Multinomial logistic regression vs Multiple logistic regression

#1
Hi All,

I have never done multinomial regression before. I am a SAS user and am working on a problem and wanted some help in determining the best solution.

I have large dataset with more than 50,000 rows. My outcome variable is a nominal variable with 4 outcomes. My predictors list contains more than 100 variables, of which some are categorical and some are continuous. The categorical predictors are not ordinal. My goal is to find regression equation to predict the outcomes.

1. Is having multiple logistic regression models, each to predict one outcome vs the rest of outcomes, better; or having one multinomial regression model better?

2. If having one multinomial regression model better, then I researched the following SAS procedures:

a. PROC GENMOD which allows to predict multinomial regression but doesn't have variable selection method.
b. PROC CATMOD, which can predict categorical outcome variables . is there a variable selection method for this? can this have both continuous and categorical predictors?
c. PROC Logistic with link = glogit option, which can predict ordinal outcome variable and has variable selection option.

I would like to know which procedure to use and with what options. Please help! Thanks.