# Heteroskedasticity, Moderation, and Extremity in Heterogeneous Choice Models - PowerPoint PPT Presentation

Title:

## Heteroskedasticity, Moderation, and Extremity in Heterogeneous Choice Models

Description:

### Ordinal Dependent Variable. Heteroskedastic ordered probit model: ... Skewed Ordinal Dependent Variable With Heteroskedasticity. Race and Ambivalence, Model 2 ... – PowerPoint PPT presentation

Number of Views:168
Avg rating:3.0/5.0
Slides: 23
Provided by: garrett68
Category:
Tags:
Transcript and Presenter's Notes

Title: Heteroskedasticity, Moderation, and Extremity in Heterogeneous Choice Models

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 ygt0, y 0 otherwise.
• First condition half of observations have larger
error variance multiplied by 2 (heteroskedasticity
)
• Second condition half of observations have
• 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.