Post-Stratification
Post-stratification is the adjustment of survey weights to improve efficiency of estimates.
Contents
Description
Certain population parameters are known for the aggregate, but not for individuals. (Or at least at the time of sample stratification.)
After measurements are collected, post-stratification is the adjustment of survey weights such that aggregated estimates match known aggregated parameters. This improves the efficiency of all estimates.
Notation
Given H design strata, each stratum (h) is divided into Nh clusters. (Generically though, number of clusters is referenced as nh.) There are n clusters altogether. Clusters can be referenced by the subscript (hi). PSUs are generally referenced by the subscript (hij).
The overall population is M. A design stratum's size is Mh. A cluster's size is Mhi. A class' size is Mc.
Population totals can be expressed like:
For each cluster, the estimated total is:
Post-stratification creates c classes that can cross-cut design strata. A class' size is Mc.
The goal of stratification is design adjustment factors for each stratum (γhi) such that the unbiased estimated population total is:
γhi is designed from the known class size in each stratum (Mhic) and corresponding estimate from the collected measurements (ˆMhic).
Methods
Weighting Class Adjustments
Commonly used for non-response bias adjustments.
Calibration
Commonly used for coverage bias adjustments.
Variance
Post-stratified estimates are ratios of two linear estimates, and therefore are nonlinear estimates.
Linearization methods
Variances of post-stratified estimates are generally computed as the variance of the Taylor linearized approximation.
Many statistical programming tools use a linear substitute method.
Replication methods
Replication estimates of variance include balanced repeated replication (BRR) and jackknife.
Degrees of freedom
The degrees of freedom for post-stratified variance is commonly approximated as the number of PSUs (n) minus the number of strata (H). This formally is a special case of the Satterthwaite approximation.