Factor analysis for ordinal variables that have different categories I have a data set that contains about 40 categorical variables that are taken as independent variables (and believed to be related to some unobservable human resource factors) and 4 categorical variables (like a company's turnover, competition for job etc.) that are taken to be the dependent variables. All these variables categories can be ordered although the variables have different number of categories. 
I want to see how the factors actually affect the dependent variables. I know how to do factor analysis with continuous variables. How do I do it with these kinds of categorical variables with different categories?  
Besides there is another categorical variable "size" representing the number of full time staffs ($\le 25$ is given 1, $26-99$ is given 2 and $>100$ is given 3) which is planned to use as a mediating or moderating variable. I want to see how the human resource factors affects the dependent variables. I mean, to make comments like “For small companies (smaller than 25 employees), human resource factor-1 impacts on profitability quite dramatically, however, there is no relationship between voice and profitability in medium and large hospitals...bla bla bla”  (for example) 
How do I relate the factors with the categorical dependent variables? Can I do whatever you suggest in R or in SPSS?
 A: I feel, from your description of the task, that it can be solved by means of quantifying (turning ordinal-level into scale-level) variables the way that the predictions or associatiations are maximized. This is known as optimal scaling and is implemented in SPSS (and, of course, in R, I believe). You might choose between 3 procedures, all adopting optimal scaling:


*

*Categorical PCA (CATPCA, or PRINCALS). Use this if you want PCA or Factor analysis. The procedure itself is PCA, not Factor analysis
in narrow sense of the word implying communalities. If you need
Factor analysis per se you may input the quantified variables
obtained in CATPCA to standard Factor analysis procedure. Having
identified components or factors behind your independent "resource"
variables and having obtained the factor scores you could then check
their effect on each dependent variable via ordinal regression (for
example).

*Categorical Canonical Correlation analysis (OVERALS). Use this to draw latent "traits" which are loaded simultaneously by both
independed and dependent sets of variables. You might want to read
something about canonical correlations if you are not familiar with
it.

*Categorical regression (CATREG). This is OVERALS in case one of the two sets of variables contains just one variable. Use it if you
want to model effects of your independent variables on each dependent
variable separately. It is like usual linear regression, only that it is nonlinear because of optimal scaling.

A: A kind of PCA applied to categorical data is MCA (Multiple Correspondence analysis) that let you detect underlying structures in a data set.
