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| Department of Mathematics |
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Special Statistics Seminar |
2016 - 2017 |
DATE: Friday, January 6, 2017 |
TIME: 11:00am - 12:00pm |
ROOM: 1308 Math Building |
Borrowing Information over Time in
Binomial/Logit Models |
Dr. Carolina Franco |
Census Bureau |
| ABSTRACT: In the analysis of survey data, linear mixed models, such as that of Fay-Herriot (1979), have been widely studied and applied to exploit the availability of covariates from administrative records and other sources when predicting population parameters. Such models face challenges when applied to discrete survey data as commonly arise from survey estimates of the number of persons possessing some characteristic, such as the number of persons in poverty. For such applications, we examine a binomial/logit normal (BLN) model that assumes a binomial distribution for rescaled survey estimates and a normal distribution with a linear regression mean function for logits of the true proportions. Effective sample sizes are defined so variances given the true proportions equal corresponding sampling variances of the direct survey estimates. We extend the BLN model to bivariate and time series versions to permit borrowing information from past survey estimates, then apply these models to data used by the U.S. Census Bureau Small Area Income and Poverty Estimates (SAIPE) program to predict county poverty for school-age children. For this application, we compare prediction results from the alternative models to see how much the bivariate and time series models reduce prediction error variances from those of the univariate BLN model. More generally, we explore analytically and empirically under what circumstances one might expect bivariate or time series extensions of small area models to result in significant improvements in prediction. |