Ordinal Data: CFA treating data accordingly vs continuously

[Saul Gabriel]

I have ordinal, that is to say Likert-type of data, with four response categories.

Bandalos (2018) and Finney & DiStefano (2013) urge researchers to avoid traditional CFA approaches with such data.

Thus, I have run exploratory factor analysis based on a polychoric matrix as well as those based on the traditional Pearson’s R (ie, with dat treated continuously) to see if results for a CFA would differ.

I have two questions: 1. Does anyone have any good citations on comparisons of these two approaches or simulation-based studies comparing the two approaches with ordinal data?

2. gllamm can accommodate CFAs with ordinal data, correct?

Thanks

[Weiwen Ng]

For Q2, I have no idea about gllamm, believe the SEM option method(adf) is one solution. It is a weighted least squares estimator, and I believe these estimators are regarded as OK for categorical data (some info in the links, more if you Google, caveat lector because this isn't my specialty). That said, you have ordinal items, and we also know from previous conversations that you are at least conversant with IRT. I view IRT as a non-linear CFA. Why not use IRT to show construct validity?

[Saul Gabriel]

Hi Weiwen, I have looked into this, and will explore it some more.
At some point, I will conduct IRT analyses, and also view it as in the same family of CFAs, but for categorical indicators. Only issue is that IRT requires unidimensional latent variables, and I do not yet know what the factor structure of my measure/data is...