Latent variables interaction and simple slope

[Damiano Girardi]

Dear all,

I would like to fit in lavaan a moderation model using SEM with latent variables, and I would also like to probe simple slopes. In this regard, I read about the “probe2WayMC” function in semTools, and I have some questions:

 

1) In the “Details” section of the documentation of semTools, there are some references to the papers by Marsh and colleagues (2004). However, as far as I understand, the lavaan syntax for the SEM model in the example of the “probe2WayMC” function is different from the syntax proposed by the authors. Is there a reference for this syntax and the model specified? Indeed, I know that several different models were proposed in the literature for latent interactions.

 

2) In the example, the values in the argument “valProbe” are -1, 0 and 1. Are these values “internal” values that reflect -1SD, mean and +1SD of the moderator, or actual values of the latent moderator variable (I suspect the former ones, given that the variances of the latent variables are freely estimated)?

 

3) Can I include continuous covariates in my model? Should I center their respective observed variables for interpretation of the results?

 

4) Is it possible to compute confidence intervals for simple slopes using percentile bootstrap? I suspect that the mean-centering procedure should not work whit bootstrap. I naïvely tried the R function “scale()” in the lavaan syntax to mean-center the observed variables in each sample, but it does not seem to work in lavaan.

 

Thank you very much

 

Best regards

Damiano

[Terrence Jorgensen]

1) In the “Details” section of the documentation of semTools, there are some references to the papers by Marsh and colleagues (2004). However, as far as I understand, the lavaan syntax for the SEM model in the example of the “probe2WayMC” function is different from the syntax proposed by the authors. Is there a reference for this syntax and the model specified? Indeed, I know that several different models were proposed in the literature for latent interactions. 

The default arguments implement the double-mean-centering approach, which is also in the References on that help page.

2) In the example, the values in the argument “valProbe” are -1, 0 and 1. Are these values “internal” values that reflect -1SD, mean and +1SD of the moderator, or actual values of the latent moderator variable (I suspect the former ones, given that the variances of the latent variables are freely estimated)? 

As the help page indicates, these are "The values of the moderator".  If your latent variances are fixed to 1 (std.lv = TRUE), then the latter and former are equivalent.

3) Can I include continuous covariates in my model? Should I center their respective observed variables for interpretation of the results?

If you mean-center the covariates, they will not affect the probing of the latent interaction.

   

 4) Is it possible to compute confidence intervals for simple slopes using percentile bootstrap? 

Why would you want to use a computationally intensive procedure like bootstrapping when it is not necessary?  If your data are not normally distributed, you can use a robust estimator.

Terrence D. Jorgensen

Postdoctoral Researcher, Methods and Statistics

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

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

[Aiden]

Just to follow up on this as I am new to latent interaction models.

2) In the example, the values in the argument “valProbe” are -1, 0 and 1. Are these values “internal” values that reflect -1SD, mean and +1SD of the moderator, or actual values of the latent moderator variable (I suspect the former ones, given that the variances of the latent variables are freely estimated)? 

As the help page indicates, these are "The values of the moderator".  If your latent variances are fixed to 1 (std.lv = TRUE), then the latter and former are equivalent.

Could you please explain how the values of the moderator (reflecting -1SD, mean and +1SD) are derived given that the moderator is made up of several indicators? 

i.e. (f2 =~ x4 + x5 + x6), where f2 is the moderator.

Thank you. 

[Alex Schoemann]

Hi Aiden,

For the latent interactions the moderator is the latent variable, not the indicators of the latent variable. So, for the purposes of probing the interaction you could look for values of the latent variable (hence -1, 0, and 1) not value of the original variable. This applies when latent variances are fixed to 1 to set the scale of the latent variables (and when latent means are set to 0), if you use another method to set the scale, you would use different values for the simple slopes.

Alex

[Aiden]

Hi Alex, 

Thank you for your response. Does this mean that I need to specify std.lv= TRUE in the sem() ? 

e.g. fitMC2way <- sem(model2, data = dat2wayMC, std.lv = TRUE, meanstructure = TRUE), so that the latent variances are fixed to 1, and set the latent means to 0 in the model syntax, in order for me to probe the interaction with values (-1, 0 and 1)? 

Aiden

[Aiden]

Hi Alex, 

Thanks a lot. I think Terrance answered it in the previous thread. 

Kind regards,

Aiden