Hello RG researchers.
The theory says that data from items for Exploratory Factor Analysis (EFA) should have a multivariate-normal distribution.
But I am working with Likert type items and their distribution is not multi-variate normal. Moreover, some answers have floor or ceiling-effects. Also, I have a subject to item ratio of about 5:1.
Please, any suggestion for doing this EFA?
Thank you.
Hey Andrés,
here is a paper with a possible idea:
http://quantpsy.org/pubs/zhang_preacher_jennrich_2012.pdf
Regards
T.
Hey Andrés,
There are also some other papers that state that linear analysis are sufficiently robust to apply even though you don't have a normal distribution. So you can go on with the EFA.
But if you really want to go to the basics this can be of help:
Costello, A., & Osborne, J. (2005). Best Practices in Exploratory Factor Analysis: Four Recommendations for Getting the Most From Your Analysis.
http://pareonline.net/pdf/v10n7.pdf
Regards
Juan Carlos Saravia
@Andrés: you may first try to transform your data on order to get more "normal" data. Classical transformations are the Box-Cox transformation. You can google this easily.
Thanks for your answers.
Regarding transformations, the current literature does not recommend that, at least for regression models. It is difficult to obtain a real "normal" distribution. Also, it is difficult to interprete the results.
Thank you.
Hi Andres,
EFA and PCA are pretty robust regarding those assumptions as stated before. Anyway, I think you could get a better normal fitting on likert scales using rank based transformation like Blom's. Attached please find a paper discussing limitations and here http://support.sas.com/documentation/cdl/en/proc/61895/HTML/default/viewer.htm#a000146840.htm find instructions using SAS proc rank. Should not be difficult to perform it with other packages...
Best
If data is deviating from the multivariate normal distribution, estimated correlation matrix can be biased. Minimum Covariance Determinant (MCD) approach can be used to reliably estimate the correlation matrix in presence of deviations from multivariate nor-maility.
See
Exploratory factor analysis revisited: How robust methods support the detection of
hidden multivariate data structures in IS research H. Treiblmaier and P. Filzmoser
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