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Heteroskedasticity, Moderation, and Extremity in Heterogeneous Choice Models

Heteroskedasticity, Moderation, and Extremity in Heterogeneous Choice Models. GARRETT GLASGOW University of California, Santa Barbara. Heterogeneous Choice Models. Uncorrected heteroskedasticity in binary and ordinal choice models will produce biased estimates.

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Heteroskedasticity, Moderation, and Extremity in Heterogeneous Choice Models

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  1. Heteroskedasticity, Moderation, and Extremity in Heterogeneous Choice Models GARRETT GLASGOWUniversity of California, Santa Barbara

  2. Heterogeneous Choice Models • Uncorrected heteroskedasticity in binary and ordinal choice models will produce biased estimates. • Heteroskedasticity may also be of substantive interest. • Heterogeneous choice models developed to model this heteroskedasticity.

  3. Heteroskedasticity or Something Else? • Unfortunately, in some cases heterogeneous choice models will produce results that look like heteroskedasticity when the error term is actually homoskedastic. • I consider three cases here: a binary dependent variable, an ordinal dependent variable, and a skewed ordinal dependent variable.

  4. Case #1: Binary Dependent Variable Heteroskedasticity or Moderation?

  5. Heterogeneous Choice, Binary Dependent Variable • Heteroskedastic probit model: • As Hi increases, choice probabilities converge to 0.5.

  6. Binary Dependent Variable With Heteroskedasticity

  7. Binary Dependent Variable With Moderation

  8. Monte Carlo Study • Generated 1000 data sets, 1000 observations each. y* = XB + e. y = 1 if y*>0, y = 0 otherwise. • First condition: half of observations have larger error variance multiplied by 2 (heteroskedasticity) • Second condition: half of observations have additional variable = –X/2 (moderation). • Estimated heteroskedastic probit under both conditions.

  9. Monte Carlo Results • Heteroskedasticity and moderation can be indistinguishable in the binary dependent variable case.

  10. Case #2: Ordinal Dependent Variable Heteroskedasticity or Extremity?

  11. Heterogeneous Choice, Ordinal Dependent Variable • Heteroskedastic ordered probit model: • As Hi increases, choice probabilities converge to 0.5 for extreme categories, 0 for middle categories.

  12. Ordinal Dependent Variable With Heteroskedasticity

  13. Ordinal Dependent Variable With Extremity

  14. Heterogeneous Choice, Ordinal Dependent Variable, Model 2 • Modified heteroskedastic ordered probit model: • As Hi increases, choice probabilities converge to 1/M for each choice category. Variance in the observed rather than latent variable.

  15. Example #1: Working and Motherhood

  16. Distribution of “Warm” by Gender

  17. Example #2: Race and Ambivalence

  18. Distribution of “Quota” by Ambivalence

  19. Case #3: Skewed Ordinal Dependent Variable Heteroskedasticity or Left-Right?

  20. Skewed Ordinal Dependent Variable With Heteroskedasticity

  21. Race and Ambivalence, Model 2

  22. Conclusions • Distinguishing heteroskedasticity from other effects on the choice probabilities is difficult. • Several models considered, but all results could be explained by effects other than heteroskedasticity. • Perhaps this is a problem that must be solved through theory and measurement rather than a statistical model.

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