# Normality for Confirmatory analysis with Likert scale data

I'm running CFA on AMOS for an attitude scale and I got a good model fit after deleting three problematic items (less than .30 factor loadings). However, my data is not normally distributed. I was reading other threads that say Likert-based data are ordinal, hence they can't be normal, but I wonder if what I did is wrong? Should I re-run my analysis after transforming my data? Many thanks for your help!!

Treating ordinal data as continuous is often a reasonable approximation, there are a few papers on this:

http://psycnet.apa.org/journals/met/9/4/466/

http://rd.springer.com/article/10.1007/s11135-008-9190-y

http://www.unc.edu/~curran/pdfs/Curran,West%26Finch(1996).pdf

Go read some papers that use CFA and you'll see that treating ordinal data as continuous is common (you'll even find some by me :). One argument for this is that this is how the instrument is used - people will sum the scores and treat those sums as a continuous scale, you can therefore translate between the meaning of your CFA and the meaning of the total score that is used.

However, if you want to address the issue you can't transform the data (well, you can, but you can't magically make the data non-ordinal). But you can analyze it more appropriately.

There are two issues: first is the parameter estimates, and particularly the standard errors of the parameter estimates, you can solve this with bootstrapping, which is straightforward in Amos. Second is the fit indices, that's not so easily solved.

It's possible using a Bayesian approach in Amos (I believe), or you an also treat the data as ordinal, in paid programs like Mplus, Lisrel, or EQS, gsem (in Stata) or free programs like Lavaan (in R), sem (in R) and Mx (stand-alone, and an R package).

Amos isn't up to the task. It used to be the case , many years ago, that Amos was the most cutting edge program, but it has barely advanced in the past 10-15 years, when other programs have overtaken it. I'm not sure why that is.