  In the analysis of survey data, sampling weights are needed for consistent
estimation of the population. However, the original inverse probability weights
from the survey sample design are typically modified to account for
non-response, to increase efficiency by incorporating auxiliary population
information, and to reduce the variability in estimates due to extreme weights.
It is often the case that no single set of weights can be found which
successfully incorporates all of these modifications because together they
induce a large number of constraints and restrictions on the feasible solution
space. For example, a unique combination of categorical variables may not be
present in the sample data, even if the corresponding population level
information is available. Additional requirements for weights to fall within
specified ranges may also lead to fewer population level adjustments being
incorporated. We present a framework and accompanying computational methods to
address this issue of constraint achievement or selection within a restricted
space that will produce revised weights with reasonable properties. By
combining concepts from generalized raking, ridge and lasso regression,
benchmarking of small area estimates, augmentation of state-space equations,
path algorithms, and data-cloning, this framework simultaneously selects
constraints and provides diagnostics suggesting why a fully constrained
solution is not possible. Combinatoric operations such as brute force
evaluations of all possible combinations of constraints and restrictions are
avoided. We demonstrate this framework by applying alternative methods to
post-stratification for the National Survey on Drug Use and Health. We also
discuss strategies for scaling up to even larger data sets. Computations were
performed in R and code is available from the authors.
