I want to run an exploratory factor analysis (EFA) on a questionnaire consisting of 9 yes/no answered questions. Is it OK to run an EFA on a scale with binary coded questions?
Hello Sedat,
You can, but it's not recommended. The reason is, one presumes in EFA that the variables are continuous (amongst other characteristics). One tactic that many will try in a situation such as yours is to factor not the Pearson correlations among the 9 variates, but to factor their tetrachoric correlations.
A tetrachoric correlation is intended to be an estimate of the relationship between two variables that genuinely have continuous underlying, bivariate normal distributions but are each quantified as dichotomous values (e.g., 0,1).
In the R statistical package, the psych module includes a tetrachoric command. LISREL will pre-process variables using tetrachoric correlations, if desired. Other packages may do likewise. SPSS does not, however.
Good luck with your analysis.
Maybe this will help:
Barendse, M. T., Oort, F. J., & Timmerman, M. E. (2015). Using exploratory factor analysis to determine the dimensionality of discrete responses. Structural Equation Modeling: A Multidisciplinary Journal, 22(1), 87-101.
If the object you're looking at is at least partially dimensional you should look directly at all possible patterns of 3,4,5,... dimensions ... by using Configural Frequency Analysis. This will yield combinations where predictions by the basic model are not met. You find links to sources, programs and rationale at http://www.biposuisse.ch/biomath
Item response theory (IRT) is designed for this. It is used. for example, in educational testing with tests that are binary. It is also called latent trait modeling. Bartholomew et al.'s book (http://www.wiley.com/WileyCDA/WileyTitle/productCd-0470971924.html) describes the relationship between EFA and IRT.
Thank you all once again. The link provided by Ertuğrul Şahin really helped me. So simple, yet so efficient!
Gottfried, most IRT uses assume that the latent parameters, in education terms the person's ability and item characteristics, are continuous and normal. The typical IRT use assumes the manifest variables are binary (though there are procedures for, for example, ordinal data). The shape of latent variable distributions is a tough one to figure out with most psychology data sets. Paul Meehl and his colleagues did lots of great work (and colleagues continueing to do great work) on what they call taxometric analyses to decide is a latent variable is dimensional or classifies people into groups.
There's also a method called "multiple correspondence analysis" where you can explore how biniary responses are associated using chi-squared distances. I don't know how it works for questionnaire methodology and how it fits into classical test theory or item response theory though.
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