Interaction Term in SEM between Categorical Indicator x Latent Variable

[Yuthika Girme]

Hi there,

 

I am currently conducting a mediation SEM using lavaan in R. However, I’m conducting an integrative data analysis across multiple samples, and I am wanting to control for the main and interaction effects of sample (dummy coded variables). I’m running into trouble with creating interaction terms – it’s fine when creating an interaction term with my dummy coded sample indicator and another indicator variable in my model, but I can’t seem to create an interaction term with my dummy coded sample indicator and latent variables in my model.

 

I have tried to simply create the term in my model as with my indicator interaction terms (e.g., DC:Latent Variable) which doesn’t work, and I’ve tried to create this term outside my model by defining the interaction (e.g., DCLVX := DC*Latent Variable) and I get the following error:

 

Error in lav_data_full(data = data, group = group, cluster = cluster,  :

  lavaan ERROR: missing observed variables in dataset: EC1_SUP

 

I have had a browse of the other forum questions, and came across two solutions, that I’m not sure really get at what I am wanting:

 

1)      I know there is the multigroup model approach, but the point of my analyses is to run a meta-analytic model rather than run the model for individual samples within my dataset.

2)      I also read about the indProd function, but from my understanding this would create interaction terms between my dummy code variable(s) and ALL indicators of my latent variable(s)? I want to avoid this if possible because I have 20 indicators for my 5 latent variables, and 2 dummy coded variables, which would give me 100 interaction terms… I don’t think my model can handle all these over and above the rest of my model parameters. Is there a way to create an interaction term with the latent variable itself rather than the indicators?

 

Kind Regards,

Yuthika Girme

[Patrick (Malone Quantitative)]

Yuthika,

Using the multiple-group approach, you can constrain or release structural paths between groups. Fully constraining them to equality is the no-interaction model. Releasing a given path across groups lets you test sample as a moderator of that path.

Hope that helps,

Pat

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[Yuthika Girme]

Thank you, Pat! That seems to work great!

 

fit1<-sem(model,data=IDASem, group = "Dataset", group.equal = c("intercepts", "loadings", "means", "residuals", "lv.variances", "lv.covariances", "residual.covariances", "regressions"))

 

One last question – the output is all identical now across models. I do ask for indirect effect pathways, but I only get the output once at the end of the output rather than separately for each group. Is it fair to assume that these are the indirect effects across all samples/would be identical across groups too?

 

Yuthika

[Patrick (Malone Quantitative)]

Yuthika,

To best answer that, we'd need to see your model syntax. But first question: Did the fully constrained model fit the data? If so, the a and b paths are identical between groups and you're done. If not, there's some probing to do.

Pat

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[Yuthika Girme]

Hi Pat,

Yea, so the fully constrained model was not as good as the default multigroup model that didn't have any constraints, but it wasn't terrible. Keep in mind, I'm trying to conduct a meta-analysis across datasets and so I'm not interested in group differences, but simply want to ensure I'm controlling for dataset source. 

Multigroup Analysis without any constraints: CFI = .931, RMSEA = .058

Multigroup Analysis with all constraints: CFI = .876, RMSEA = .071

My syntax for the multigroup analysis with constraints looks like this (below) and it's the bit in bold that appears at the end of my output rather than individually for each group like the rest of the SEM output.

model2 <- '

  #measurement model

  WB =~ lifesat1+lifesat2+lifesat3+lifesat4+lifesat5

  SUP =~ supav1+supav2+supav3+supav4+supav5+supav6+supav7+supav8

  AH =~ AH1+AH2+AH3

  PH =~ PH1+PH2+PH3

  AF =~ AF1+AF2+AF3

  PF =~ PF1+PF2+PF3

  #regressions

  WB ~ c*REL.STATUS + b1*SUP + b2*AH + b3*PH + b4*AF + b5*PF + gender + age_c

  SUP ~ a1*REL.STATUS + gender + age_c

  AH ~ a2*REL.STATUS + gender + age_c

  PH ~ a3*REL.STATUS + gender + age_c

  AF ~ a4*REL.STATUS + gender + age_c

  PF ~ a5*REL.STATUS + gender + age_c

  #stigma to support regressions

  SUP ~ d2*AH + d3*PH + d4*AF + d5*PF

  #residual covariances

  AH ~~ PH + AF + PF

  PH ~~ AF + PF

  AF ~~ PF

  

  #define direct and indirect pathways

  indirect_sup := a1*b1

  indirect_ah  := a2*b2

  indirect_ph  := a3*b3

  indirect_af  := a4*b4

  indirect_pf := a5*b5

  indirect_ah_sup := a2*d2*b1

  indirect_ph_sup := a3*d3*b1

  indirect_af_sup := a4*d4*b1

  indirect_pf_sup := a5*d5*b1

  direct := c

  total := c + (a1*b1) + (a2*b2) + (a3*b3) + (a4*b4) + (a5*b5) + (a2*d2*b1) + (a3*d3*b1)+ (a4*d4*b1)+ (a5*d5*b1)'

fit1<-sem(model2,data=IDASem, group = "Dataset", group.equal = c("intercepts", "loadings", "means", "residuals", "lv.variances", "lv.covariances", "residual.covariances", "regressions"))

summary(fit1, standardized = TRUE, fit.measures = TRUE, rsq = TRUE)

[Patrick (Malone Quantitative)]

Yuthika,

The multiple-group model, whether constrained or unconstrained, is probably the best way to "control" for dataset source.

If the constrained model does not fit, it indicates heterogeneity by dataset source, which is important to note in a meta-analysis.

However, allowing heterogeneity in the means and intercepts of a path analysis still controls for dataset source, in the sense of applying it as a covariate. If a model with means and intercepts freed fits well, you can still interpret the constrained path coefficients (and therefore the indirect effects) as being homogenous across studies. So I suggest checking that next.

The reason you're only getting one set of indirect effects is that the label constraints are applied across groups. So for indirect_sup, a1 is the a path for all groups because of the way you constrained it in the ~ regression part of the formula--with only one label--and similar for b1. You'd have to have different labels for the paths in different groups to get varying indirect effects, and manage the constraints to equality separately.

Hope that helps,

Pat

To view this discussion on the web visit https://groups.google.com/d/msgid/lavaan/366c9606-c2c7-491c-a565-e6d668faf131n%40googlegroups.com.

[Yuthika Girme]

Gotcha! That all makes sense. Thank you SO much for your help, Pat! :)