Structural Equiation Modeling - Likert variable and fit indices

Hello everybody!

Thank you in advance for reading, and for trying to help!

To put it briefly.. I am working with Structural Equiation Modeling (for the first time :S). In this study, we have 1000+ participants and we are studying the relationship between alcohol use and a personality construct.

Personality is measured with different validated questionnaires, but alcohol use is measured using a Likert-type scale on the number of times the participant has used alcohol in the last month (this is the usual way to measure alcohol use), so that: 0 (never), 1 (1-3 times), 2 (4-7 times), 3 (8-12 times), etc... up to 7 (40+ times)

My question is..

Other models with other alcohol use outcomes (validated questionnaires for example) show a pretty decent fit. However, models with this Likert-type variable usually show good CFI (>.95)... but low TLI (0.70-0.85) and sufficiently high RMSEA (0.10 - 0-13) as to reject the models..

Is it possible that this Likert-type format is hindering our chances to find a good fit? Is there any way (e.g. recoding the variable? reducing levels of the variable?) that could help improving the fit? i.e. reducing RMSEA...

Otherwise I'm guessing I'll just have to reject the models... what else :D

Thank you very much in advance!!




Doesn't actually exist
Are you using the proper estimator to handle this kind of non-normality (Likert scale)? The literature usually recommends diagonally-weighted least squares or some other type of least-squares estimator (not the unweighted one though. That one is always bad and ugly and should never be used) with adjustments to the mean and variance of the chi-square test of fit, from which all the other measures of fit are derived.

If you fitting these models with normal-theory maximum likelihood (the default estimator in most cases) all kinds of things are prone to go wrong.