The Case for Generalized Estimating Equations in State-level Analysis

Presentation on the benefits of using GEE in state level studies.

1. The Case for Generalized Estimating Equations
in State-level Analysis
Tucker Staley
Department of Political Science
University of Central Arkansas
[email protected]
Prepared for the Annual Meeting of the Southern Political Science Association, Jan. 9-11, 2014.
New Orleans, LA.

2. Correlated Data
Assume data are independent and identically
distributed.
However, often not the case.
Panel studies
Cross-sectional time-series
Dyadic studies
Decision making environments
Specifically concerned with intra-class
correlations resulting from grouped
observations.

3. Dealing with Intraclass Correlations
Adjust standard errors of GLM
Ignore impact of coefficient estimates
Better Options
Generalized Linear Mixed Models
Generalized Estimating Equations

4. GLMM
Most common
Vectors for both fixed and random effects
accounted for
Generalized for non-normal responses with a
known link function

5. Issues with GLMM
Designed specifically for exchangeable
correlation between groups (clusters).
For the most part, mainly allows for an
individual level interpretation.

6. GEE
Marginal model
population-averaged expectations of the dependent
variables as functions of the covariates
No individual effects included
intracluster variation accounted for by adjusting the
covariance matrix
Average effect across entire sub-population
Note: We get this interpretation with independent observations
in any model and when there is an identity link in hierarchical
models.
Flexible correlation structures (“working
correlation”)

7. GEE Model Overview
Extension of a generalized linear model (GLM)
postulate relationship b/t DV and IV and the
conditional mean and variance of DV
GEE reduces to GLM when T=1
estimates are solutions to a set of “quasi-score”
differential equations
residuals from Fisher scoring used to consistently
estimate structure of the unknown parameters

8. Model Specification
Most Simply
Goal: minimize this objective function

9. Process
Estimate coefficients iteratively.
Estimate regression coefficients.
Use residuals from these to estimate the covariance
term.
Repeat until convergence.
Does not require a lot of parametric
assumptions as does MLE.

10. Issues w/ GEE
Specify the correct correlation structure
Should be based on theory. However, asymptotically efficient if incorrect.
Sample size
Smaller N may have issues with convergence.
Missing Data
Important to specify true correlation matrix.
Goodness-of-fit
Correlated residuals, so can't use standard statistics.
Uncertainty
Need to adjust s.e. (robust, bootstrapped)

11. Initiative and Party Power
Justin Phillips (2008)
“Direct democracy alters the ability of partisan
legislative majorities...to shape the size...of the
public sector.”
DV: Tax effort
IVs:
Partisan Control
State-level characteristics
Interactions

13. 100 Miles of Dry
John Frendreis & Raymond Tatalovich (2010)
What factors identified as important for
Prohibition remain important today?
DV: Dry county
IVs:
Religion
Demographics
Partisan voting

15. Conclusions
Often deal with correlated data in the real-world.
GEE allows us to deal with intraclass
correlations and produces efficient coefficient
estimates.
More flexible than GLMM: correlation
structures, interpretation
Estimates may differ once correlated data are
accounted for.
Toss in the methodological toolbox.