Multicollinearity in Zero Intercept Regression: They Are Not Who We Thought They Were
Models and Methods Track
Asked about the identity of the members the opposing team after being defeated by them, a famous football coach once said, “They are…who we thought they were.” Unfortunately, this is not the case when it comes to multicollinearity in zero intercept linear regression. It is not what we think it is, and the consequences of ignoring the distinction between it and its nonzero intercept counterpart can be devastating.
This presentation addresses the issue, viewed in the context of both of conventional wisdom (“multicollinearity is correlation among the regressors… can be checked with a correlation matrix”) and our earlier paper on the same general topic (Muticollinearity: Coping with the Persistent Beast, 2007 DoDCAS). As we stated in that paper, high correlation among regressors is sufficient, but not necessary, for multicollinearity to occur in standard regression, and true multicollinearity is revealed through variance inflation factors (VIFs).
Here, we show that zero intercept regression presents the opposite problem: high correlation among regressors, is necessary, but not sufficient, for multicollinearity to occur. While VIFs are again the best measure, the standard formula for calculating VIFs does not apply in zero intercept regression. The consequences of incorrectly using the standard formula (which implicitly assumes the existence of a nonzero intercept term) are enormous. VIFs can be overstated by 1,000% or more, potentially leading analysts to needlessly drop explanatory variables from cost estimating relationships, rework regressions that needn’t be reworked, and worry about a problem that in fact doesn’t exist.
We present a revised VIF formula that works in all cases (zero intercept or traditional) and show that (in the traditional case) the two formulas are equivalent. Unfortunately, a major regression-based cost estimating software tool does not use the revised VIF formula, and dramatically overstates zero-intercept multicollinearity statistics as a result. We give examples of this problem, and offer techniques to adjust the tools output.
Kevin Cincotta is a Senior Cost Analyst at Technomics. His primary areas of expertise are cost analysis, database creation and management, and statistics. Mr. Cincotta leads projects for the Defense Acquisition University (DAU) and Naval Center for Cost Analysis (NCCA). The projects focus on development and maintenance of training materials for cost analysts at all levels; and analysis of cost growth in time series data relating to contract obligations, respectively. In addition, he serves as Director of the Technomics Training Institute, which trains junior and mid-level costs analysts with the aim of building core knowledge and facilitating professional certification.
From 2003 to 2009, Mr. Cincotta was a Research at Fellow at LMI (formerly the Logistics Management Institute). He led myriad projects for clients in the Departments of Defense and Homeland Security. These include analysis of cost per flying hour calibration factors for the Air Force Cost Analysis Agency (AFCAA), development of the Program-Budget/Joint Capability Area (P-B/JCA) data structure for the Office of the Secretary of Defense, Capability Assessment and Program Evaluation (OSD CAPE), and various applied estimates and comparative analyses for the Coast Guard Research and Development Center (RDC). He was also a lead instructor for LMI’s internal cost estimating and analysis training.
From 2001 to 2003, Mr. Cincotta served as a Senior Cost Analyst at MCR, LLC. He worked closely with government clients at the Missile Defense Agency (MDA) to develop a radar cost model, which was presented by MCR at the 2004 Society of Cost Estimating and Analysis (SCEA) conference.
Mr. Cincotta also led several cost analysis-related tasks at the New Vectors (formerly Vector Research, Incorporated and the Altarum Institute) from 1997 to 2001. As a Senior Cost Analyst and Systems Developer, he assisted in creating life cycle cost estimates (LCCEs) for myriad DOD projects, including the Standard Procurement System (SPS), the Defense Occupational Health Readiness System (DOHRS), and the Simplified Tax and Wage Reporting System (STAWRS). He is a frequent presenter at both the Department of Defense Cost Analysis Symposium (DODCAS) and SCEA conferences. Mr. Cincotta is a (SCEA)-Certified Cost Estimator/Analyst (C/CEA). He created several model questions for the current C/CEA exam, and currently serves at the SCEA Training Chair. Known as Crystal City’s original Nature Boy, Cincotta holds a master’s degree in economics and philosophy from the London School of Economics and Political Science, and a bachelor’s in the same fields from the University of Virginia.