I need to tip to estimate the interaction effect among latent variables

[Seongho Bae]

Dear all.

I need to tip to estimate the interaction effect among latent variables for hierarchical factor structure what I constructed 2nd ordered structure.

Here is my syntax of parts. 

Fit <- '

# Entrepreneurs action

EA_information =~ EA_Buntler3 + EA_Buntler4 + EA_Buntler5 + EA_Buntler6

EA_plan =~ EA_Koo1 + EA_Koo2

EA_worker_edu =~ EA_Koo3 + EA_Koo4

EA_intervention =~ EA_Koo6 + EA_Koo7 + EA_Koo8 + EA_Koo9 + EA_Koo10 + EA_Koo11

EA =~ EA_information + EA_plan + EA_worker_edu + EA_intervention

# environment (mediator moderator)

EV_finance =~ finance1 + finance2 + network4

EV_information =~ network1 + network2 + network3

EV =~ EV_information + EV_finance

# Entrepreneurs Performance

EP_objective =~ performance2 + performance3 + performance4 + performance5 + performance6

EP_career =~ performance7 + performance8

EP_subjective =~ performance9 + performance10 + performance11

EP =~ EP_objective + EP_career + EP_subjective

# main effect

EP ~ EA + EV

# moderating effect

EP ~ EA * EV

'

I know this: In the lavaan, I have to make new variables for interaction terms in data.frame by myself before execute lavaan. 

But, I want to make a testing interaction hypothesis (or a term) directly. Because, factor structures are 2nd-ordered structure. I don't know how make new interaction terms in data.frame for 2nd-ordered structure.

Please give me some tips.

Thanks a lot every writing new topic for my questions.

--

Seongho Bae

[Terrence Jorgensen]

I know this: In the lavaan, I have to make new variables for interaction terms in data.frame by myself before execute lavaan. 

But, I want to make a testing interaction hypothesis (or a term) directly. Because, factor structures are 2nd-ordered structure. I don't know how make new interaction terms in data.frame for 2nd-ordered structure.

lavaan cannot estimate interactions among latent variables.  The only software that can do so in the way you want, is Mplus, using the "XWITH" operator.  In any other software, your alternatives are to use the product-indicator approach (see the indProd() function in the semTools package to make this task easier) or to extract your factor scores from the hierarchical CFA of your latent variables, then fit a regression model with lm() that can include the interaction term.  I would not recommend the factor scores unless you evaluate them and they have very high correspondence with the latent factors (e.g., high validity measures, almost identical correlation matrices) -- if the factor scores are not well estimated, then any interaction effect would likely be attenuated.

Another option would be to use WinBUGS or OpenBUGS to estimate a Bayesian model, which draws factor scores at every iteration before drawing parameters, so you can get a posterior distribution of the interaction effect as easily as you can for the main effects.  Details are in a recent book that includes syntax examples for all their models:

http://www.wiley.com/WileyCDA/WileyTitle/productCd-0470669527.html


Terry

[Ulrich Schroeders]

Dear Terry, dear Yves,

I was just curious if there has been any new development on this topic.

Any intention to add the functionality of Mplus' XWITH into lavaan in the near future, so that moderation effects on a latent mean can be estimated?

Keep up the good work, kind regards,

Ulrich

[Carlo Chiorri]

Hi all,

you can find a tutorial about latent variable interaction in R here.

http://rstudio-pubs-static.s3.amazonaws.com/16521_c51516aca5a1430cabf9f6dec4b7ddb5.html

C.

[yrosseel]

On 02/20/2015 10:56 PM, Ulrich Schroeders wrote:
> Dear Terry, dear Yves,
>
> I was just curious if there has been any new development on this topic.
> Any intention to add the functionality of Mplus' XWITH into lavaan in
> the near future, so that moderation effects on a latent mean can be
> estimated?

Have a look at this new package:

http://cran.r-project.org/web/packages/nlsem/index.html

which implements the LMS method among others.

I will try to provide a lavaan interface for this package in the near
future.

Yves.

[Njål Foldnes]

Yes, Yves, this will be a major update to lavaan. Hope you find time to knit nlsem into lavaan!