CFA in R (lavaan) with ordinal data - polychoric correlation included?

Question

I would like to compute a confirmatory factor analysis (CFA) with ordinal data in R using lavaan. The data is from a questionnaire, containing 16 items structured on a Likert-scale.

I assume a 4-factor-model to be the best fit to my data. To compute the CFA I searched for information and found some useful advise in this paper.

The recommendation is to use DWLS-estimation and polychoric correlation. I've managed to compute the CFA with DWLS in R using the lavaan package. I found out that in Mplus the DWLS estimation, or WLSMV which is the same, uses polychoric correlation , unfortunately I never used Mplus and would like to work with R, so I was wondering if in lavaan it's the same.

So far I computed the CFA like this:

I specified a model (model.4) with 4 factors (AV, AW, AB, AA), (each factor has 4 items)

model.4='
AV =~ AVf1_+AVf2+AVf3+AVf4 
AW =~ AWf1+AW2+AWf3+AWf4 
AB =~ ABf1+ABf2+ABf3+ABf4 
AA =~ AAf1+AAf2+AAf3+AAf4'

Then I used the "ordered" function because of my ordered data, which is recommended in the lavaan package

model.ord = cfa(model.4,data=Data,ordered=c(
"AVf1","AVf2","AVf3","AVf4",
"AWf1","AWf2","AWf3","AWf4",
"ABf1","ABf2","ABf3","ABf4",
"AAf1","AAf2","AAf3","AAf4"))

This worked well. I got an output with all the relevant fit-indices (CFI, RMSEA etc.). Now my question is, if this automatically based upon polychoric correlation like in Mplus? If it's not - how can I add a command to use polychoric correlation? There is some information in the lavaan package about polychoric correlation, lavCor, but I don't know if it's useful for my problem and unfortunately I don't know how to use it.

I tried like this:

model.ord1 <- lavCor(cfa(model.4,data=Data,ordered=c(
 "AVf1","AVf2","AVf3","AVf4",
"AWf1","AWf2","AWf3","AWf4",
"ABf1","ABf2","ABf3","ABf4",
"AAf1","AAf2","AAf3","AAf4"))

))

But > summary(model.ord1, fit=T) didn't work. I did not receive any results.

To sum up: Is my CFA automatically based upon polychoric correlation? If not, how can I change my function to implement polychoric correlation?

Answer 1

The following link contains a similar use case I guess: https://www.packtpub.com/books/content/structural-equation-modeling-and-confirmatory-factor-analysis - scroll down to: "The lavaan syntax":

With the argument ordered = c, which you have used, you have told lavaan that some variables are ordinal in nature. In response, lavaan estimates polychoric correlations for these variables.

But I don't know if its true/correct. Can anybody confirm it?

Answer 2

Yes, according to folks in the lavaan user group, using the "ordered" option will use DWLS with polychoric correlations for the ordinal variables.

You can double check this by comparing the output of

inspect(fit, "sampstat")$cov  

where fit is the output of a cfa() model with ordered variables, and

lavCor(fit, ordered = TRUE, group = NULL, output = "cor")

which reports polychoric correlations