Help needed with moderation in SEM using lavaan package

[walkywalky]

Dear all,

I am trying to run a moderation analysis using lavaan.

I have a model with a number of latent variables and single-item observed indicators. 

First, I defined the measurement model as follows

1) measurement model

mod.PE <-' PE =~ V2_PE1 + V2_PE2 

EE =~ V2_EE1 + V2_EE2 + V2_EE3

SI =~ V2_SI1 + V2_SI2 + V2_SI3 

BI =~ V2_BI1 + V2_BI2 + V2_BI3

HM =~ V2_HM1 + V2_HM2 + V2_HM3

FC =~ V2_FC1 + V2_FC2 + V2_FC4 

PE ~~ EE

PE ~~ SI

PE ~~ HM

PE ~~ FC

EE ~~ SI

EE ~~ HM

EE ~~ FC

SI ~~ HM

SI ~~ FC

HM ~~ FC

BI ~~ PE

BI ~~ EE

BI ~~ SI

BI ~~ FC

BI ~~ HM '

fit.PE <- lavaan::cfa(mod.PE,

data = Datensatz_neu.sav,

missing="FIML",

estimator = "ML")

summary(fit.PE, standardized=TRUE, fit.measures=TRUE)

2)I then defined the structural model as follows and included observed single-item indicators as well:

mod.PE <-' PE =~ V2_PE1 + V2_PE2 

EE =~ V2_EE1 + V2_EE2 + V2_EE3 

SI =~ V2_SI1 + V2_SI2 + V2_SI3

BI =~ V2_BI1 + V2_BI2 + V2_BI3

HM =~ V2_HM1 + V2_HM2 + V2_HM3

FC =~ V2_FC1 + V2_FC2 + V2_FC4 

BI ~ PE + EE + SI + FC + HM + CarUse + PublicTransportUse + TechAcceptance + NoInteractions + NoUses + EE * CarUse

PE ~ FC + EE + HM + SI + CarUse + PublicTransportUse + TechAcceptance + NoInteractions + NoUses 

EE ~ FC + SI + HM + CarUse + PublicTransportUse + TechAcceptance + NoInteractions + NoUses 

HM ~ FC + SI + CarUse + PublicTransportUse + TechAcceptance + NoInteractions + NoUses 

FC ~ SI + CarUse + PublicTransportUse + TechAcceptance + NoInteractions + NoUses 

SI ~ TechAcceptance

'

fit.PE <- lavaan::cfa(mod.PE,

data = Datensatz_neu.sav,

missing="FIML",

estimator = "ML")

summary(fit.PE, standardized=TRUE, fit.measures=TRUE, rsquare = TRUE)

I noticed that the effect of car use on BI is significant and that EE becomes significant when car use is included in the model. Hence, I want to check whether car use moderates the relation between EE and BI.  

3) I performed mean centering now using this function for BI, EE and car use: variableCarUse.c <- scale(Datensatz_neu.sav$CarUse, center = TRUE, scale = FALSE)

4) I then performed a simple regression using the lm function and find a significant moderation effect.

Coefficients:

                             Estimate Std. Error t value Pr(>|t|)    

(Intercept)                  -0.03953    0.07905  -0.500   0.6174    

variableEEc                   0.55832    0.06579   8.487  8.8e-16 ***

variableCarUse.c             -0.06340    0.02722  -2.329   0.0205 *  

variableEEc:variableCarUse.c -0.05975    0.02715  -2.201   0.0285 *  

--Now my question: Ideally I want to include all latent variables as defined in the measurement model to see whether moderating effect is robust in the multivariate latent context, or is it also ok to check for moderating effects only with the M, the IV and DV in one model as I did with the function lm?

If it is not ok, how do I have to specify my measurement model? Somehow I don't know now how to include the interaction term in the model. 

-- I also added the interaction term in the structural model of step 2 before  (EE*Car Use) and I also found a significant effect but I think this is not correct because I when I add the interaction effect of Car use * SI or car use * FC, the interaction term is 1) always the same for every variable and 2) it is the same as the single effect of car use on the outcome variable. 

Something is wrong here I guess. 

Thanks a lot.

I hope my clarifications are clear. 

[Terrence Jorgensen]

I noticed that the effect of car use on BI is significant and that EE becomes significant when car use is included in the model.

This is called "suppression", not moderation.

https://doi.org/10.1023/A:1026595011371 (suppression, confounding, mediation)

http://quantpsy.org/interact/interactions.htm (moderation)

I don't know now how to include the interaction term in the model. 

Use product indicators of a latent interaction, as you tried in one of your other 2 posts on this topic:

https://groups.google.com/d/msg/lavaan/VBrSXtevSAg/kXVcJD3IBAAJ

I also added the interaction term in the structural model of step 2 before  (EE*Car Use) 

That syntax does not multiple 2 variables to create an interaction term.  lavaan's ?model.syntax is a character string that does NOT follow all the rules of a ?formula object.  This syntax just labels the CarUse slope "EE".

Terrence D. Jorgensen

Assistant Professor, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

UvA web page: http://www.uva.nl/profile/t.d.jorgensen

[Sina Nordhoff]

Thanks a lot! 

--
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 view this discussion on the web visit https://groups.google.com/d/msgid/lavaan/4eb1e9f3-e3bb-405f-be73-bfffd803a17f%40googlegroups.com.