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Generalised Linear Models Incorporating Population Level Information: An Empirical Likelihood Based Approach.
Sanjay Chaudhuri1, Mark S Handcock, Michael S Rendall
1National University of Singapore.
Journal of the Royal Statistical Society. Series B, Statistical Methodology
|June 29, 2012
Summary
This study introduces an empirical likelihood method to integrate population data into statistical models, improving parameter estimation efficiency. The approach simplifies complex constraints, offering a more accurate way to analyze individual and population data relationships.
Area of Science:
- Statistics
- Demography
- Econometrics
Background:
- Individual-level data analysis often benefits from supplementary population-level information.
- Incorporating population data can reduce bias and enhance the efficiency of parameter estimates.
- Traditional methods for integrating population data involve complex nonlinear constraints, complicating maximum likelihood estimation.
Purpose of the Study:
- To develop an alternative approach for incorporating population-level information into statistical models.
- To simplify the estimation process by transforming nonlinear constraints into linear ones.
- To apply the developed method to demographic hazard modeling for estimating birth probabilities.
Main Methods:
- Utilizing the concept of empirical likelihood to handle population-level information.
- Developing a two-step algorithm for parameter estimation using unconstrained estimation.
- Deriving computable expressions for standard errors.
Main Results:
- The empirical likelihood approach transforms population-level information into linear constraints within generalized linear models.
- A two-step algorithm allows for parameter estimation through unconstrained estimation, simplifying the process.
- The method was successfully applied to demographic hazard modeling, combining survey and registration data.
Conclusions:
- The empirical likelihood method provides an efficient and less complex way to integrate population data.
- This approach enhances the accuracy of parameter estimates in statistical modeling.
- The study demonstrates a practical application in demographic research for estimating birth probabilities.
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