2. Generating synthetic populations from single survey data that accounts for complex sampling designs
Qi Dong, Michael R. Elliott and Trivellore E. Raghunathan
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Dong et al. (2014)
extended work in the finite population Bayesian bootstrap to develop a
non-parametric approach to the generation of posterior predictive
distributions. A summary of the algorithm to draw the
of
synthetic populations for
stratified, clustered sample designs with unequal probabilities of selection is
as follows:
- Use the
Bayesian Bootstrap (BB) (Rubin 1981) to adjust for stratification and
clustering. Draw a simple random sample with replacement (SRSWR) of size
from the
clusters within each stratum
and calculate bootstrap replicate
weights for each of the
observations in each cluster as
where
and
denotes the number of times that
cluster
is selected. To ensure all the
replicate weights are non-negative,
here and below we take
- Use the
finite population Bayesian bootstrap (FPBB) (Lo 1986; Cohen 1997) for unequal
probabilities of selection to adjust for unequal probabilities of selection. For
each cluster
in stratum
of population size
draw a sample of size
denoted by
by drawing
from cluster data
with probability
where
is the replicate weight of unit
in cluster
in stratum
and
is the number of bootstrap
selections of
among
Form the FPBB population
- Produce
FPBB samples for each BB sample,
denoted by
Pool the
FPBB samples to produce one
synthetic population,
(Because
may be unrealistically large,
generating a sample of size
for large
is sufficient.)
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