Latent Moderated Structural Equations (LMS)

[Angeline Fernando]

Hello,

I used Lavaan to assess my measurement model and run a multi group analysis.

I also had to investigate the effect of a continuous moderator.  I tried working with the  "em" option with nlsem since Lavaan doesn't support latent variable interactions.

However, right now I get a error saying "Model with interaction effects and num.eta > 1 cannot be fitted (yet).". The model has two latent endogenous variables.

I would like to continue to use R , since I don't have access to MPlus. Are there other libraries that support such interaction effects ?

Can someone help me with this ?

Thanks ,

Angeline

[Edward Rigdon]

Angeline--

     You could use a product of indicators approach. The indProd() function in the semTools package makes it easy to create product indicators for interaction models, including fairly up-to-date options like double mean centering. These approaches generally sacrifice a bit in terms of statistical efficiency, especially in the "ideal" case where all distributional assumptions hold, but you may find that any differences are swamped by the impact of research design decisions. Also, I may be wrong here, but I believe the nlsem approach is actually QML, itself an approximation to LMS.

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[Angeline Fernando]

Thank you very much. I will explore the indicator approach with semTools. 

On Sunday, November 19, 2017 at 7:32:30 PM UTC+5:30, Edward Rigdon wrote:

Angeline--

     You could use a product of indicators approach. The indProd() function in the semTools package makes it easy to create product indicators for interaction models, including fairly up-to-date options like double mean centering. These approaches generally sacrifice a bit in terms of statistical efficiency, especially in the "ideal" case where all distributional assumptions hold, but you may find that any differences are swamped by the impact of research design decisions. Also, I may be wrong here, but I believe the nlsem approach is actually QML, itself an approximation to LMS.

On Sun, Nov 19, 2017 at 8:13 AM, Angeline Fernando <angeline...@gmail.com> wrote:

Hello,

I used Lavaan to assess my measurement model and run a multi group analysis.

I also had to investigate the effect of a continuous moderator.  I tried working with the  "em" option with nlsem since Lavaan doesn't support latent variable interactions.

However, right now I get a error saying "Model with interaction effects and num.eta > 1 cannot be fitted (yet).". The model has two latent endogenous variables.

I would like to continue to use R , since I don't have access to MPlus. Are there other libraries that support such interaction effects ?

Can someone help me with this ?

Thanks ,

Angeline

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[Angeline Fernando]

Hello,

I used the product indicator approach. I tried indprod. Then I did the mean-centering by adding a function.

However, the fit indices have gone for a toss by adding the interaction terms. Initially, the CFI was around 0.95 for the base model-post running the interactions , it is 0.810

I did check with the PROCESS macro where I got significant results for the interaction term

Where am I going wrong?

This is my model. 

m2 <- 'p =~x_1+x_2+x_3+x_4

a=~a1+a2+a3

b=~b1+b2+b3+b4+b5+b6+b7

m=~m1+m2+m3+m4+m5+m6+m7+m8

INT1=~x_1_c.m1_c+x_1_c.m2_c+x_1_c.m3_c+x_1_c.m4_c+x_1_c.m5_c+x_1_c.m6_c+x_1_c.m7_c+x_1_c.m8_c+x_2_c.m1_c+x_2_c.m2_c+x_2_c.m3_c+x_2_c.m4_c+x_2_c.m5_c+x_2_c.m6_c+x_2_c.m7_c+x_2_c.m8_c

a ~ p+INT1 

b ~ a'

m2.fit <- sem(m2, bata = mybata, estimator="MLR")

Here INT1 is the interaction which is a product of the mean centered variables.

Thank you in advance

Angeline

[Edward Rigdon]

Angeline--

     Yes, this is predictable. The indProd() function offers an option, match, which if FALSE multiplies all indicators by all indicators (as you chose, apparently), but if TRUE it mutiplies the first indicators of each set, the second indicators of each set, and so forth. Multiplying all by all creates a complex pattern of correlated residuals--because the same x1, for example, is now part of multiple different observed variables. It also multiplies (pardon me) the number of nonnormal observed variables in your model.

     You have choices. A recent paper by Foldnes and Hagtvedt (2014) recommends the all by all over the matching approach. You can use that approach, but to obtain a correctly specified model you must include the free residual covariances implied. If x1 is one of your original indicators, then all of the product indicator that used x1 as a component will now have residual covariance. You may have trouble getting such a model to converge.

     The other approach is to use Herbert Marsh's matching. That obviates the need for residual covariances but may be statistically inferior, at the margin.

http://psycnet.apa.org/journals/met/19/3/444/

--Ed Rigdon

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[Angeline Fernando]

Ed.. 

Thank you very much for the directions.  I guess I need to investigate parceling approaches to use Marsh's match approach as I have unequal numbers of indicators .

Did a first level analysis and the fit indices seem much better now. 

Thank you once again.

-Angeline

[Terrence Jorgensen]

I guess I need to investigate parceling approaches to use Marsh's match approach as I have unequal numbers of indicators .

The matching procedure assumes an equal number of indicators per factor.  If you read the references provided on the ?indProd help page, you will find an example analysis with appropriate residual covariances in the residual-centering article.  Residual centering is better than mean-centering, but double-mean-centering has additional advantages you might want (again, the article is in the help-page references).

Terrence D. Jorgensen

Postdoctoral Researcher, 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

[Angeline Fernando]

Thank you for this. The fit measures are not good when I try double mean center. Must be missing something in the specification.

Will check Lin et al.,  further and try to work on the specification 

-Angeline

[Lucas Sempe]

Dear Terrence,

First, thanks for all the support given! 

I have a question related to the topic: Is it appropriate to apply a product of indicators approach to ordinal (exogenous) variables? I couldn't find any clear reference to that in literature or ?indProd.

Thanks in advance and best wishes, Lucas

[Terrence Jorgensen]

Is it appropriate to apply a product of indicators approach to ordinal (exogenous) variables? 

No, a product of category ranks doesn't mean anything.  Conceptually, you would want to calculate the product of the (normally distributed) latent item responses, but if you could do that, you wouldn't need to because you could do the same thing to the latent common factors.

Terrence D. Jorgensen

Assistant Professor, Methods and Statistics

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

http://www.uva.nl/profile/t.d.jorgensen