I have been studying so many things on factor analysis with categorical variables. I am frustrated studying these many pdfs. I have 40 variables obtained from 40 questions. All of them are categorical. I can take them to be ordinal. The questions are different, so the answers are different too. It is not something like Likert scale where, for example, 1 means good for all questions, 2 means moderate for all questions, 3 means bad for all questions etc. It is like for one question:
"How often do senior management visit the wards to talk to staff?" rarely or never ..................... 1 around once a year................... 2 around once a month.................. 3 around once a week................... 4
For another question:
"What is the average amount of training (per person) received by a management staff?" Less than a day ..................... 1 Less than a week .................... 2 One to two weeks .................... 3
I want to factor analyze these variables: as can be seen here, 1, 2, 3 etc. differ in their meaning, and also the number of categories for each question differ.
Another problem is that I have non-response (missing values) in the data.
Here are my questions:
- What is the actual and best method of factor analysis with this kind of data. Besides could you please give me one good reference with your suggested methodology? I will be grateful for your help.
- If possible, please also give me indication on what to do with the missing values.
- I need to calculate factor scores from the analysis. I have tried polychoric correlation, but can't get factor scores by this. Factor scores are very important for my analysis. I can't make further analysis without them.
@this.is.not.a.nick: Thank you so much for your kind advice. I was suggested to use CATPCA too. But if using polychoric correlation can solve the problem of calculating factor scores then it's really great. But Andrea, chl and ttnphns, could you please confirm me whether
fa.parallel.poly() use principal component solution of the loadings and the specific factor or they just use maximum likelihood method for estimation of these parameters like
factanal() command does? As I can not assume the data to be normally distributed so I guess using principal component method for estimating parameters will be good in this case.
If these functions don't use principal component solution then I think I can do one thing here-
Calculate the polychoric correlation matrix r using package psych.
f <- principal(r,nfactors=3,rotate="varimax",scores=T,residuals=T) #say, 3 factors taken l <- print(f$loadings[c(1:ncol(data)),],cutoff=.0001) #data means original data
h <- t(l)%*%l #communality s <- h%*%t(l) #as fhat_i=(L'L)^(-1)*L'*Z_i data1 <- t(data[1,]) f1 <- s%*%data1 f1
And thus I can get $f_i$, $i=1,\dots,n$, manually from Bartlett's formula for scores for PC solution. (Reference: Applied Multivariate Statistical Analysis by Johnson and Wichern)
Now, for this procedure to be implemented there should not be any missing value (NA). So, if I take the missing values to be 0 by which for each question means "no comment" is there any problem? I think it will then act as just another category of my categorical variables. As the variables are categorical I think I should not take mean or median.
Am I right in my thoughts? Please suggest me. If possible please send me the paper regarding Polychoric versus Pearson correlations. I really had a lot of help from you and looking forward to contribute when I grow up.