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Discrete Dependent Variables

Discrete Dependent Variables. Linear Regression, Dummy Variables If discrete dependent variable: need new technique Examples: Firm join Energy Star or not. Parcel of land developed as urban, agriculture, or open space. Species goes extinct or not. We’ll focus on: “Binary Choice Estimators”.

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Discrete Dependent Variables

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  1. Discrete Dependent Variables • Linear Regression, Dummy Variables • If discrete dependent variable: need new technique • Examples: • Firm join Energy Star or not. • Parcel of land developed as urban, agriculture, or open space. • Species goes extinct or not. • We’ll focus on: “Binary Choice Estimators”

  2. Example: Tumors and ETU • Big question: How does exposure affect chance of contracting disease? • Treated foods contain ETU – may be harmful to health. • Some rats exposed to ETU contracted tumors. • How does prob of tumor depend on dose? • What dose associated with 10% tumor rate (To advise on regulation)?

  3. Evidence • 6 dose groups (0,5,25,125,250,500) • ~70 rats per group.

  4. How ‘bout a Linear Model? • Linear Model: Y=-.04889+.00167 X+e

  5. Problems with Linear Model • How do we interpret dependent variable? (“chance of tumor?”) • If Dose=0, chance of tumor < 0. • If Dose large, chance of tumor > 1. • Doesn’t make sense, and chance is linear in dose.

  6. Binary Choice Models • Logit (based on logistic cdf) and Probit (based on Normal cdf). • Logistic cdf: • Draw on board.

  7. Adding Explanatory Variables • Interpretation of Binary Choice Estimator: Probability of “Yes”. • Replace “X” with function of explanatory variables:

  8. Probability of Tumor

  9. Dose @ 10% Tumor Chance • What dose gives a 10% chance of contracting a tumor? • After a bunch of math (see handout), D=170.24

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