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The Independent Sign Bias: Gaining Insight from Multiple Linear Regression

The Independent Sign Bias: Gaining Insight from Multiple Linear Regression. Michael J. Pazzani and Stephen D. Bay University of California, Irvine. Background. Knowledge Discovery in Databases: The process of identifying valid , novel , useful , and understandable patterns in data

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The Independent Sign Bias: Gaining Insight from Multiple Linear Regression

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  1. The Independent Sign Bias: Gaining Insight from Multiple Linear Regression Michael J. Pazzani and Stephen D. Bay University of California, Irvine

  2. Background • Knowledge Discovery in Databases: The process of identifying valid, novel, useful, and understandable patterns in data • “Drowning in data, but starving for knowledge”

  3. Modeling Salaries • Social Science Professors Salary =45,647 -66YaT + 1784YsD -346YsH • BaseBall Players Salary = -180 +10runs +5hits +0.9obp +15hr + 14rbi -0.8ave -18db -39tr Do the models make sense?

  4. Applications • Credit Scoring • Explanations of credit rejection are important • Medical “algorithms” • Models for predicting dementia levels from diagnostic tests • Models must be acceptable to administrator

  5. Goals • Identify conditions under which linear models of data prove credible. • Produce linear models that • are as accurate as standard regression techniques • are more acceptable to people knowledgeable about the domain

  6. Outline • Why are the signs wrong? • The Independent Sign Bias and Constrained Regression • Accuracy • Subject Ratings • Conclusions

  7. Why are the signs wrong? • computational error • numerical (rounding, truncation) • variance in estimates • coefficients do not differ significantly from zero • multicollinearity: predictor variables are highly correlated • true sign is reversed when other variables are considered

  8. The Independent Sign Bias Hypothesis: Models are more acceptable when the sign of each variable in the regression equation is the same as the sign of the variable in isolation

  9. Constrained Regression • Multiple Linear Regression Salary = -180 +10runs +5hits +0.9obp +15hr + 14rbi -0.8 ave -18db -39tr • Independent Sign Regression (ISR) minimize subject to Salary = -207 +15runs +0.8hits +11hr +11rbi +0.33ave +5db

  10. Forward Selection • Forward Selection Salary = -114 +16runs +17rbi -59tr • Independent Sign Forward Regression (ISFR) • add variables as long as constraint is not violated Salary = -148 +15runs +15rbi

  11. Constrained Regression • Mean Coefficient Regression (MCR) Salary = -162 + 4runs +2hits +1.1obp +10hr +3rbi +1.2ave +9db +16tr

  12. Accuracy of Regression 7 4 3 1 3 5 MLR violations:

  13. Accuracy: Forward Selection 0 1 1 0 0 2 FS violations:

  14. Baseball Salary Experiment 47 Subjects

  15. Experiment Results F(4,184)=22.11 p < 0.0001 All differences significant with Tukey-Kramer test at 0.05 level ISR > MLR MCR > MLR ISFR >SFR

  16. Biasing KDD to improve understandability • Related Work • Clark, P. & Matwin, S. (1993). Using Qualitative Models to Guide Inductive Learning. MLC 49-56. • Monotonicity Constraints: Pazzani, Subramani and Shankle. Proc. Cog Sci 1996.

  17. Conclusions • The independent sign bias affects the willingness of subjects to use linear models • new constrained regression routines • as accurate as unconstrained regression • more acceptable to users

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