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Let's suppose I have an outcome variable that is not continuous. For example, it could be an ordered categorical variable or a nominal (unordered) categorical variable. This implies that I would need to model the variable as an ordered logit model or as a multinomial model.

I know lavaan and other softwares does not include the option to fit a whole structural equation model SEM with outcome variables that are not continuous (there is only a workaround for binary variables). As I would like to still use latent variables in the categorical model, I was wondering if it is correct to calculate the factor scores using the lavPredict() function and just include these latent variables as regressors in an external categorical model. I have seen many examples where people follow this approach but using Exploratory Factor Analysis EFA or Principal Component Analysis PCA. I would preper to rely on CFA since I do have a clear and solid theory about the latent variables.

Moreover, the lavPredict() function has the argument method with the options regression and Bartlett. Should I use the regression or the Bartlett factor scores? what are the differences among the two alternatives?

In other words:

library(lavaan)
HS.model <- ' visual  =~ x1 + x2 + x3 
              textual =~ x4 + x5 + x6
              speed   =~ x7 + x8 + x9 '

fit <- cfa(HS.model, data=HolzingerSwineford1939)

Latents <- lavPredict(fit)
Latents <- as.data.frame(Latents)

Latents_Bartlett <- lavPredict(fit, method = "Bartlett")
Latents_Bartlett <- as.data.frame(Latents_Bartlett) 

It is correct to use the latent variables visual, textual, and speed in the dataframes Latents or Latents_Bartlett as regressors in a subsequent ordered logit model or multinomial model?

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