Guidance on Conducting MGCFA with Ordered Data Using lavaan and semTools

[David Giofrè]

Hello,

I am currently conducting a Multigroup Confirmatory Factor Analysis (MGCFA) with ordered data and have come across various materials online. However, I am seeking comprehensive guidelines on performing these analyses using lavaan and semTools.

My model is relatively simple:

MgCfa01 <- '
  Fact01 =~ AmasS01 + AmasS02 + AmasS03 + AmasS04 + AmasS05 + AmasS06 + AmasS08 + AmasS09
'

ModMGCFA01 <- sem(model = MgCfa01, data = x, std.lv = TRUE, group = "sex", ordered = c("AmasS01", "AmasS02", "AmasS03", "AmasS04", "AmasS05", "AmasS06", "AmasS07", "AmasS08", "AmasS09"))

ModMGCFA02 <- sem(model = MgCfa01, data = x, std.lv = TRUE, group = "sex", group.equal = c("loadings"), ordered = c("AmasS01", "AmasS02", "AmasS03", "AmasS04", "AmasS05", "AmasS06", "AmasS07", "AmasS08", "AmasS09"))

ModMGCFA03 <- sem(model = MgCfa01, data = x, std.lv = TRUE, group = "sex", group.equal = c("loadings", "thresholds"), ordered = c("AmasS01", "AmasS02", "AmasS03", "AmasS04", "AmasS05", "AmasS06", "AmasS07", "AmasS08", "AmasS09"))

I have a few questions that I hope you can assist me with:

1. Does lavaan automatically select the appropriate estimator for ordered data? If not, which estimator would you recommend using?
2. Can I only test for configural invariance, weak invariance (loadings), and strong invariance (loadings and thresholds) with ordered data?
3. Which fit indices should be reported (scalar, robust)?
4. Is there a built-in method for comparing two or more models, for example, using semTools?
5. Which fit indices would you recommend reporting (e.g., CFI, TLI, RMSEA, and SRMR)?
6. When comparing the Comparative Fit Index (CFI), for two models should I compare the robust or the scalar CFI?
7. Are there any tutorials or guidelines online that you would recommend? I would be happy to cite any relevant tutorial if available.
8. I had some missing pattern in one item and I decided to remove it, but I was wondering if there is any way to also include this item (error: lavaan->lav_samplestats_step1():      some categories of variable `AmasS07' are empty in group 1)
   

Thank you very much for any help you can provide.

David