Both Principal Components and Cronbach's alpha are based on correlations. So if you consider it acceptable to run the first of those on binary data, then the same assumptions would also apply to alpha.

There are two parts of this question. The first is can Cronbach's alpha be used with binary data. The answer is YES. More discussion is here (https://www.researchgate.net/post/What_is_the_difference_between_Kuder-richardson_KR20_and_Cronbachs_Alpha_and_how_do_you_formulate_both).

The second question is if this is telling you what you want about "internal consistency". See discussions about the use, misuse, and misinterpretation of Cronbach's alpha (google that).

It is also worth adding that you might consider IRT (item response theory), as this is widely used for binary variables when you hypothesize their responses are caused by a latent variable (or a few latent variables). It is also called latent trait modeling, which is a little more descriptive of the statistical procedure.

Emilio, I agree with Daniel, you might consider using IRT. There is an article by Raykov et al. which deals with reliability of binary measures:

Tenko Raykov , Dimiter M. Dimitrov & Tihomir Asparouhov (2010). Evaluation of Scale Reliability With Binary Measures Using Latent Variable Modeling, Structural Equation Modeling: A Multidisciplinary Journal, 17:2, 265-279, DOI: 10.1080/10705511003659417

These authors argue that coefficient alpha cannot be considered in general a dependable estimator of scale reliability with continuous or discrete components.

This article is available online:

https://www.statmodel.com/download/RDASEM.pdf

Regards, Karin

Both Principal Components and Cronbach's alpha are based on correlations. So if you consider it acceptable to run the first of those on binary data, then the same assumptions would also apply to alpha.

Along with the methods, also try cluster analysis to see to what extent a cluster structure explains variability in your data/factors.

Kuder-Richardson's coefficient (KR20) is a special case for Cronbach's alpha when items are dichotomous.

Cronbach's alpha is a generalization of the KR20 formula.

When using dichotomous data, Pearson's r is equivalent to the Phi coefficient. Recently, there has been some advocacy for calculating alpha with the tetrachoric r instead. This is because calculating reliability using alpha with Pearson's r yields a "downward bias" (i.e., the calculated alpha is a minimum possible value, but the actual reliability may be higher). Presumably using the tetrachoric r yields a better estimate of reliability.

I have the same question, and all of the answers provided here have been very helpful. Thanks to all.

thank you for the support