Abstract 1. Because of the importance of identifying mediating variables in psychological researc... more Abstract 1. Because of the importance of identifying mediating variables in psychological research, methods to assess mediation are an area of active research. The purpose of this chapter is to outline current thinking about mediation analysis in psychology, but the length of the chapter precludes addressing all new developments, which can be found in other sources (MacKinnon, 2008; MacKinnon, Fairchild, & Fritz, 2007). This chapter first defines mediation and other third-variable effects. Statistical mediation methods using a single ...
British Journal of Mathematical and Statistical Psychology, 2013
Multilevel mediation analysis examines the indirect effect of an independent variable on an outco... more Multilevel mediation analysis examines the indirect effect of an independent variable on an outcome achieved by targeting and changing an intervening variable in clustered data. We study analytically and through simulation the effects of an omitted variable at level 2 on a 1-1-1 mediation model for a randomized experiment conducted within clusters in which the treatment, mediator, and outcome are all measured at level 1. When the residuals in the equations for the mediator and the outcome variables are fully orthogonal, the two methods of calculating the indirect effect (ab, c - c') are equivalent at the between- and within-cluster levels. Omitting a variable at level 2 changes the interpretation of the indirect effect and will induce correlations between the random intercepts or random slopes. The equality of within-cluster ab and c - c' no longer holds. Correlation between random slopes implies that the within-cluster indirect effect is conditional, interpretable at the grand mean level of the omitted variable.
In mediation analysis, there are occasions where the causal chain has more than two mediators, wh... more In mediation analysis, there are occasions where the causal chain has more than two mediators, which is termed a micromediational chain. The extension and application of methods to test and build confidence intervals (CIs) for an indirect effect in a micromediational chain with more than two mediators are necessary. We extended the application of the Monte Carlo method to build CIs for indirect effects in micromediational chains. We also implemented the Monte Carlo method in the RMediation package. Finally, we conducted a simulation study comparing the Type I error rates and power of the Monte Carlo CIs with percentile bootstrap and asymptotic normal distribution with multivariate delta standard error (Asymptotic–Delta) CIs. The results indicated that the Monte Carlo and percentile bootstrap methods performed similarly while both methods, in general, outperformed the Asymptotic–Delta method in terms of the Type I error rate and power.
... Craig K. Enders a & Davood Tofighi a pages 75-95. ... “Identifying the correct number of ... more ... Craig K. Enders a & Davood Tofighi a pages 75-95. ... “Identifying the correct number of classes in a growth mixture models”. In Advances in latent variable mixture models , Edited by: Hancock, GR and Samuelsen, KM 317–341. Greenwich, CT: Information Age. ...
This article describes the RMediation package,which offers various methods for building confidenc... more This article describes the RMediation package,which offers various methods for building confidence intervals (CIs) for mediated effects. The mediated effect is the product of two regression coefficients. The distribution-of-the-product method has the best statistical performance of existing methods for building CIs for the mediated effect. RMediation produces CIs using methods based on the distribution of product, Monte Carlo simulations, and an asymptotic normal distribution. Furthermore, RMediation generates percentiles, quantiles, and the plot of the distribution and CI for the mediated effect. An existing program, called PRODCLIN, published in Behavior Research Methods, has been widely cited and used by researchers to build accurate CIs. PRODCLIN has several limitations: The program is somewhat cumbersome to access and yields no result for several cases. RMediation described herein is based on the widely available R software, includes several capabilities not available in PRODCLIN, and provides accurate results that PRODCLIN could not.
Abstract 1. Because of the importance of identifying mediating variables in psychological researc... more Abstract 1. Because of the importance of identifying mediating variables in psychological research, methods to assess mediation are an area of active research. The purpose of this chapter is to outline current thinking about mediation analysis in psychology, but the length of the chapter precludes addressing all new developments, which can be found in other sources (MacKinnon, 2008; MacKinnon, Fairchild, & Fritz, 2007). This chapter first defines mediation and other third-variable effects. Statistical mediation methods using a single ...
British Journal of Mathematical and Statistical Psychology, 2013
Multilevel mediation analysis examines the indirect effect of an independent variable on an outco... more Multilevel mediation analysis examines the indirect effect of an independent variable on an outcome achieved by targeting and changing an intervening variable in clustered data. We study analytically and through simulation the effects of an omitted variable at level 2 on a 1-1-1 mediation model for a randomized experiment conducted within clusters in which the treatment, mediator, and outcome are all measured at level 1. When the residuals in the equations for the mediator and the outcome variables are fully orthogonal, the two methods of calculating the indirect effect (ab, c - c') are equivalent at the between- and within-cluster levels. Omitting a variable at level 2 changes the interpretation of the indirect effect and will induce correlations between the random intercepts or random slopes. The equality of within-cluster ab and c - c' no longer holds. Correlation between random slopes implies that the within-cluster indirect effect is conditional, interpretable at the grand mean level of the omitted variable.
In mediation analysis, there are occasions where the causal chain has more than two mediators, wh... more In mediation analysis, there are occasions where the causal chain has more than two mediators, which is termed a micromediational chain. The extension and application of methods to test and build confidence intervals (CIs) for an indirect effect in a micromediational chain with more than two mediators are necessary. We extended the application of the Monte Carlo method to build CIs for indirect effects in micromediational chains. We also implemented the Monte Carlo method in the RMediation package. Finally, we conducted a simulation study comparing the Type I error rates and power of the Monte Carlo CIs with percentile bootstrap and asymptotic normal distribution with multivariate delta standard error (Asymptotic–Delta) CIs. The results indicated that the Monte Carlo and percentile bootstrap methods performed similarly while both methods, in general, outperformed the Asymptotic–Delta method in terms of the Type I error rate and power.
... Craig K. Enders a & Davood Tofighi a pages 75-95. ... “Identifying the correct number of ... more ... Craig K. Enders a & Davood Tofighi a pages 75-95. ... “Identifying the correct number of classes in a growth mixture models”. In Advances in latent variable mixture models , Edited by: Hancock, GR and Samuelsen, KM 317–341. Greenwich, CT: Information Age. ...
This article describes the RMediation package,which offers various methods for building confidenc... more This article describes the RMediation package,which offers various methods for building confidence intervals (CIs) for mediated effects. The mediated effect is the product of two regression coefficients. The distribution-of-the-product method has the best statistical performance of existing methods for building CIs for the mediated effect. RMediation produces CIs using methods based on the distribution of product, Monte Carlo simulations, and an asymptotic normal distribution. Furthermore, RMediation generates percentiles, quantiles, and the plot of the distribution and CI for the mediated effect. An existing program, called PRODCLIN, published in Behavior Research Methods, has been widely cited and used by researchers to build accurate CIs. PRODCLIN has several limitations: The program is somewhat cumbersome to access and yields no result for several cases. RMediation described herein is based on the widely available R software, includes several capabilities not available in PRODCLIN, and provides accurate results that PRODCLIN could not.
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