A global optimisation approach to range-restricted survey calibration

Abstract

Survey calibration methods modify minimally sample weights to satisfy domain-level benchmark constraints (BC), e.g. census totals. This allows exploitation of auxiliary information to improve the representativeness of sample data (addressing coverage limitations, non-response) and the quality of sample-based estimates of population parameters. Calibration methods may fail with samples presenting small/zero counts for some benchmark groups or when range restrictions (RR), such as positivity, are imposed to avoid unrealistic or extreme weights. Userdefined modifications of BC/RR performed after encountering non-convergence allow little control on the solution, and penalisation approaches modelling infeasibility may not guarantee convergence. Paradoxically, this has led to underuse in calibration of highly disaggregated information, when available. We present an always-convergent flexible twostep global optimisation (GO) survey calibration approach. The feasibility of the calibration problem is assessed, and automatically controlled minimum errors in BC or changes in RR are allowed to guarantee convergence in advance, while preserving the good properties of calibration estimators. Modelling alternatives under different scenarios using various error/change and distance measures are formulated and discussed. The GO approach is validated by calibrating the weights of the 2012 Health Survey for England to a fine age-gender-region cross-tabulation (378 counts) from the 2011 Census in England and Wales.

Marginal-Preserving Imputation of Three-Way Array Data in Nested Structures, with Application to Small Areal Units

“…There are numerous strategies for this problem, ranging from simpler strategies such as uniform imputation (completely uninformed at the small geographic unit) or spatial smoothing techniques such as kriging that attempt to flexibly exploit spatial autocorrelation across units (Bennett, Haining, and Griffith 1984; Mooney et al 2020), to more informed model-based approaches (Cohen and Zhang 1988; Steinberg 1979). Related to this work, some researchers have specifically examined maintaining structural constraints and the use of model assisted approaches (Espuny-Pujol, Morrissey, and Williamson 2018; Luna et al 2015; Moretti and Whitworth 2020).…”

Development and Evaluation of an Optimal Composite Estimator in Spatial Microsimulation Small Area Estimation

“…Calibration estimators are known to be model-assisted by which is meant that it is only necessary that the population is reasonably well described by an assumed model in order for that model to be valid for use, this is a property of model-assisted estimators (Särndal et al, 1992;Espuny-Pujol, et al, 2018). Nonetheless, if the model assumptions fail then the gains in efficiency of the IPF estimator compared to a design-based direct estimator may be small.…”

Estimating the Uncertainty of a Small Area Estimator Based on a Microsimulation Approach

“…We refer to Rao and Molina (2015), Whitworth (2013), Rahman and Hardin (2017), and Marshall (2010) for useful methodological reviews on both regression-based and microsimulation-based SAE methods. Spatial microsimulation approaches, sometimes referred to as survey calibration approaches (Espuny-Pujol, Morrissey, and Williamson 2018), represent a family of reweighting approaches to SAE in which the challenge is to reweight the survey units such that they optimally fit the demographic and socioeconomic profile of each small area according to a selected set of benchmark constraints. Part of the appeal of spatial microsimulation approaches to SAE for both researchers and policy users is their intuitive and accessible appeal without much of the complex statistical expertise required within many regression-based SAE methods, particularly as assumptions fail or more complex outcomes are desired.…”