Which method(s) can I use to predict a response when the inputs have various combinations and proportions of of categorical and numeric variables? I don't think a question like this has been asked before but please excuse me if it already has.
I’m hoping someone can help me by pointing me in the right direction with my problem as stated below.
I have a need to derive predictors for several continuous variables (let’s call them A, B and C), from a combination of two categorical variables (let’s call them U and V), an ordinal variable (W) and several continuous variables (let’s call them X, Y and Z).
At this stage I’m not sure how important each input variable will be and indeed if some of them can be ignored e.g. W and Z may prove to be of little use.
A, B and C are likely to be correlated, but probably not linearly.  
X, Y and Z show some roughly linear correlations if I look at them split by combinations of U and V.
I have some doubts about the reproducibility of U, V and W as they are logged subjectively, but on the whole they should be OK.
I have a database of several thousand records that give me values for A, B and C on a daily basis.
However, the values for U, V and X, Y and Z are given in shorter, irregular time frames, and I have around 8,000 such records.
An example of the data is given below (note that I’ve copied the values of A, B and C to each row on the same day but these values are the averages for the day):

My initial idea was to use something like a Regression Tree to come up with an equation for A for each combination of U, V and W (and then do the same for B and C).
However, the data set has around 10 unique values for both U and V and 5 for W, so the potential number of unique combinations is very large, even if I were to remove one of the categorical variables.  Also, I do not have values of A, B and C available that I can map perfectly to these combinations i.e. there are always two or more combinations of U and V in any day. 
 A: This seems a straight-forward problem. You have multiple predictors which you can use in a regression model as independent variables. However, several things complicate matters somewhat:


*

*There are multiple observations per day of variables U-Z for different time periods;

*These time periods are of unequal length, in irregular intervals and the number of periods varies over days;

*There are multiple outcome variables A, B and C;

*These are time series data, and as such you may have to model the time dimension so as not to induce bias.


The first point does not have to be a problem. A simple solution would be to just use all the variables as different inputs into the regression, where you put in variables U-Z multiple times for different periods of the day.
The second point requires more attention. Probably the easiest way is to use some rule to bin some time periods in a fixed number of periods, e.g. morning, afternoon, night. 
If you want to tackle the third issue depends on whether you want to model the correlations between A, B and C. You can do this with multiple equation models. 
The fourth point can be addressed with time-series analysis. Combined with the third, you can create a vector autoregressive model (VAR). 
However I would start with a simple model, just to get a feel for how the model predicts by checking its performance. Since you have lots of data, I would also include interaction terms between the different independent variables. You do not run a high risk of over-fitting the data, but you should still be carefull and use e.g. cross-validation methods afterwards. 
NB: these points are just a handful of the things I can think of that warrant attention. Since we cannot see what the actual case is about, you have to see for yourself what measures are necessary in this particular case.
