Bootstrapping The Standard Error Of The Mediated Effect
Contents |
Health Search databasePMCAll DatabasesAssemblyBioProjectBioSampleBioSystemsBooksClinVarCloneConserved DomainsdbGaPdbVarESTGeneGenomeGEO DataSetsGEO ProfilesGSSGTRHomoloGeneMedGenMeSHNCBI Web SiteNLM CatalogNucleotideOMIMPMCPopSetProbeProteinProtein ClustersPubChem BioAssayPubChem CompoundPubChem SubstancePubMedPubMed HealthSNPSRAStructureTaxonomyToolKitToolKitAllToolKitBookToolKitBookghUniGeneSearch termSearch Advanced Journal list Help Journal ListHHS Author ManuscriptsPMC2843527 Psychol Sci. bootstrapping standard errors in stata Author manuscript; available in PMC 2010 Mar 22.Published in final edited bootstrapping standard deviation form as:Psychol Sci. 2007 Mar; 18(3): 233–239. doi: 10.1111/j.1467-9280.2007.01882.xPMCID: PMC2843527NIHMSID: NIHMS173983Required Sample Size to Detect the Mediated
Bootstrap Values
EffectMatthew S. Fritz and David P. MacKinnonArizona State UniversityAddress correspondence to Matthew S. Fritz, Department of Psychology, Arizona State University, Box 871104, Tempe, AZ 85287-1104, Email: ude.usa@ztirf.ttamAuthor information â–º
Mediation Effect
Copyright and License information â–ºCopyright notice and DisclaimerThe publisher's final edited version of this article is available at Psychol SciSee other articles in PMC that cite the published article.AbstractMediation 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 bootstrapping mediation analysis 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.Since the publication of Baron and Kenny’s (1986) article describing a method to evaluate mediation, the use of mediation models in the social sciences has increased dramatically. Using the Social Science Citation Index, MacKinnon, Lockwood, Hoffman, West, and Sheets (2002) found more than 2,000 citations of Baron and Kenny’s article. A more recent search of the Social Science Citation Index that we conducted found almost 8,000 citations, though a number of these publications examined moderation rather than mediation.Although there are a number of methods to test for mediation, including structural equation modeling (SEM; Cole & Maxwell, 2003; Holmbeck, 1997; Kenny, Kashy, & Bolger, 1998) and bootstrapping (MacKinnon, Lockwood, & Williams, 2004; Shrout & Bolger, 2002), many researchers prefer to use regression-based
my mediation webinars (small charge is requested). MEDIATION Introduction The Four Steps Indirect Effect Power Specification Error Additional Variables Extensions Causal Inference Approach Links to Other Sites References Introduction Consider
Mediation Analysis Spss
a variable X that is assumed to cause another variable Y. The variable X is moderation analysis called the causal variable and the variable that it causes or Y is called the outcome. In diagrammatic form, the unmediated model sobel test is Path c in the above model is called the total effect. The effect of X on Y may be mediated by a process or mediating variable M, and the variable X may still affect Y. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2843527/ The mediated model is
(These two diagrams are essential to the understanding of this page. Please study them carefully!) Path c' is called the direct effect. The mediator has been called an intervening or process variable. Complete mediation is the case in which variable X no longer affects Y after M has been controlled, making path c' zero. Partial mediation is the case in which the path from X to http://davidakenny.net/cm/mediate.htm Y is reduced in absolute size but is still different from zero when the mediator is introduced. Note that a mediational model is a causal model. For example, the mediator is presumed to cause the outcome and not vice versa. If the presumed causal model is not correct, the results from the mediational analysis are likely of little value. Mediation is not defined statistically; rather statistics can be used to evaluate a presumed mediational model. The specific causal assumptions are detailed below in the section onSpecification Error. There is a long history in the study of mediation (Hyman, 1955; MacCorquodale & Meehl, 1948; Wright, 1934). Mediation is a very popular topic. (This page averages over 200 visitors a day and Baron and Kenny (1986) has over 60,000 citations, according to Google Scholar, and there are four books on the topic (Hayes, 2013; Jose, 2012; MacKinnon, 2008;VanderWeele, 2015.) There are several reasons for the intense interest in this topic: One reason for testing mediation is trying to understand the mechanism through which the causal variable affects the outcome. Mediation and moderation analyses are a key part of what has been called process analysis, but mediation analyses tend to be more powerful than moderation analyses. Moreover, when most causal or structural models athe sem command? The sem command introduced in Stata 12 makes the analysis of mediation models much easier as long as both the dependent variable and http://www.ats.ucla.edu/stat/stata/faq/sem_mediation.htm the mediator variable are continuous variables. We will illustrate using the sem command with the hsbdemo dataset. The examples will not demonstrate full mediation, i.e., the effect of the independent variable will not go from being significant to being not significant. Rather, the examples will show partial mediation in which there is a decrease in the direct effect. A note about covariates If your model standard error contains control variables, i.e., covariates, you must include these in each of the sem equations. Thus, your sem model will look something like this:sem (MV <- IV CV1 CV2)(DV <- MV IV CV1 CV2) where DV stands for the dependent variable; IV stands for the independent variable; MV stands for the mediator variable; and CVs stand for the covariates. Simple mediation model The simplest mediation model bootstrapping the standard had one IV, one MV and a DV. Here is the symbolic version of the model. sem (MV <- IV)(DV <- MV IV) In our simple mediation example the independent variable is math, the mediator variable is read and the dependent variable is science. use http://www.ats.ucla.edu/stat/data/hsbdemo, clear sem (read <- math)(science <- read math) Endogenous variables Observed: read science Exogenous variables Observed: math Fitting target model: Iteration 0: log likelihood = -2098.5822 Iteration 1: log likelihood = -2098.5822 Structural equation model Number of obs = 200 Estimation method = ml Log likelihood = -2098.5822 ------------------------------------------------------------------------------ | OIM | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- Structural | read chi2 = . We follow up the sem command with estat teffects to get the direct and indirect effects. estat teffects Direct effects ------------------------------------------------------------------------------ | OIM | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- Structural | read |z| [95% Conf. Interval] -------------+---------------------------------------------------------------- Structural | read |z| [95% Conf. Interval] -------------+---------------------------------------------------------------- Structural | read <- | math | .724807 .0579824 12.50 0.000 .6111636 .8384504 -----------+---------------------------------------------------------------- science <- | read | .3654205 .0658305 5.55 0.000 .2363951 .4944459 math | .66658 .05799 11.49 0.000 .5529217 .7802384 ---