The Case for Generalized Estimating Equations in State-level Analysis
- 1. The Case for Generalized Estimating Equations in State-level Analysis Tucker Staley Department of Political Science University of Central Arkansas tstaley@uca.edu 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.