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PCA/Factor Analysis with ordinal data

I have a dataset from social sciences that contains many ordinal categorical variables with > 2 levels which are linked to scores like 1 2 3..

I was asked if there are correlations between these ordinal variables so question: how to carry out correlation and PCA/Factor Analysis with this kind of data? Thanks for help!

Re: PCA/Factor Analysis with ordinal data

Correlations are for continuous variables. Associations are for categorical variables.

 

I suggest that you try Multiple Correspondence Analysis. See the chapters in the Help > JMP Documentation Library > Multivariate Methods guide.

Re: PCA/Factor Analysis with ordinal data

Marc, thanks for input this multiple correspondence analysis works fine for categorical data!

I also have data that are discrete numeric such as 1 2 4 5 . Is it possible to carry out a reliable PCA/factor analysis on such data i.e. will factor analysis give a correct grouping of the correlated discrete effects? Is it not better to use the spearman correlation approach? 

Re: PCA/Factor Analysis with ordinal data

No, PCA or factor analysis are not appropriate to analyze your ordinal data. The values are not numeric. They are just labels. They could be "A" through "E". You wouldn't use PCA or factor analysis with "A" through "E", right?

Re: PCA/Factor Analysis with ordinal data

Ok if odinal hower numbers can also be counts or scores

Re: PCA/Factor Analysis with ordinal data

You can have counts of discrete levels. Are the variables categorical? Are you counting these levels? It is still categorical data analysis.

Re: PCA/Factor Analysis with ordinal data

Think there is a misunderstanding related to the title of my dicussion referring to ordinal data; this can be handled with multiple correspondence.

However on top of ordinal variables my data set also contains many factors that are discrete numeric like counts (#defects) and scores (ratings 1 - 5) so my question is if factor analysis for these discrete numeric variables is possible in order to find the underlying correlation structure? I am confused about correlation between these discrete variables: when I make a mulltivariate plot correlations look terrible.. on the other hand when I loo to the color map many re& pink spots appear indicating correlation? How to correctly analyse these discrete factors?

Re: PCA/Factor Analysis with ordinal data

I agree that there is a misunderstanding.

 

Please see this article.

Re: PCA/Factor Analysis with ordinal data

Thanks for article on MCA, how about Latent Class Analyis; is this an equivalent approach for classifying ordinal variables? 

Re: PCA/Factor Analysis with ordinal data

LCA clusters rows based on frequency. Latent semantic analysis clusters levels (variables).

Re: PCA/Factor Analysis with ordinal data

MCA works fine, great tool for finding associations! I only don't know how to inerpret "dimension" what means a low or high score on dimension 1 or 2? 

Re: PCA/Factor Analysis with ordinal data

The dimension in MCA is the same as in PCA. The continuous data for the PCA here are the chi square distances from MCA and scaled before the PCA.