MBESS (version 4.3.0)

upsilon: A function for estimating the mediation effect size as discussed in Lachowicz, Preacher, & Kelley (submitted).

Description

This function implements the upsilon effect size statistic for general mediation from Lachowicz, Preacher, & Kelley (submitted).

Usage

upsilon(data, x, m, y, covs = NULL, parallel.med = NULL, seq.med = NULL)

Arguments

data

data is the data that contains the variable that are to be used in the mediation model.

x

The x is the independent variable or variables (listed in a vector) that are included in data. That is, this is a string identifying the x variables.

m

The m is the mediator variable or variables (listed in a vector) that are included in data. That is, this is a string identifying the m variables.

y

The y is the outcome or dependent variable or variables (listed in a vector) that are included in data. That is, this is a string identifying the y variables.

covs

Covariates to include in the mediation model are identified in covs. That is, this is a string identifying the covs (covariates) to inlucde.

parallel.med

Identifies which of the mediators are parallel mediators. Not that the parallel mediators listed in parallel.med are also included in m.

seq.med

Identifies which of the mediators are sequential and in the order in a list. That is, seq.med identifying the sequential mediators and their order. The order is such that list('m2~m1','m3~m2') m2 is caused by m1 and m3 is caused by m2.

Value

IE

is the value of the indirect effect for the path noted. Note that the total, specific, and unconditional paths will be produced (depending on the model)

Upsilon

is the value of the effect size for the path noted. Note that the total, specific, unconditional and unique paths will be produced (depending on the model)

%% ...

Details

See the examples below for example applications of the function.

References

Lachowicz, M. J., Preacher, K. J., & Kelley, K. (submitted). A novel measure of effect size for mediation analysis. Submited for publication.

Preacher, K. J., & Kelley, K. (2011). Effect size measures for mediation models: quantitative strategies for communicating indirect effects. Psychological Methods, 16, 93--115.

Wen, Z., & Fan, X. (2015). Monotonicity of effect sizes: Questioning kappa-squared as mediation effect size measure. Psychological Methods, 20, 193--203.

See Also

mediation

Examples

# To generate the multivariate data for the examples. 
require(MASS)

# Generate data for example 1 and 2. 
X<-matrix(c(1,.4,.2,.3,
            .4,1,.4,.1,
            .2,.4,1,.3,
            .3,.1,.3,1),4,4,byrow=TRUE)
data<-mvrnorm(500,c(0,0,0,0),X,empirical=TRUE)
colnames(data)<-c('x','m1','m2','y')

data <- as.data.frame(data)

#3 Example 1; three variable mediation; simple mediation model. 
x<-'x'
m<-'m1'
y<-'y'

upsilon(data,x,m,y)

## Example 2; four variable mediation; 2 mediators 
data<-mvrnorm(100,c(0,0,0,0),X,empirical=TRUE)
colnames(data)<-c('x1','x2','m','y')
data <- as.data.frame(data)

x <- c('x1','x2')
m <- 'm'
y <- 'y'

B <- upsilon(data,x,m,y)
B


# Generate data for example 3.
X1<-matrix(c(1,.4,.3,.3,.1,
             .4,1,-.2,.1,.2,
             .3,-.2,1,-.1,.3,
             .3,.1,-.1,1,.4,
             .1,.2,.3,.4,1),5,5,byrow=TRUE)

data<-mvrnorm(100,c(0,0,0,0,0),X1,empirical=TRUE)
colnames(data)<-c('x1','x2','x3','m','y')
data <- as.data.frame(data)

## Example 3; 3 predictors, 1 mediator, 1 outcome 
x <- c('x1','x2','x3')
m <- 'm'
y <- 'y'

C<-upsilon(data,x,m,y)
C

# Generate data for example 4.
X1<-matrix(c(1,.2,.3,.3,.1,
             .2,1,-.2,.3,.2,
             .3,-.2,1,.3,.3,
             .3,.3,.3,1,.4,
             .1,.2,.3,.4,1),5,5,byrow=TRUE)

data<-mvrnorm(100,c(0,0,0,0,0),X1,empirical=TRUE)
colnames(data)<-c('x1','x2','x3','m','y')
data <- as.data.frame(data)

## Example 4; 2 predictors, 1 mediator, 1 outcome, 1 covariate 
x <- c('x1','x2')
m <- 'm'
y <- 'y'
cov <-'x3'

upsilon(data,x,m,y,covs=cov)

# Generate data for example 5.
data<-mvrnorm(100,c(0,0,0,0),X,empirical=TRUE)
colnames(data)<-c('x','m1','m2','y')
data<-as.data.frame(data)

## Example 5; 1 predictor, 1 outcome, 2 parallel mediators 
x <- 'x'
m <- c('m1','m2')
y <- 'y'
meds <- c('m1+m2')

upsilon(data,x,m,y,parallel.med=meds)

# Generate data for example 6. 
data<-mvrnorm(100,c(0,0,0,0,0),X1,empirical=TRUE)
colnames(data)<-c('x','m1','m2','m3','y')
data<-as.data.frame(data)

## Example 6, 1 predictor, 1 outcome, 3 parallel mediators 
x <- 'x'
m <- c('m1','m2','m3')
y <- 'y'
meds <- c('m1+m2+m3')

upsilon(data,x,m,y,parallel.med=meds)

# Generate data for example 7.
data<-mvrnorm(100,c(0,0,0,0,0),X1,empirical=TRUE)
colnames(data)<-c('x1','x2','m1','m2','y')
data <- as.data.frame(data)

# Example 7; 2 predictors, 1 outcome, 2 parallel mediators 
x <- c('x1','x2')
m <- c('m1','m2')
y <- 'y'
parallel.med <- c('m1+m2')

upsilon(data,x,m,y,parallel.med=parallel.med)

# Generate data for example 8. 
data<-mvrnorm(100,c(0,0,0,0),X,empirical=TRUE)
colnames(data)<-c('x','m1','m2','y')
data<-as.data.frame(data)

## Example 8; 2 mediators, serial 
x <- 'x'
m <- c('m1','m2')
y <- 'y'
seq.med <- c('m2~m1')

upsilon(data,x,m,y,seq.med=seq.med)

# Generate data for example 9.
X1<-matrix(c(1,.4,.3,.3,.1,
             .4,1,-.1,.3,.2,
             .3,-.1,1,.3,.3,
             .3,.3,.3,1,.4,
             .1,.2,.3,.4,1),5,5,byrow=TRUE)

data<-mvrnorm(100,c(0,0,0,0,0),X1,empirical=TRUE)
colnames(data)<-c('x','m1','m2','m3','y')
data <- as.data.frame(data)

# Example 9; 3 sequential mediators
x <- c('x')
m <- c('m1','m2','m3')
y <- c('y')
seq.med <- list('m2~m1','m3~m2')

upsilon(data,x,m,y,seq.med=seq.med)