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Gains and Lift plots for binary-response models

PURPOSE:

The %GainLift macro produces cumulative and noncumulative plots of the following statistics for a binary response model such as a logistic or probit model:

• Gains
• Lift
• Percent Captured
• Percent Response

All possible plots can be displayed in a single panel, or plots can be individually presented.

HISTORY:

Version	Update Notes
1.0	Initial version

REQUIREMENTS:

SAS 9.2 TS1M0 or later and SAS/GRAPH.

USAGE:

Follow the instructions in the Downloads tab of this sample to save the %GainLift macro definition. Before calling the %GainLift macro, specify the following %INC statement in your SAS program or in the SAS editor window to define the macro and make it available for use. In the %INC statement, replace the text within quotes with the location of the %GainLift macro definition file on your system.

%inc "<location of your file containing the GainLift macro>";

Following this statement, you can call the %GainLift macro using the following syntax. Macro arguments can be listed in any order.

%GainLift(<list of macro arguments separated by commas>)

See the Results tab for an example.

The following macro arguments are required:

response=variable-name

Specifies the name of the variable containing the observed response values. This is typically the variable specified to the left of the equal sign in the MODEL statement of procedures such as PROC LOGISTIC, PROC GENMOD, and PROC PROBIT.

event=value | "value" | 'value'

Specifies the value of the response variable which represents the event level that was modeled. If the RESPONSE= variable is a character variable, value must be enclosed in quotes.

p=variable-name

Specifies the name of the variable containing the predicted event probabilities produced by the model. This variable is typically produced by the P= option in the OUTPUT statement of procedures such as PROC LOGISTIC, PROC GENMOD, and PROC PROBIT.

The following macro arguments are optional:

data=SAS-data-set

Specifies the name of the data set containing observed response values and predicted probabilities from the fitted model. This data set is typically produced by the OUT= option in the OUTPUT statement of procedures such as PROC LOGISTIC, PROC GENMOD, and PROC PROBIT. If not specified, the data set last created is used.

groups=20 | 10

Specifies the number of groups produced from the predicted event probabilities. By default, 20 groups (demi-deciles) are produced. GROUPS=10 produces deciles.

panel=YES | NO

The default PANEL=YES produces a single panel of all eight possible plots. All eight plots are produced individually and full-sized when PANEL=NO. If you also specify the ONEPLOT= option, PANEL=NO is implied and only the requested plot is produced.

oneplot=CGAIN | GAIN | CLIFT | LIFT | CCAPT | PCAPT | CRESP | PRESP

Requests a single, full-size plot rather than all eight plots. Specify one of CGAIN (cumulative gains), GAIN (gains), CLIFT (cumulative lift), LIFT (lift), CCAPT (cumulative percent captured), PCAPT (percent captured), CRESP (cumulative percent response), or PRESP (percent response).

graph=LINE | BAR | NONE

The default GRAPH=LINE produces line graphs. Bar graphs are produced when GRAPH=BAR. If only the OUT= data set is needed, specify GRAPH=NONE.

xaxis=SelectedPCT | Percentile | GroupNum

The default XAXIS=SelectedPct displays the selected percentile values of the predicted probability groups on the horizontal axis. The group with the highest predicted probability has the lowest selected percentile. The group with selected percentile 100 has the lowest predicted probability. The opposite is true when XAXIS=Percentile since the groups with the lowest predicted probability has the lowest percentile. Group numbers are displayed when XAXIS=GroupNum. Group 1 has highest predicted probability.

grid=ON | OFF

By default, a set of grid lines is added to the graphs when GRID=ON. No grid lines are displayed when GRID=OFF.

out=SAS-data-set

Names the data set created by the macro which contains the statistics needed to generate the plots. If not specified, the data set is named _GainLift.

The version of the %GainLift macro that you are using is displayed in the SAS log when you specify version (or any string) as the first argument. For example:

    %GainLift(version, ...other options...)

DETAILS:

The plots produced by the %GainLift macro are commonly used to assess the predictive ability of a binary response model, such as a logistic or probit model. Gains and lift plots are popular in direct marketing and credit scoring fields. Another plot, the ROC plot, also summarizes predictive ability. The ROC plot can be produced directly by the LOGISTIC procedure.

The gains plot shows, for each group, the percent difference between the overall proportion of events and the observed proportion of observations in the group that are events. The cumulative gains plot shows the percent difference between the overall proportion of events and the observed proportion of events in all groups up to the current group. The lift plot gives, for each group, the ratio of the proportion of observations in the group that are events to the overall proportion of events. The cumulative lift plot gives event rate up to the current group over the overall event rate. The percent captured plot gives, for each group, the percentage of total events in the group. The cumulative percent captured plots gives the percentage of total events up to the current group. The percent response plot gives the percentage of observations in the group that are events. The cumulative percent response plot gives the percentage of observations up to the current group that are events. Note that percent response and cumulative percent response are often considered gains and cumulative gains.

The statistics are computed as follows:

   E  = total number of events
   N  = number of observations
   G  = number of groups (10 for deciles or 20 for demi-deciles)
   P  = overall proportion of observations that are events (P = E/N)
   ei = number of events in group i , i=1,2,...,G
   ni = number of observations in group i
   pi = proportion of observations in group i that are events (pi = ei/ni)

   %Response = 100*pi
   Cumulative %Response = 100*Σiei/Σini
   %Captured = 100*ei/E
   Cumulative %Captured = 100*Σiei/E
   Lift = pi/P
   Cumulative Lift = (Σiei/Σini)/P
   Gain = 100*(pi-P)/P = 100*(Lift-1)
   Cumulative Gain = 100*(Cumulative Lift-1)

Assuming an unpredictive model which randomly puts observations into groups using the overall observed proportion of events, baselines for each statistic can be computed as follows:

   %Response = 100*P
   Cumulative %Response = 100*P
   %Captured = 100*ni/N
   Cumulative %Captured = 100*Σini/N
   Lift = 1
   Cumulative Lift = 1
   Gain = 0
   Cumulative Gain = 0

Macro Updates

The %GainLift macro attempts to check for a later version of itself. If it is unable to do this (such as if there is no active internet connection available), the macro will issue the following message:

   GainLift: Unable to check for newer version

The computations performed by the macro are not affected by the appearance of this message.

LIMITATIONS:

Only unaggregated data can be used. That is, the %GainLift macro cannot be used on data which were fitted using "events/trials" syntax in the MODEL statement of the fitting procedure, or if a FREQ statement was used. To use the macro for such data, the data must be expanded so that each observation represents a single individual or item. This can be done using a DATA step and DO loops containing OUTPUT statements.

MISSING VALUES:

Observations that resulted in missing predicted probability (such as when a predictor value is missing) are ignored and do not influence the statistics.

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These sample files and code examples are provided by SAS Institute Inc. "as is" without warranty of any kind, either express or implied, including but not limited to the implied warranties of merchantability and fitness for a particular purpose. Recipients acknowledge and agree that SAS Institute shall not be liable for any damages whatsoever arising out of their use of this material. In addition, SAS Institute will provide no support for the materials contained herein.

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These sample files and code examples are provided by SAS Institute Inc. "as is" without warranty of any kind, either express or implied, including but not limited to the implied warranties of merchantability and fitness for a particular purpose. Recipients acknowledge and agree that SAS Institute shall not be liable for any damages whatsoever arising out of their use of this material. In addition, SAS Institute will provide no support for the materials contained herein.

EXAMPLE: Modeling cancer remission data

The following example uses the cancer remission data presented in the stepwise logistic regression example in the LOGISTIC documentation. The first model uses only a single predictor. The performance of the model is assessed by the ROC curve provided by PROC LOGISTIC and by the plots from the %GainLift macro. The area under the ROC curve is 0.586 indicating only a slight improvement in predictive ability of this model over a model containing only an intercept (with area 0.5). The cumulative plots from the %GainLift macro show curves for the model that do not deviate much from baseline which again indicates a poorly performing model.

      ods graphics on;
      title "Cancer remission model (smear)";
      proc logistic data=remission plots(only)=roc;
         model remiss(event='1') = smear;
         output out=out p=p;
         run;
         
      %inc "<location of your file containing the GainLift macro>";
      
      %GainLift(data=out, response=remiss, p=p, event=1)
      title;

Cancer remission model (smear) The LOGISTIC Procedure

The final model found by stepwise selection in the LOGISTIC documentation example is assessed next. The area under the ROC curve for this model is 0.889 indicating much better performance. The plots from the %GainLift macro also show much greater deviation from baseline. The cumulative percent captured plot shows that over 50% of the remissions were captured using only the top 25% of predicted remission probabilities. The cumulative percent response plot shows that the top 20% of predicted remission probabilities contain 80% remissions. This is a factor of 2.4 (the cumulative lift value) times the base (overall) remission rate of 33%, or a 140% (the cumulative gain value) increase.

      title "Cancer remission model (li temp cell)";
      proc logistic data=remission plots(only)=roc;
         model remiss(event='1') = li temp cell;
         output out=out p=p;
         run;
         
      %GainLift(data=out, response=remiss, p=p, event=1)

Cancer remission model (li temp cell) The LOGISTIC Procedure

The following macro call produces a bar chart version of the cumulative percent captured plot for the final model.

      %GainLift(data=out, response=remiss, p=p, event=1, oneplot=ccapt, graph=bar)

Cancer remission model (li temp cell)

Right-click on the link below and select Save to save the %GainLift macro definition to a file. It is recommended that you name the file GainLift.sas.

Download and save GainLift.sas

Operating System and Release Information