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?