The equation of the direct effect

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Min-Jeong Yang

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Jul 13, 2018, 11:00:55 AM7/13/18
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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

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Jul 13, 2018, 12:38:22 PM7/13/18
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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", ]



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MJ

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Jul 13, 2018, 12:59:43 PM7/13/18
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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
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Christopher David Desjardins

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Jul 13, 2018, 1:11:25 PM7/13/18
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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.

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Christopher David Desjardins

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Jul 13, 2018, 1:15:01 PM7/13/18
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and the total effect is c + (a * b) as it's listed in the tutorial
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MJ

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Sep 3, 2019, 8:05:54 PM9/3/19
to lavaan
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

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