Add Maximum R Square Improvement (MAXR) to GLM

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SAS has Maximum R square Improvement (MAXR):

The maximum R2 improvement technique does not settle on a single model. Instead, it tries to find the "best" one-variable model, the "best" two-variable model, and so forth, although it is not guaranteed to find the model with the largest R2 for each size.
The MAXR method begins by finding the one-variable model producing the highest R2. Then another variable, the one that yields the greatest increase in R2, is added. Once the two-variable model is obtained, each of the variables in the model is compared to each variable not in the model. For each comparison, the MAXR method determines if removing one variable and replacing it with the other variable increases R2. After comparing all possible switches, the MAXR method makes the switch that produces the largest increase in R2. Comparisons begin again, and the process continues until the MAXR method finds that no switch could increase R2. Thus, the two-variable model achieved is considered the "best" two-variable model the technique can find. Another variable is then added to the model, and the comparing-and-switching process is repeated to find the "best" three-variable model, and so forth.

The difference between the STEPWISE method and the MAXR method is that all switches are evaluated before any switch is made in the MAXR method . In the STEPWISE method, the "worst" variable may be removed without considering what adding the "best" remaining variable might accomplish. The MAXR method may require much more computer time than the STEPWISE method.

Reference: https://v8doc.sas.com/sashtml/stat/chap55/sect29.htm

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JIRA Issue Details

Jira Issue: PUBDEV-8235
Assignee: Wendy
Reporter: Neema Mashayekhi
State: Resolved
Fix Version: 3.34.0.1
Attachments: N/A
Development PRs: Available

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Linked PRs from JIRA

#5627