NPS ARCHIVE 1997 PURCELL, T. NAVAL POSTGRADUATE SCHOOL MONTEREY, CALIFORNIA THESIS THE USE OF CLASSIFICATION TREES TO CHARACTERIZE THE ATTRITION PROCESS FOR ARMY MANPOWER MODELS by Terence S. Purcell September, 1997 Thesis Advisor: Robert R. Read Second Reader: Samuel E. Buttrey Thesis P9482 Approved for public release; distribution is unlimited. !0XLIBRARY STGRADUATESCHOOL Y CA 93943-5101 REPORT DOCUMENTATION PAGE FormApprovedOMBNo. 0704-0188 Publicreportingburdenforthiscollectionofinformationisestimatedtoaverage 1 hourperresponse, includingthetimeforreviewinginstruction,searchingexistingdata sources, gatheringandmaintainingthedataneeded, andcompletingandreviewingthecollectionofinformation. Sendcommentsregardingthisburdenestimateorany otheraspectofthiscollectionofinformation, includingsuggestionsforreducingthisburden,toWashingtonHeadquartersServices, DirectorateforInformation Operationsand Reports, 1215JeffersonDavisHighway, Suite 1204,Arlington, VA22202-4302, andtotheOfficeofManagementandBudget, PaperworkReduction Project(0704-0188)WashingtonDC20503. 1. AGENCY USE ONLY (Leaveblank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED September 1997 Master's Thesis title and subtitle The Use of Classification Trees to Characterize FUNDING NUMBERS the Attrition Process for Army Manpower Models 6. author(S) Terence S. Purcell 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) PERFORMING Naval Postgraduate School ORGANIZATION Monterey CA 93943-5000 REPORTNUMBER 9. SPONSORING/MONITORING AGENCYNAME(S) AND ADDRESS(ES) 10. SPONSORING/MONITORING AGENCYREPORT NUMBER ii. supplementary notes The views expressed in this thesis are those ofthe author and do not reflect the official policy or position ofthe Department of Defense or the U.S. Government. 12a. DISTRIBUTION/AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE Approved for public release; distribution is unlimited. 13. ABSTRACT (maximum 200 words) The U.S. Army has a system of large personnel-flow models to manage the soldiers. The partitioning ofthe soldiers into groups having common behavior is an important aspect of such models. This thesis presents Breiman's Classification and Regression Trees (CART) as a method of studying partitions CART relative to loss behavior. It demonstrates that is a simple technique to use and understand while at the same time still being a powerful forecasting tool. A CART example is included that provides the reader a thorough understanding ofthe method. The analysis explores the structure found in the current Classification Groups (C-Groups) used by the Army. CART is used to review the structure of the C-Groups and conduct some exploratory work to demonstrate that different combinations of factors result in greater internal homogeneity in forecasting. Recommendations are provided on how to approach the process of modifying the C-Groups. The use of CART results in obtaining insights into the Army force structure that would not have been found with any other forecasting technique. This thesis reveals the power of CART as a forecasting tool. 14. subjectterms Loss Rates, CART, Partition, Attributes, Cross-Validation, 15. NUMBER OF Tree PAGES 96 16. PRICE CODE 17. SECURITY CLASSIFICA- 18. SECURITY CLASSIFI- 19. SECURITY CLASSIFICA- 20. LIMITATION OF TION OFREPORT CATION OF THIS PAGE TION OF ABSTRACT ABSTRACT UL Unclassified Unclassified Unclassified NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89) PrescribedbyANSI Std. 239-18 298-102 11 Approved for public release; distribution is unlimited. THE USE OF CLASSIFICATION TREES TO CHARACTERIZE THE ATTRITION PROCESS FOR ARMY MANPOWER MODELS Terence S. Purcell Lieutenant Commander, United States Navy B.S., Pennsylvania State University, 1981 Submitted in partial fulfillment ofthe requirements for the degree of MASTER OF SCIENCE IN OPERATIONS RESEARCH from the NAVAL POSTGRADUATE SCHOOL September 1997 /I/ i OXLIBRARY SCHOOL TGRADUATE ABSTRACT The U.S. Army has a system of large personnel-flow models to manage the soldiers. The partitioning of the soldiers into groups having common behavior is an important aspect of such models. This thesis presents Breiman's Classification and Regression Trees (CART) as a method ofstudying partitions relative to loss behavior. It demonstrates that CART is a simple technique to use and understand while at the same time still being a powerful forecasting tool. A CART example is included that provides the reader a thorough understanding of the method. The analysis explores the structure found in the current Classification Groups (C-Groups) used by the Army. CART is used to review the structure of the C-Groups and conduct some exploratory work to demonstrate that different combinations offactors result in greater internal homogeneity in forecasting. Recommendations are provided on how to approach the process of modifying the C-Groups. The use of CART results in obtaining insights into the Army force structure that would not have been found with any other forecasting technique. This thesis reveals the power ofCART as a forecasting tool. VI TABLE OF CONTENTS INTRODUCTION I. 1 BACKGROUND A. 1 B. THESIS OBJECTIVES AND ORGANIZATION 5 DATA EVOLUTION II. 7 A SOURCE 7 FORMAT AND MANIPULATION B. 7 METHODOLOGY III. 13 INTRODUCTION TO CART A. 13 B. S-PLUS AND CART 15 C. CART EXAMPLE 20 IV. ANALYSIS AND RESULTS 33 A. C*-GROUP DATA 34 B. REGULARDATA 46 SUMMARY C. 58 V. CONCLUSION AND RECOMMENDATIONS 61 CONCLUSIONS A. 61 B. RECOMMENDATIONS FOR FURTHER STUDY 62 APPENDIX A. SUMMARY STATISTICS 65 APPENDIX B. SAMPLE FILE (FIRST 40 ROWS) 67 APPENDIX C. CROSS VALIDATION METHOD IN S-PLUS 69 Vll APPENDIX D EXAMPLE DATA AND S-PLUS COMMANDS 71 APPENDIX E C*-GROUP DATA AND S-PLUS COMMANDS 73 APPENDIX F. S-PLUS COMMANDS USED ON THE REGULAR DATA 77 LIST OF REFERENCES 81 INITIAL DISTRIBUTION LIST 83 vin