I have 26 binary variables (Yes and No) and want to do Cluster Analysis (my sample size is 275), some references suggest to do factor analysis or principal component analysis on the binary variables first and then saving the factor or component scores as new variables and finally clustering the cases on the basis of those scores. Thus, the data being clustered are no longer binary.
My questions are:
1- Can I do factor analysis on binary data?
2- I also have 8 low observation variables, should I exclude them from my analysis or I should let the factor analysis decide about them?
3- Do you suggest any other analysis for Binary data?
I appreciate any comment and advice.
Searching on yields lots of hits. Here is one that looks useful:
- https://www.bristol.ac.uk/media-library/sites/cmm/migrated/documents/chapter8.pdf
PS- That chapter appears to be from this book:
- https://www.routledge.com/Analysis-of-Multivariate-Social-Science-Data/Bartholomew-Steele-Galbraith-Moustaki/p/book/9781584889601
And this page has relevant data files & syntax for R, SPSS and Stata (and other packages for some chapters):
- https://www.lse.ac.uk/Statistics/Research/Social-Statistics/Multivariate-data-analysis/Data-and-Syntax
Babak Jamshidi , I want to know how many clusters or groups exist based on 27 binary variables and then check the relationship between these cluster and dependent variables which are scale by doing another test for instance regression.
With binary observed variables the latent variable model is usually item response theory (also called latent trait modeling) or latent class modeling, depending on whether the latent variables define dimensions or groups. For a principle component approach see GIFI. But there are also clustering algorithms for binary data if you choose to skip the latent/PC step.
Daniel Wright thank you for your advice, I read that first I should do hierarchical and then two step cluster analysis, do you have any other suggestions? Can you name clustering algorithms for binary data
For clustering algorithms you just need to create distance matrices for person and/or items, and there metrics for different sorts of data for this, including binary. Check whichever cluster proc or function you are using.
ps. Some metrics, as used in a popular package, are discussed in: https://cran.r-project.org/web/packages/proxy/vignettes/overview.pdf
The study of how the probability of success depends on expanatory variables and grouping of materials.
The analysis of binary data also involves goodness-of-fit tests of a sample of binary variables to a theoretical distribution, as well as the study of 2×2
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