Parceling works because of the nature
of logistic regression. Logistic regression essentially is modeling
the linear relationship between the independent variables and the
natural log of the odds of 1 to 0. If we look at the process of
duplicating observations and giving them weights proportional to
their “1-ness” or “0-ness” then the 1/0 odds become the Loss
Ratio or % recovery or Profit/Cost ratio.
One advantage of modeling this
continuous target using logistic regression instead of linear
regression is that it simplifies the modeling assumptions on the
distribution of the target ratio since the kind of ratios discussed
here often quite skewed due to a high percentage of 0 or small values
and a few very large values. This technique and also has added power
to the “goodness” or “badness” for the true 0’s and 1’s
that may be ignored in a linear regression of a ratio.
For example:
- Loan Collections – In a charged off loan with no recoveries the recovery % is zero regardless of how much was owed. In the parceling technique, this “Bad” account is extra bad if the amount owed was high, but not nearly as bad if the amount owed was small.
- Insurance Risk –When an insurance policy has a no claims it is Good, but it’s Loss Ratio is 0 regardless of how much premium is paid. In the parceling technique, that account is extra “Good” if the premium paid is large and not so good when the premium paid is small. Likewise, when a claim is paid that is large then that account is extra “Bad.”
- Profitability – If an account in any sort of business has no revenue, then the revenue cost ratio is 0 regardless as to how much that account has cost the company. With parceling a zero revenue account is extra bad if its associated costs are high and not so bad if its costs are low.
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