psych (version 1.7.8)

mediate: Estimate and display direct and indirect effects of mediators and moderator in path models

Description

Find the direct and indirect effects of a predictor in path models of mediation and moderation. Bootstrap confidence intervals for the indirect effects. Mediation models are just extended regression models making explicit the effect of particular covariates in the model. Moderation is done by multiplication of the predictor variables. This function supplies basic mediation/moderation analyses for some of the classic problem types.

Usage

mediate(y, x, m, data, mod = NULL, n.obs = NULL, use = "pairwise", n.iter = 5000, 
       alpha = 0.05, std = FALSE,plot=TRUE)
mediate.diagram(medi,digits=2,ylim=c(3,7),xlim=c(-1,10),show.c=TRUE,
     main="Mediation model",...)
moderate.diagram(medi,digits=2,ylim=c(2,8),main="Moderation model",...)

Arguments

y

The dependent variable (or a formula suitable for a linear model)

x

One or more predictor variables

m

One (or more) mediating variables

data

A data frame holding the data or a correlation or covariance matrix.

mod

A moderating variable, if desired

n.obs

If the data are from a correlation or covariance matrix, how many observations were used. This will lead to simulated data for the bootstrap.

use

use="pairwise" is the default when finding correlations or covariances

n.iter

Number of bootstrap resamplings to conduct

alpha

Set the width of the confidence interval to be 1 - alpha

std

standardize the covariances to find the standardized betas

plot

Plot the resulting paths

digits

The number of digits to report in the mediate.diagram.

medi

The output from mediate may be imported into mediate.diagram

ylim

The limits for the y axis in the mediate and moderate diagram functions

xlim

The limits for the x axis. Make the minimum more negative if the x by x correlations do not fit.

show.c

If FALSE, do not draw the c lines, just the partialed (c') lines

main

The title for the mediate and moderate functions

...

Additional graphical parameters to pass to mediate.diagram

Value

total

The total direct effect of x on y (c)

direct

The beta effects of x (c') and m (b) on y

indirect

The indirect effect of x through m on y (c-ab)

mean.boot

mean bootstrapped value of indirect effect

sd.boot

Standard deviation of bootstrapped values

ci.quant

The upper and lower confidence intervals based upon the quantiles of the bootstrapped distribution.

boot

The bootstrapped values themselves.

a

The effect of x on m

b

The effect of m on y

b.int

The interaction of x and mod (if specified)

Details

When doing linear modeling, it is frequently convenient to estimate the direct effect of a predictor controlling for the indirect effect of a mediator. See Preacher and Hayes (2004) for a very thorough discussion of mediation. The mediate function will do some basic mediation and moderation models, with bootstrapped confidence intervals for the mediation/moderation effects.

Functionally, this is just regular linear regression and partial correlation with some different output.

In the case of two predictor variables, X and M, and a criterion variable Y, then the direct effect of X on Y, labeled with the path c, is said to be mediated by the effect of x on M (path a) and the effect of M on Y (path b). This partial effect (a b) is said to mediate the direct effect of X --c--> Y: X --a -> M --b--> Y with X --c'--> Y where c' = c - ab.

Testing the significance of the ab mediation effect is done through bootstrapping many random resamples (with replacement) of the data.

For moderation, the moderation effect of Z on the relationship between X -> Y is found by taking the (centered) product of X and Z and then adding this XZ term into the regression.

In the case of being provided just a correlation matrix, the bootstrapped values are based upon bootstrapping from data matching the original covariance/correlation matrix with the addition of normal errors. This allows us to test the mediation/moderation effect even if not given raw data.

The function has been tested against some of the basic cases and examples in Hayes (2013) and the associated data sets.

Unless there is a temporal component that allows one to directly distinguish causal paths (time does not reverse direction), interpreting mediation models is problematic. Some people find it useful to compare the differences between mediation models where the causal paths (arrows) are reversed. This is a mistake and should not be done (Thoemmes, 2015).

For fine tuning the size of the graphic output, xlim and ylim can be specified in the mediate.diagram function. Otherwise, the graphics produced by mediate and moderate use the default xlim and ylim values.

References

Hayes, Andrew F. (2013) Introduction to mediation, moderation, and conditional process analysis: A regression-based approach. Guilford Press.

Preacher, Kristopher J and Hayes, Andrew F (2004) SPSS and SAS procedures for estimating indirect effects in simple mediation models. Behavior Research Methods, Instruments, \& Computers 36, (4) 717-731.

Thoemmes, Felix (2015) Reversing arrows in mediation models does not distinguish plausible models. Basic and applied social psychology, 27: 226-234.

Data from Hayes (2013), Preacher and Hayes (2004), and from Kerchoff (1974)

See Also

setCor and setCor.diagram

Examples

# NOT RUN {
#data from Preacher and Hayes (2004)
sobel <- structure(list(SATIS = c(-0.59, 1.3, 0.02, 0.01, 0.79, -0.35, 
-0.03, 1.75, -0.8, -1.2, -1.27, 0.7, -1.59, 0.68, -0.39, 1.33, 
-1.59, 1.34, 0.1, 0.05, 0.66, 0.56, 0.85, 0.88, 0.14, -0.72, 
0.84, -1.13, -0.13, 0.2), THERAPY = structure(c(0, 1, 1, 0, 1, 
1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 
1, 1, 1, 0), value.labels = structure(c(1, 0), .Names = c("cognitive", 
"standard"))), ATTRIB = c(-1.17, 0.04, 0.58, -0.23, 0.62, -0.26, 
-0.28, 0.52, 0.34, -0.09, -1.09, 1.05, -1.84, -0.95, 0.15, 0.07, 
-0.1, 2.35, 0.75, 0.49, 0.67, 1.21, 0.31, 1.97, -0.94, 0.11, 
-0.54, -0.23, 0.05, -1.07)), .Names = c("SATIS", "THERAPY", "ATTRIB"
), row.names = c(NA, -30L), class = "data.frame", variable.labels = structure(c("Satisfaction", 
"Therapy", "Attributional Positivity"), .Names = c("SATIS", "THERAPY", 
"ATTRIB")))
 #n.iter set to 50 (instead of default of 5000) for speed of example
mediate(1,2,3,sobel,n.iter=50)  #The example in Preacher and Hayes

#the pmi covariance matrix from Hayes. 2013.
#data set from Hayes, 2013 has 123 cases instead of the covariance matrix used here 

C.pmi <- structure(c(0.251232840197254, 0.119718779155005, 0.157470345195255, 
0.124533519925363, 0.03052112488338, 0.0734039717446355, 0.119718779155005, 
1.74573503931761, 0.647207783553245, 0.914575836332134, 0.0133613221378115, 
-0.0379181660669066, 0.157470345195255, 0.647207783553245, 3.01572704251633, 
1.25128282020525, -0.0224576835932294, 0.73973743835799, 0.124533519925363, 
0.914575836332134, 1.25128282020525, 2.40342196454751, -0.0106624017059843, 
-0.752990470478475, 0.03052112488338, 0.0133613221378115, -0.0224576835932294, 
-0.0106624017059843, 0.229241636678662, 0.884479541516727, 0.0734039717446355, 
-0.0379181660669066, 0.73973743835799, -0.752990470478475, 0.884479541516727, 
33.6509729441557), .Dim = c(6L, 6L), .Dimnames = list(c("cond", 
"pmi", "import", "reaction", "gender", "age"), c("cond", "pmi", 
"import", "reaction", "gender", "age")))

 #n.iter set to 50 (instead of default of 5000) for speed of example
mediate(y="reaction",x = "cond",m=c("pmi","import"),data=C.pmi,n.obs=123,n.iter=50)



#Data from sem package taken from Kerckhoff (and in turn, from Lisrel manual)
R.kerch <- structure(list(Intelligence = c(1, -0.1, 0.277, 0.25, 0.572, 
0.489, 0.335), Siblings = c(-0.1, 1, -0.152, -0.108, -0.105, 
-0.213, -0.153), FatherEd = c(0.277, -0.152, 1, 0.611, 0.294, 
0.446, 0.303), FatherOcc = c(0.25, -0.108, 0.611, 1, 0.248, 0.41, 
0.331), Grades = c(0.572, -0.105, 0.294, 0.248, 1, 0.597, 0.478
), EducExp = c(0.489, -0.213, 0.446, 0.41, 0.597, 1, 0.651), 
    OccupAsp = c(0.335, -0.153, 0.303, 0.331, 0.478, 0.651, 1
    )), .Names = c("Intelligence", "Siblings", "FatherEd", "FatherOcc", 
"Grades", "EducExp", "OccupAsp"), class = "data.frame", row.names = c("Intelligence", 
"Siblings", "FatherEd", "FatherOcc", "Grades", "EducExp", "OccupAsp"
))

 #n.iter set to 50 (instead of default of 5000) for speed of demo
mod.k <- mediate("OccupAsp","Intelligence",m= c(2:5),data=R.kerch,n.obs=767,n.iter=50)
mediate.diagram(mod.k) 
#print the path values 
mod.k

#Compare the following solution to the path coefficients found by the sem package

mod.k2 <- mediate(y="OccupAsp",x=c("Intelligence","Siblings","FatherEd","FatherOcc"),
     m= c(5:6),data=R.kerch,n.obs=767,n.iter=50)
mediate.diagram(mod.k2,show.c=FALSE) #simpler output 

#print the path values
mod.k2

# }