The equation of the direct effect

[Min-Jeong Yang]

Hi everyone,

I have been running mediation models with latent variables and I came up with a question: the equation of the direct effect from the tutorial seems reflecting rather total effect but not the direct effect. I wonder if I am missing anything. Please see below.

In the tutorial (http://lavaan.ugent.be/tutorial/mediation.html), the equation of the direct effect reads like below:

model <- ' # direct effect
             Y ~ c*X
           # mediator
             M ~ a*X
             Y ~ b*M
           # indirect effect (a*b)
             ab := a*b
           # total effect
             total := c + (a*b)

However, in my understanding of mediation, the equation of the direct effect would rather read like below (i.e., adding the term b*M):

model <- ' # MY direct effect
             Y ~ c*X + b*M
           # mediator
             M ~ a*X
             Y ~ b*M
           # indirect effect (a*b)
             ab := a*b
           # total effect
             total := c + (a*b)

Could anyone let me know if there's anything I am missing? Any comments would be much appreciated. Thank you!

MJ

[Christopher David Desjardins]

Your model won't run and will error because you have that second Y ~ b*M line.

Did you mean do this? If so, they are equivalent.

library("lavaan")
set.seed(1234)
X <- rnorm(100)
M <- 0.5*X + rnorm(100)
Y <- 0.7*M + rnorm(100)
Data <- data.frame(X = X, Y = Y, M = M)

# tutorial model

model1 <- '

# direct effect
Y ~ c*X
# mediator
M ~ a*X
Y ~ b*M
# indirect effect (a*b)
ab := a*b
# total effect
total := c + (a*b)

'
fit1 <- sem(model1, data = Data)
fit1.PE <- parameterEstimates(fit1)

# your model???

model2 <- '
# my direct effect

Y ~ c*X + b*M
# mediator
M ~ a*X

# Y ~ b*M # NOTE I commented this line out

# indirect effect (a*b)
ab := a*b
# total effect
total := c + (a*b)

'
fit2 <- sem(model2, data = Data)
fit2.PE <- parameterEstimates(fit2)

# identical
fit1.PE[fit1.PE$label == "c", ]
fit2.PE[fit2.PE$label == "c", ]

--
You received this message because you are subscribed to the Google Groups "lavaan" group.
To unsubscribe from this group and stop receiving emails from it, send an email to lavaan+unsubscribe@googlegroups.com.
To post to this group, send email to lav...@googlegroups.com.
Visit this group at https://groups.google.com/group/lavaan.
For more options, visit https://groups.google.com/d/optout.

--

https://cddesja.github.io/

[MJ]

Thank you so much for your quick response! That makes sense to remove the Y<-b*M while keeping Y <-b*M + c*X, where c refers to direct effect. I guess the tutorial needs some edits as the current equation of the "direct effect" in the tutorial actually reflects total effect.

Hope you have a nice weekend!

MJ

To unsubscribe from this group and stop receiving emails from it, send an email to lavaan+un...@googlegroups.com.

To post to this group, send email to lav...@googlegroups.com.
Visit this group at https://groups.google.com/group/lavaan.
For more options, visit https://groups.google.com/d/optout.

--

https://cddesja.github.io/

[Christopher David Desjardins]

Hi again,

The tutorial is correct because

Y ~ c*X + b*M

and

Y ~ c*X

Y ~ b*M

are equivalent syntax.

c is estimated the same way in both models and is the direct effect.

To unsubscribe from this group and stop receiving emails from it, send an email to lavaan+unsubscribe@googlegroups.com.

To post to this group, send email to lav...@googlegroups.com.
Visit this group at https://groups.google.com/group/lavaan.
For more options, visit https://groups.google.com/d/optout.

--

https://cddesja.github.io/

[Christopher David Desjardins]

and the total effect is c + (a * b) as it's listed in the tutorial

--

https://cddesja.github.io/

[MJ]

I see that lavaan was designed to work with those equations having c as direct effect. I've run the mediation models in various ways and I see that the results remain the same. Thank you so much for your clarification. I really appreciate it.

MJ