Ordinal + Continuous interaction in lavaan

Question

I'm completing a moderation mediation analysis in lavaan.

All of my variables are continuous other than my mediator, which is an ordinal with 3 levels (0,1,2). Lavaan can't handle interactions between ordinal and continuous variables, so I am troubleshooting the best way around this.

Some folks have suggested treating my ordered variable as pseudocontinuous, however with only 3 levels, I'm worried I'll get push back from reviewers. I could create the interaction term between the ordinal variable (but treated as continuous here) and the continuous outside of the model and then use it as a variable in the model while keeping the ordinal variable itself as ordered in the model.

Is there anything wrong with doing this? Any other suggestions?

data$int <- data$ordinal_cont * data$continuous
data[, "ordinal"] <- lapply(data["ordinal"], ordered)

model -> `
L1 =~ X1 + X2 + X3 
L2 =~ Z1 + Z2 + Z3

L1 ~ a*L2 + c*Continuous + d*Ordinal + e*int
ordinal ~ b*L2

ab := a*b 

L2 ~~ Continuous
L2 ~~ ordinal
Continuous ~~ ordinal
`
fit <- sem(model,
            se = "bootstrap",
            bootstrap = 2000,
            data = data,
            parallel = "snow",
            ncpus = 8,
            ordered = "pubertal_onset",
            estimator = "DWLS")

Thanks,

Clare

Answer 1

Is there anything wrong with doing this?

Yes, the interpretations would not match:

• the simple effect of Ordinal would be on the continuous latent-response scale
• the degree to which it is moderated by continuous would be on the observed discrete-response scale

The observed and latent responses don't share locations or scales, so you wouldn't actually be testing/interpreting an interaction effect.

Any other suggestions?

A tedious, time-consuming, but very flexible option would be parameter moderation (often called moderated nonlinear factor analysis (MNLFA), but it is really more general than that). That is not available in lavaan, but it is available in the OpenMx package:

Kolbe, L., Molenaar, D., Jak, S., & Jorgensen, T. D. (2022). Assessing measurement invariance with moderated nonlinear factor analysis using the R package OpenMx. Psychological Methods. https://doi.org/10.1037/met0000501

The tutorial is about testing invariance (which you should consider testing for your 2 common factors, one of which you consider to be affected by Ordinal and by continuou). However, you can fit any kind of SEM (in your case, a simple mediation model at the structural level: L2 --> Ordinal --> L1) and have any model parameters (including variances) moderated by continuous.