Did you use installment/income term in addition to loan amount/income and FICO in your multivariate logistic regression? Did you also use separate monthly income term in your regression? If not, then your statement is ingenuous as you didn't considered the relative importance of these terms in respect to each other. If you had considered relative merits of these terms together in your regression, you would know that monthly income is a very important "borrower characteristics" datapoint and any transformation containing monthly income will be weighted heavily in a regression. The first step of any regression analysis is to identify important and influential attributes to include in the regression.
The English language explanation for loan amount/income transformation is simple. This transformation represents whether a borrower given certain income can pay back the loan amount or not
irrespective of duration. The installment/income transformation represents whether a borrower given certain income can make
regular payment of installment amount over certain duration to payback loan amount or not. It is a "borrower indebtedness" datapoint and goes along with DTI.
When you are lending on LC primary market, you are deciding whether to lend on the LC given terms of lending (interest rate, duration installment). If you were deciding the terms of lending yourself (for ex: Prosper 1.0), then your strategy of not considering platform recommended terms of lending in assessing the loan quality will be effective and you will come up with your own acceptable terms of lending at which you will lend.
Sorry to see you discontinue the lending but not surprised.
Installment to income represents capability to pay, what does loan amount to income represent?
My answer would simply be "something very important".
In a multi-variate logistic regression its statistical significance is quite large; only surpassed by FICO. Using words of the English language to describe a relationship seems sensible enough but our own personal biases attach a significance or lack there-of that may not be accurate. I'll go where the numbers take me and prefer to exclude all LC model results from being inputs my own model, period. That permits my model to be a completely unbiased observer so to speak when evaluating the outputs of the LC model to determine which loans meet my own investment criteria and which do not.
For those that may not already know I no longer invest in LC loans and its been a long time since I participated in any of this.
Judging from the Cumulative ROI's I posted recently I don't plan to resume. But then again I never planned to resume anyway.
https://forum.lendacademy.com/index.php/topic,5076.0.html
EDIT: Changed "linear regression" to "logistic regression" which was used. Like I said, it's been quite a while.