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Model-based Properties of Replication Variance Estimators for Sample Surveys

Replication variance estimation in surveys of finite populations is a standard tool of survey statisticians and researchers. Two of the most common methods used are the jackknife & balanced repeated replication (BRR). Replication is popular and useful because it provides a simple means of estimating variances without requiring the derivation of explicit variance formulas that are often complicated. One of the main advantages of replication is its ease of use at the analysis stage. The same estimation procedure is used for the full sample and for each replicate. The variance estimates are then readily computed by a simple procedure, & the same procedure is applicable to most statistics desired, such as means, percentages, ratios, correlations, & so forth. These estimates can also be calculated for analytic groups or subpopulations. A user need not necessarily understand the sampling or estimation methods if the replicate weights are included with the data. An important advantage of replication is that it provides a simple way to account for adjustments that are made in weighting. Frequently, sampling weights are adjusted for nonresponse, poststratification, or raking to control totals. By separately computing the weighting adjustments for each replicate, the hope is to reflect the effects of weight adjustments in the estimates of variance. There is a substantial amount of theory available for the replication methods when they are implemented in standard ways described in textbooks & journal articles. However, in practice, these methods are operationalized in ways that often do not fit the standard theoretical requirements. In the jackknife, for example, the basic approach is to delete one first-stage sample unit, compute an estimate based on the remaining sample units, cycle through all first-stage sample units, & compute a variance among the resulting set of estimates. In practice, groups of units are formed by combining units within or across strata. Entire groups are then dropped-out in order to compute a jackknife variance estimate. Theory for these grouped methods is limited, & it is unclear that the methods used in practice always have good theoretical properties. The ramifications of poor implementation of replicate variance estimation can be important because of the way that data bases are constructed. Weights for the full sample and for subsamples (or replicates) are created by the database constructor who appends the weights to each record in the database. Users are then instructed to use those weights to compute variances for all statistics. regardless of how complex. If a poor set of replicate weights is created, this affects all analysts. This project will evaluate methods used in practice and investigate potential improvements to current methods using the model-based approach to finite population sampling. In particular, this work will study weight adjustments in the grouped jackknife and partially balanced BRR and model-based properties of these two methods of variance estimation. The general regression estimator of population totals & other nonlinear estimators will be emphasized. The research is intended to provide guidance on how to implement these grouped methods in surveys, particularly ones concerning the economy, health status of the population, & other applications in the social sciences.

Funding Period: 09/01/2004 to 08/31/2008

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Analysis and Modeling (Methodology)

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