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Understanding Binary Choice Estimators in Discrete Dependent Variables Regression

Explore the use of Binary Choice Estimators in Linear Regression with Discrete Dependent Variables. Learn how to analyze scenarios such as tumor contracting likelihood based on exposure dose. Discover the application of Logit and Probit models for binary choices. Enhance your understanding of how explanatory variables affect the probability of outcomes.

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Understanding Binary Choice Estimators in Discrete Dependent Variables Regression

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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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