I have two very important things to know. Can anyone help?
Question-1
If I have three categorical dependent variables and a continuous dependent variable, which are correlated (or associated), then if I conduct separate regressions with each dependent variable instead of a multivariate regression, what should actually be the basic problem?
Shouldn't the change be only in the standard errors?
Am I going to get correct p-values (I understand probably I will not) in both logistic regressions with the categorical DVs and in the linear regression?
Question-2
If one of my dependent variables is in proportions (the one that is continuous as I mentioned previously), how should I analyze it? My interest is not prediction. I just want to see the effect of the independent variables. But still I am not feeling confident with linear regression. The predictions will surely give values outside the range of the proportions (0.00-1.00).
Can logistic regression be an option? So that log(p/(1-p)) can be used as the dependent variable? So how do I define this log transform in SPSS?
Best Answer
Continuous proportions are sometimes modelled using beta regression. Logit transformation of the proportions are sometimes used. If there are multiple proportions that sum to 1 (compositional data), this is sometimes done via Dirichlet models.
These terms should help you find many relevant questions and answers here on CV, and good pointers more generally (google searches are highly productive).
references - e.g. Smithson, M. and Verkuilen, J. (2006). A better lemon squeezer? maximum-likelihood regression with beta-distributed dependent variables. Psychological Methods, 11(1):54-71.
http://psychology3.anu.edu.au/people/smithson/details/betareg/Smithson_Verkuilen06.pdf
Also see http://nw08.american.edu/~jernigan/comp.pdf