On certain occasions, a single publication opens up an enormous field of engagement. Such was the case with the publication of the MANN model papers. The ‘Multidimensional Analysis of Nearest Neighbors’ was characterized as a novel way of aggregating cohorts of borrowers into neighborhoods – or into collections that shared similar attributes.
The initial paper was published as: Allen, Craig M., “Credit scoring and risk-adjusted pricing: a review of techniques,” in Fabozzi, F. ed., Subprime Consumer Lending, Frank J. Fabozzi and Associates, New York, 1999.
The nearby graphic of the cover of Fabozzi’s book contains a link to the chapter – or at least to a version of the chapter that contains all of the detail of the chapter. This particular version, however, contains a bit about the math as an appendix / section at the end. For publication purposes, this math section was omitted in the version that was published.
But, for those that might be interested, the chapter is available at the associated link. The book is still available on Amazon.
The basic premise of this MANN model is that the measures that can be taken of a borrower (for example) – and let’s say that there are k measures taken of N borrowers, things like age, income, etc. And that these k measures can be reduced, via principal component analysis to some smaller number p (where p < k) of ‘rotated’ variables that are almost as good as the whole set of k variables at describing the variance in the N borrowers’ data.
This reduced set of p measures (or principal component values) of the borrower data can all be rank ordered, based upon the “Eigen value” associated with each Eigen vector. These p measures can also be rank ordered based upon the “information” contained in that dimension (using the Shannon-type measure of information) relating to each borrower’s behavior – like default frequency or delinquency.
By combining the information content of those p measures with the Eigen vector coordinate of those N borrower data points, the borrowers are clustered into groups. (Think of k-means clustering – although a much more efficient mechanism was utilized.) These groups have similar characteristics – and the similarity is weighted along dimensions that contain performance information.
The net result of the MANN process was to create clusters of borrowers that had very similar performance. When the measurements for a ‘new’ candidate for lending were taken (e.g., by that borrower filling out a loan application) – the new borrower could be placed, with good accuracy, into a cohort of similar borrowers, and the expected performance of the new borrower could be estimated quite effectively.
This MANN model was very useful for many different applications and became one of the staples of the Delphi analytics processes.
Other papers were written that also described this process.