How to perform moderated mediation

[czw0102]

Hi there!

Thank you for creating such a useful tool! I have a question regarding the capabilities of the package: Is it possible to perform moderated mediation using this package?

We attempted to define the moderated mediation using a1 * X:W and then multiply it by one of the indirect effects, but encountered an issue since it involves a three-way interaction.

Could you please advise on how to implement this in the package?

Victor

[Kss2k]

Hey Victor,

I don't see why this would create a three-way interaction, can I perhaps see the code you tried to run?

Kjell

[czw0102]

Thank you!

model1 <- "

X =~ x1 + x2 + x3
Y =~ y1 + y2 + y3
M = ~ m1+m2+m3
Z = ~ z1 + z2 + z3

M ~ X+Z+a1 * X:Z
Y~X+b2 * M

medmod=: a1*b2

"
est1 <- modsem(m1, oneInt, "lms")
summary(est1, ci = TRUE, scientific = TRUE)

In this case, mediated moderation cannot be calculated because lavaan doesn't recognize the "a1*X:Z
" syntax, as it involves the multiplication of three elements. Is there anyway to solve this ?

Thanks again!

[Kss2k]

Assuming you've added m1-3, the problem here should be that the ':=' operator hasn't been implemented for the lms/qml approach yet . It is basically just a post-estimation procedure, which you could calculate by hand after estimating the model. We're working on getting this to work with the rmedsem package. Have you tried using any of the other approaches?

[czw0102]

BTW, do you know how to calucaute manually using boostrapping method?

[Kss2k]

If you want to use bootstrap, you will have to bootstrap the model as well. This is not recommended as it will take a looong time with the LMS and QML approach. Instead you can use the Monte-Carlo Approach. Here is an example using a fork of the rmedsem package, with the latest development version of modsem

devtools::install_github("kss2k/modsem")
devtools::install_github("kss2k/rmedsem-modsem")
library(modsem)
library(rmedsem)

tpb <- "
# Outer Model (Based on Hagger et al., 2007)
  ATT =~ att1 + att2 + att3 + att4 + att5
  SN =~ sn1 + sn2
  PBC =~ pbc1 + pbc2 + pbc3
  INT =~ int1 + int2 + int3
  BEH =~ b1 + b2

# Inner Model (Based on Steinmetz et al., 2011)
  INT ~ ATT + SN + PBC
  BEH ~ INT + PBC
  INT ~ PBC:SN
  BEH ~ PBC:SN
"

est <- modsem(tpb, TPB, method = "qml")
rmedsem::rmedsem(est, indep = "PBC:SN", med = "INT", dep = "BEH")

#> Significance testing of indirect effect (standardized)
#> Model estimated with package 'modsem'
#> Mediation effect: 'PBC:SN' -> 'INT' -> 'BEH'
#> 
#>                              Sobel              Delta        Monte-Carlo
#> Indirect effect            0.00378            0.00378            0.00378
#> Std. Err.                  0.00347            0.00349            0.00348
#> z-value                    1.08935            1.08443            1.04309
#> p-value                      0.276              0.278              0.297
#> CI              [-0.00302, 0.0106] [-0.00305, 0.0106] [-0.00302, 0.0107]
#> 
#> Baron and Kenny approach to testing mediation
#>    STEP 1 - 'PBC:SN:INT' (X -> M) with B=0.019 and p=0.271
#>    STEP 2 - 'INT:BEH' (M -> Y) with B=0.204 and p=0.000
#>             As either STEP 1 or STEP 2 (or both) are not significant,
#>             there is no mediation.
#> 
#> Zhao, Lynch & Chen's approach to testing mediation
#> Based on p-value estimated using Monte-Carlo
#>   STEP 1 - 'PBC:SN:BEH' (X -> Y) with B=0.143 and p=0.000
#>             As the Monte-Carlo test above is not significant and STEP 1 is
#>             significant there is direct-only nonmediation (no mediation).
#> 
#> Effect sizes
#>    RIT = (Indirect effect / Total effect)
#>          Total effect 0.147 is too small to calculate RIT
#>    RID = (Indirect effect / Direct effect)
#>          (0.004/0.143) = 0.026
#>          That is, the mediated effect is about 0.0 times as
#>          large as the direct effect of 'PBC:SN' on 'BEH'

[Kss2k]

Update := is now supported in modsem

The := operator now works with the LMS and QML approach as well.
The above example should now work, without having to use rmedsem.

Example

devtools::install_github("kss2k/modsem")
library(modsem)

tpb <- "
# Outer Model (Based on Hagger et al., 2007)
  ATT =~ att1 + att2 + att3 + att4 + att5
  SN =~ sn1 + sn2
  PBC =~ pbc1 + pbc2 + pbc3
  INT =~ int1 + int2 + int3
  BEH =~ b1 + b2

# Inner Model (Based on Steinmetz et al., 2011)
  INT ~ ATT + SN + PBC
  BEH ~ b_i * INT + PBC
  INT ~ i_ps * PBC:SN
  BEH ~ b_ps * PBC:SN
  indirect_effect := i_ps * b_i
  total_effect := b_ps + indirect_effect
"

est <- modsem(tpb, TPB, method = "qml")
summary(est)

Shortened Output

#> modsem (version 1.0.3):
#>
#>   ...
#>
#> Regressions:
#>                   Estimate  Std.Error  z.value  P(>|z|)
#>   INT ~ 
#>     PBC              0.212      0.030     7.15    0.000
#>     ATT              0.210      0.026     8.03    0.000
#>     SN               0.186      0.028     6.69    0.000
#>     PBC:SN  (i_ps)   0.017      0.015     1.10    0.271
#>   BEH ~ 
#>     PBC              0.244      0.023    10.66    0.000
#>     INT      (b_i)   0.183      0.025     7.39    0.000
#>     PBC:SN  (b_ps)   0.115      0.016     7.38    0.000
#> 
#>   ...
#>
#> Defined Parameters:
#>                   Estimate  Std.Error  z.value  P(>|z|)
#>     indrct_          0.003      0.003     1.10    0.273
#>     ttl_ffc          0.118      0.016     7.46    0.000