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Gains vs % response charts

Posts: 38

Gains vs % response charts

Hi everyone,

I have been looking online for an explanation to this and came here as a last resort.


- Can anyone tell me tell me the difference between the gains chart and the % response chart in SAS EM and their applications.


- The gains chart plots positive predicted value (or gains) vs depth and therefore i believe can be used in optimising response rates for target marketing projects. However, the %response chart plots %response on depth but generates different results to the gains chart. Please can someone clarify?



SAS Employee
Posts: 180

Re: Gains vs % response charts

[ Edited ]

The short answer is that Gains are calculated relative to the baseline (overall average) rate while Response rates are computed without adjusting for the overall rate.   The SAS Enterprise Miner help utility is available by openging the application and then clicking on Help --> Contents to display the help topics.   You can click on the magnifying glass near the top and type "Gains" and hit enter.  In the panel on the left, click on Model Comparison node and then scroll down in the panel on the rigtht until you see the Data Mining Measures section under which you will see something like the following (some information omitted here):


The following terminology is used for the Gains and Lift Chart:

Decile or Demi-Decile -- 10% or 5% cuts of the posterior probability, arranged in descending order.
% Response -- the proportion of true responders in each decile.
Cumulative % Response -- the cumulative proportion of responders. At the last decile, the Cumulative % Response indicates the baseline percentage of responders.
% Captured Response -- the proportion of total responders that are captured in a decile or demi-decile.
Cumulative % of Captured Response -- the cumulative proportion of total responders that are captured in a decile or demi-decile.
Gain -- ((% of events in decile / random % events in decile) – 1)
Lift -- the ratio of % Captured Response within each decile to the baseline % Response.
Cumulative Lift -- the cumulative ratio of % Captured Responses within each decile to the baseline % Response.


By way of example, suppose the response rate (aka  % Response) is 12% in a particular bin, but the overall average response rate for the whole population is 4%.   The % Response for the bin = 12% but Gain = ((12%/4%)-1) = (3-1) = 2 (or 200%) gain since the gain from 4% to 12% represents a change of 8% which is twice as large as the baseline value of 4%.   In this way, Gain might be negative but % Response cannot ever be negative.  In my example, SAS Enterprise Miner the axis for Gain was marked using a % scale so my example above would have displayed the Gain as 200 for that decile.  


In practice, the Gain plot in SAS Enterprise Miner represents the cumulative gain at a particular bin and produces exactly the same plot as the Cumulative % Response graph but with different axis markings on the vertical axis.  Suppose you are looking at the 3rd decile.   In this example, the % Response plot only shows the percent of respondents in the 3rd decile while the Cumulative % Response plot shows the percent response for the top 3 deciles.  


Hope this helps!


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