Hello,
I am currently looking at the results of confirmatory factor analyses (CFA) that were conducted by another person. There are a few analysis and model choices that don’t seem quite right to me. I would greatly appreciate if anyone with enough experience with CFA could let me know what they think of the following points:
1) Is maximum-likelihood (ML) estimation ever an acceptable method to use in CFA if variables are ordinal (e.g., Likert scales) or nominal?
2) Is ML estimation ever an acceptable method to use in CFA if data are not normally distributed?
3) Is it acceptable to keep an item with a factor loading > 1 (heywood case) if the model’s fit indices and parameter estimates are otherwise acceptable?
Thank you vey much!
Hi Alexandra
1) if the indicators are ordinal and have >=5 categories, it's acceptable. There are estimators such as DWLS or WLMSV that are explicitly designed for categorical indicators but they rely on the (unreasonable) assumption that there is a normally distributed latent response variable which underlies the indicators.
2) Depends on the extend and form of the deviation. Normally, it is easy in nowadays software to apply corrections (e.g., the Satorra-Bentler or Yuan-Bentler correction). Severe kurtosis, especially is problematic. Nonnormality creases if I remember correctly the chisquare and decreases the standard errors.
3) If the factor loading is standardized, then I would view this as a problem. Fit of a model is one thing but plausibility is an important second thing. Unreasonable coefficients or heywoods raise doubt whether the identification and estimation procedure really worked.
Best
Holger
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