Nonparametric Bootstrapping for Binary Hierarchical Data

• Activity Number: 284 - GMM, Triple Joint Modeling, Bootstrapping, and Multiple Membership of Correlated Data
• Type: Topic Contributed
• Date/Time: Tuesday, August 1, 2017 : 8:30 AM to 10:20 AM
• Sponsor: WNAR
• Author(s): Bei Wang*
• Keywords: Generalized linear mixed model ; Resampling schemes ; Small sample sizes ; Interval estimation

Abstract

This is the LAST of four related papers addressing the interval estimation due to the hierarchical structure of the data. The theoretical distribution of parameter estimators is not readily available from generalized linear mixed models as the joint likelihood is not readily available. While large sample theory provides approximations to allow construction of confidence intervals based on statistical tests, interval estimation from small hierarchical datasets often results in non-convergence. We present bootstrapping methods as they provide indirect approaches to assess the properties of the underlying distribution of interest irrespective of the size of sample. This method greatly supersedes previous bootstrapping methods in terms of the accuracy of interval estimation with very small loss in the precision. We show that this method can provide useful interval estimation without convergence problems with relatively small hierarchical data. Further, we compare our bootstrapping confidence intervals with both the Wald's and profile likelihood's through a simulation study and with applications to a numerical example.