Discrete Dependent Variables

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.
• Well 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 Xe

5
Problems with Linear Model

• How do we interpret dependent variable? (chance
  of tumor?)
• If Dose0, chance of tumor lt 0.
• If Dose large, chance of tumor gt 1.
• Doesnt 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 _at_ 10 Tumor Chance

• What dose gives a 10 chance of contracting a
  tumor?
• After a bunch of math (see handout), D170.24