Everyday we allocate mortgages between two investor platforms. Within each risk segment and term (length of mortgage in years), mortgages are allocated based on investor demand randomly. ie 70/30 split.
Mortgages/borrowers can have a number of attributes, fico, dti, loan amount, borrower income, number of revolving accounts, etc.
I want to validate that the random allocation is truly random across time and across various attributes.
I am thinking of using Welch's t-test and testing each attribute separately (unequal sample sizes and unequal variances). Is this approach valid or should I look at some type of multivariate test? ie Hotellings T-squared.
On some days, there are only a handful of loans per platform, so I think using a window size of couple days, a week or even month. What do think for the time dimension and monitoring the overall process on an ongoing basis?