Decile Analysis Primer:
Cum Lift for Response Model
Bruce Ratner, Ph.D.
The decile analysis is a tabular display of model performance. I illustrate the construction and interpretation of the response decile analysis in Table I. (The response model, on which the decile analysis is based, is not shown.) But, keep in mind that the decile analysis only indicates the accuracy of a response model. There are two additional concepts of model assessment - precision and separability - that are needed to complete the picture of response model performance.
Construction of the Response Decile Analysis
1. Score the validation sample or file using the response model under consideration. Every individual receives a model score, Prob_est, the model's estimated probability of response.
2. Rank the scored file, in descending order by Prob_est.
3. Divide the ranked and scored file into ten equal groups. The Decile variable is created, which takes on ten ordered 'values': top(1), 2, 3, 4, 5, 6, 7, 8, 9, and bottom(10). The 'top' decile consists of the best 10% of individuals most-likely to respond; decile 2 consists of the next 10% of individuals most-likely to respond. And so on, for the remaining deciles. Accordingly, Decile separates and orders the individuals on an ordinal scale ranging from most to least likely to respond.
4. Number of Individuals is the number of individuals in each decile; 10% of the total size of the file.
5. Number of Responses (actual) is the actual - not predicted - number of responses in each decile. The model identifies 911 actual responders in the top decile. In decile 2, the model identifies 544 actual responders. And so on, for the remaining deciles.
6. Decile Response Rate is the actual response rate for each decile group. It is Number of Responses divided by Number of Individuals for each decile group. For the top decile, the response rate is 12.3% (= 911/7,410). For the second decile, the response rate is 7.3% (=544/7,410). Similarly for the remaining deciles.
7. Cumulative Response Rate for a given depth-of-file (the aggregated or cumulative deciles) is the response rate among the individuals in the cumulative deciles. For example, the cumulative response rate for the top decile (10% depth-of-file) is 12.3% (=911/7,410). For the top two deciles (20% depth-of-file), the cumulative response rate is 9.8% = ( [911+544]/[7410+7410] ). Similarly for the remaining deciles.
8. Cum Lift - for a given depth-of-file - is the Cumulative Response Rate divided by the overall response rate of the file, multiplied by 100. It measures how much better one can expect to do with the model than without a model. For example, a Cum Lift of 294 for the top decile means that when soliciting to the top 10% of the file based on the model, one can expect 2.94 times the total number of responders found by randomly soliciting 10%-of-file. The Cum Lift of 235 for top two deciles, means that when soliciting to 20% of the file based on the model, one can expect 2.35 times the total number of responders found by soliciting 20%-of-file without a model. Similarly for the remaining deciles. (My SAS-code program is available upon request: click here .)
Rule: The larger the Cum Lift value the better the accuracy, for a given depth-of-file.
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