Possible to get conditional indirect effects using probe2WayMC?

[Onur Şahin]

Hi all, I have a few questions.

I have a model with conditional indirect effects using an observed (1 item) exogenous variable, the rest of the model consists of only latent variables. I have one (latent) moderator, for which I used semTools' indProd function (double mean centering) to create the interaction products. I use probe2WayMC to probe the interaction, which works great.

The SEM has an alright fit, using 'MLM': CFI = .920, TLI = .913, RMSEA = .047, SRMR = .116

I am also interested in the conditional indirect effect. If I would use an observed moderator, I would define parameters I want using ':=' in lavaan, like this:

## include moderator in model like this:

climate ~ mean_of_climate*1

climate ~~ var_of_climate*climate

## define the parameters I'm interested in:

minus1SD := a1*b1 + c2*(mean_of_climate - sqrt(var_of_climate))

mean := a1*b1 + c2*(mean_of_climate)

plus1SD := a1*b1 + c2*(mean_of_climate + sqrt(var_of_climate))

However, I don't know how to do this using latent variables. Is this possible?

Other questions I have, if I am allowed to ask multiple questions in one topic:

I have one negative variance of a first-order latent variable (only have two first-order latent variables loading on a second-order variable), it is -0.015, p = .381. I know this means there is a misspecification in the model, but is a negative variance that is this small a big problem?

In my CFA before this SEM, I included a Common Latent Factor and saw that for some items of one latent variable, the standardized loadings differed more than .200, so I included the same CLF in the SEM. Since the interaction products and the new latent variable that consists of the interaction products were not in my original CFA, I was unsure whether I needed to let the interaction products also load on the CLF (and set the covariance between the CLF and the moderator latent variable to 0 like I do for the other latent second-order variables). I did do this but based on intuition. If there is no correct answer, readings are also welcome! 

I have multiple mediators that are theoretically correlated, so I specified covariances between these mediators. I think this is fine (according to Preacher and Hayes if I understoord correctly) but had a discussion with someone who said I shouldn't do this. Just checking.

I should probably not use 'MLM', but preferably bootstrapped test and SE since I am interested in indirect effects, right?

Thanks in advance!

[Terrence Jorgensen]

We discuss this and provide syntax example in our online supplement:

https://www.mdpi.com/2624-8611/3/3/24/htm

Yes, you can define them in your syntax, using values appropriate for your latent moderator (e.g., did you set its mean/variance to 0/1?)

Negative variance could also just be sampling error:  https://doi.org/10.1177/0049124112442138

Product indicators load only on the latent interaction factor (see ?indProd References).

Residual covariances among parallel mediators is reasonable, unless you really think the only reason they correlate is the predictor(s) you included. It is an empirically testable assumption (compare models with estimated correlation vs. fixed to 0).

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