Multivariate regression for 100 binary output variables I was asked to do some regression analysis on anonymised data, which I don't have yet. It will have a few categorical inputs and ~100 boolean outputs, something like this:
Category   Type         Size       Blood pressure     Y1   Y2    Y3  ....   Y99  
-------------------------------------------------------------------------------
cat        persian      small      high               1    0     0   ....   1
cat        persian      big        low                0    1     1   ....   0
dog        wolfhound    big        normal             1    1     0   ....   0
...        ...          ...        ...                      ......   
duck       scoter       small      above normal       0    1     1   ....   1  

(I just made up the meanings here). The number of samples in the real data set will be about a million, without missing values. The task is to predict the output, eg P(Y86 = 1 | {cat, siamese, big, low}) and generally understand the relationship between inputs and outputs. 
My questions: 


*

*which approaches are worth trying, what are the pros/cons?

*which R packages can be of help?

 A: Personally, I'd go about like this:


*

*Test for correlation between the input variables (eg, Category clearly looks always identifiable by Type and thus can be dropped), and between the output ones (via cor??) and leave only non-correlating ones in each group.

*Run multivariate regression via glm(cbind(Y1:Y99)~category+type+size+blood, family=binomial)

*For each of Y1..Y99 predictions, test significance level.. Well, here I'm a bit concerned because looks like with 1M of records any little change would look significant (because significance is proportional to SampleSize/Variability and the former clearly dominates).


Though I'm a bit concerned by the size of the data (which, to me, seems to render all statistical tests useless due to sample size), and I'm also worried whether it's legitimate to run those 100 regressions without somehow assuring they're independent or we're not doing some sort of multiple comparison. 
I also wonder whether I'm not missing anything important - in approach to the problem or in the tools.
A: Partial Least Sqaures Regression(there are R packages such as caret can deal with Binary classification problems too ) is the first thing that comes to my mind.
Y ~ X
I like PLS because it automatically finds a lower-dimension space (like-PCA does, but it tries to find components which capture most variation across both X & Y).
If you spend enough time then you should be able to extract meaningful patterns from the loading/score plots from the PLS model.
