A grouping genetic algorithm for joint stratification and sample allocation designs
Section 5. Conclusion and further work
We created a GGA as an alternative to the existing SamplingStrata GA in R. We then compared the two algorithms using a number of datasets. The GGA compares favourably with the GA at finding the correct solution and meeting constraints on smaller datasets, but significantly outperforms the GA on larger datasets where the number of iterations was restricted. This is useful for datasets where the number of iterations has to be constrained owing to computational burden. We have also reported faster processing times by integrating the bethel.r function with C++ using the Rcpp package.
This work can be developed in several ways. Alternative evaluation techniques to speed up the algorithm could be considered. Further research could also be undertaken into other machine learning techniques for solving this problem.
The GGA could be applied to other problems which tackle more general sampling designs with modifications required only for the algorithm evaluating the fitness of chromosomes (i.e., the Bethel-Chromy algorithm). For example instead of searching for a stratified simple random sample to meet precision constraints based on population totals or means, the GGA could consider stratified probability proportional to size sampling with an evaluation algorithm that uses more general estimators (e.g., regression or ratio estimators) or more general parameters (e.g., a correlation coefficient).
The evaluation algorithm might also be modified to look at scenarios in which the population variances are not known. In these cases, data from previous censuses, administrative records, or proxy surveys can be used to estimate the population variance. However, estimation of the population variance in a large number of atomic strata requires more careful research.
Finally, the groupings of atomic strata by the GGA can be difficult to interpret. For instance, an ordinal auxiliary variable taking values 1 to 4 may be unnaturally separated, where the atomic strata corresponding to values 1 and 3 are grouped in one design stratum and those with values 2 and 4 are grouped in another design stratum. It might be interesting to explore less-than-optimal sample sizes for stratifications that are easier to interpret. For instance, one may impose constraints on the admissible groupings. This would require research into the formulation of appropriate admissibility constraints and their effective implementation in the GGA.
Acknowledgements
We wish to acknowledge Steven Riesz of the Economic Statistical Methods Division of the U.S. Census Bureau and Brian J. McElroy of the Economic Reimbursable Survey Division of the U.S Census Bureau, both of whom answered questions which were of assistance in choosing which U.S. Census Bureau data to use. We would also like to thank Giulio Barcaroli and Marco Ballin, the co-authors of (Ballin and Barcaroli, 2013), for independently testing our GGA. Last but not least we are extremely grateful to the editorial staff and reviewers of Survey Methodology for their constructive suggestions in the review process for this journal submission, especially their suggestions for future work.
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