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Boris Lorenc

-- licentiate thesis --

Double Samples for Web Surveys and Similar Situations

Inference about the general population drawn using unadjusted web
survey data is biased if there is a dependence between the study
variable and the selection mechanism providing participation in the
survey. This work presents two adjustment techniques that may reduce the
bias, both based on the double samples procedure, and also studies the
effectiveness of the techniques under varying circumstances.
With double samples is meant a procedure whereby two samples are
taken from the same population, one a random sample on which only
auxiliary variables are measured, and another a sample with unknown
inclusion probabilities possibly from a subset of the population but on
which a more extensive measurement of the study variables is done.
One of the techniques, the propensity score weighting, was
introduced by George Terhanian (also the originator the double samples
procedure), who reported its successful application in the 2000
elections in the USA. Nevertheless, a formal treatment of the technique
was never presented, why the first of the studies, "Effectiveness of
weighting by stratification on the propensity score using double
samples", gives an analytic justification of the technique and
illustrates it using a simple trivariate model.
While expression for variance of the propensity score adjusted
estimator has not been worked out, the variance estimate suggested in
the literature is conditional on the model through which the propensity
scores are estimated, and was suspected to be underestimating the true
variance. Further, while it was known from the analytic demonstration
that the adjusted estimator contains a residual bias, it was not known
what the bias reducing performance of the estimator would be under
varying circumstances regarding for instance correlations of relevant
variables and violations of the assumptions on which the technique is
laid. To do this, a simulation study was performed, the results of which
are reported in "Propensity score weighting with double samples: a
simulation study".
The second adjustment technique is multiple imputation. It treats
the values of the study variables in the random sample---not measured in
this sample by design---as missing data, and imputes them using the
multiple imputation technique due to Rubin. Amongst the advantages of
the technique are the readily available expressions for variance of the
point estimator as well as existing software for performing the
imputations. In order to study the performance of this technique under
the same circumstances as for the propensity score weighting, another
simulation study was performed, on which it is reported in "Multiple
imputation with double samples: a simulation study".


Download report 1; Effectiveness of Weighting by Stratification on the Propensity Score Using Double Samples -->>

Download report 2; Propensity Score Weighting with Double Sampes: A Simulation Study -->> Download appendix -->>

Download report 3; Multiple Imputation with Double Samples: A Simulation Study-->> Download appendix -->>