomes are compared in terms of the means of the estimated indirect effects to demonstrate the scaling problem and the effects of its remedies. In simulation study 2, confidence and credible intervals of indirect effects for binary outcomes were compared in terms of powers, coverage rates, and type I error rates. The bias-corrected (BC) bootstrap confidence intervals performed better than did other intervals.

Keywords

Indirect effects, Binary outcome, Confidence intervals, Bootstrap, Delta

References

• Allison, P. D. (1999). Comparing logit and probit coefficients across groups. Sociological Methods & Research, 28, 186-208.
• Alwin, D. F., & Hauser, R. M. (1975). The decomposition of effects in path analysis. American Sociological Review, 40, 37-47.
• Baron, R. M., & Kenny, D. A. (1986). The moderator–mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations. Journal of Personality and Social Psychology, 51, 1173-1182.
• Bollen, K. A. (1987). Total, direct, and indirect effects in structural equation models. Sociological Methodology, 17, 37-69.
• Bollen, K. A., & Stine, R. (1990). Direct and indirect effects: Classical and bootstrap estimates of variability. Sociological Methodology, 20, 15-140.
• Bradley, J. V. (1978). Robustness? British Journal of Mathematical and Statistical Psychology, 31, 144-152.
• Breen, R., Karlson, K. B., & Holm, A. (2013). Total, direct, and indirect effects in logit and probit models. Sociological Methods & Research, 42, 164-191.
• Carpenter, J., & Bithell, J. (2000). Bootstrap confidence intervals: when, which, what? a practical guide for medical statisticians. Statistics in Medicine, 19, 1141-1164.
• Clogg, C. C., Petkova, E., & Shihadeh, E. S. (1992). Statistical methods for analyzing collapsibility in regression models. Journal of Educational and Behavioral Statistics, 17, 51-74.
• Davison, A. C., & Hinkley, D. V. (1997). Bootstrap methods and their application. Cambridge University Press.
• Freedman, L. S., & Schatzkin, A. (1992). Sample size for studying intermediate endpoints within intervention trials or observational studies. American Journal of Epidemiology, 136, 1148-1159.
• Gardner, M. J., & Altman, D. G. (1986). Confidence intervals rather than p values: estimation rather than hypothesis testing. British Medical Journal (Clinical Research), 292, 746-750.
• Harlow, L. L., Mulaik, S. A., & Steiger, J. H. (2013). What if there were no significance tests? Psychology Press.
• Karlson, K. B., Holm, A., & Breen, R. (2012). Comparing regression coefficients between same-sample nested models using logit and probit a new method. Sociological Methodology, 42, 286-313.
• MacKinnon, D. P. (2008). Introduction to statistical mediation analysis. Routledge.
• MacKinnon, D. P., & Cox, M. C. (2012). Commentary on mediation analysis and categorical variables: The final frontier by dawn iacobucci. Journal of Consumer Psychology: the official journal of the Society for Consumer Psychology, 22 , 600-602.
• MacKinnon, D. P., & Dwyer, J. H. (1993). Estimating mediated effects in prevention studies. Evaluation Review, 17, 144-158.
• MacKinnon, D. P., Lockwood, C. M., Brown, C. H., Wang, W., & Hoffman, J. M. (2007). The intermediate endpoint effect in logistic and probit regression. Clinical Trials, 4, 499-513.
• MacKinnon, D. P., Lockwood, C. M., Hoffman, J. M., West, S. G., & Sheets, V. (2002). A comparison of methods to test mediation and other intervening variable effects. Psychological Methods, 7, 83-104.
• MacKinnon, D. P., Lockwood, C. M., & Williams, J. (2004). Confidence limits for the indirect effect: Distribution of the product and resampling methods. Multivariate Behavioral Research, 39, 99-128.
• MacKinnon, D. P., Warsi, G., & Dwyer, J. H. (1995). A simulation study of mediated effect measures. Multivariate Behavioral Research, 30, 41-62.
• Muthen, B. (1979). A structural probit model with latent variables. Journal of the American Statistical Association, 74, 807-811.
• Muthen, B. (1984). A general structural equation model with dichotomous, ordered categorical, and continuous latent variable indicators. Psychometrika, 49, 115-132.
• Muthen, L. K., & Muthen, B. O. (2010). Mplus: Statistical analysis with latent variables: User’s guide. Muthen & Muthen.
• Preacher, K. J., & Kelley, K. (2011). Effect size measures for mediation models: quantitative strategies for communicating indirect effects. Psychological Methods, 16, 93-115.
• R Core Team. (2014). R: A language and environment for statistical computing [Computer software manual]. Vienna, Austria. Retrieved from http://www.R-project.org/
• Sobel, M. E. (1982). Asymptotic confidence intervals for indirect effects in structural equation models. Sociological Methodology, 13, 290-312.
• Winship, C., & Mare, R. D. (1983). Structural equations and path analysis for discrete data. American Journal of Sociology, 89, 54-110.
• Yuan, Y., & MacKinnon, D. P. (2009). Bayesian mediation analysis. Psychological Methods, 14, 301-322.