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Testing and adjusting for informative sampling in survey data




Herndon, Wade Wilson, author
Breidt, F. Jay, advisor
Opsomer, Jean, advisor
Cooley, Daniel, committee member
Meyer, Mary, committee member
Doherty, Paul, committee member

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Fitting models to survey data can be problematic due to the potentially complex sampling mechanism through which the observed data are selected. Survey weights have traditionally been used to adjust for unequal inclusion probabilities under the design-based paradigm of inference, however, this limits the ability of analysts to make inference of a more general kind, such as to characteristics of a superpopulation. The problems induced by the presence of a complex sampling design can be generally contained under the heading of informative sampling. To say that the sampling is informative is to say that the distribution of the data in the sample is different from the distribution of the data in the population. Two major topics relating to analyzing survey data with (potentially) informative sampling are addressed: testing for informativeness, and model building in the presence of informative sampling. First addressed is the problem of running formal tests for informative sampling in survey data. The major contribution contained here is to detail a new test for informative sampling. The test is shown to be widely applicable and straight-forward to implement in practice, and also useful compared to existing tests. The test is illustrated through a variety of empirical studies as well. These applications include a censored regression problem, linear regression, logistic regression, and fitting a gamma mixture model. Results from the analogous bootstrap test are also presented; these results agree with the analytic versions of the test. Alternative tests for informative sampling do in fact exist, however, the existing methods each have significant drawbacks and limitations which may be resolved in some situation with this new methodology, and overall the literature is quite sparse in this area. In a simulation study, the test is shown to have many desirable properties and maintains high power compared to alternative tests. Also included is discussion about the limiting distribution of the test statistic under a sequence of local alternative hypotheses, and some extensions that are useful in connecting the work contained here with some of the previous work in the area. These extensions also help motivate the semiparametric methods considered in the chapter that follows. The next topic explored is semiparametric methods for including design information in a regression model while staying within a model-based inferential framework. The ideas explored here attempt to exploit relationships between design variables (such as the sample inclusion probabilities) and model covariates. In order to account for the complex sampling design and (potential) bias in estimating model parameters, design variables are included as covariates and considered to be functions of the model covariates that can then be estimated in a design-based paradigm using nonparametric methods. The nonparametric method explored here is kernel smoothing with degree zero. In principle, other (and more complex) kinds of estimators could be used to estimate the functions of the design variables conditional on the model covariates, but the framework presented here provides asymptotic results for only the more simple case of kernel smoothing. The method is illustrated via empirical applications and also through a simulation study in which confidence band coverage rates from the semiparametric method are compared to those obtained through regular linear regression. The semiparametric estimator soundly outperforms the regression estimator.


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