A Model-Over-Design Integration for Estimation from Purposive Supplements to Probability Samples

at NORC at the University of Chicago

For purposive samples, design-based methods are clearly not suitable. There is the possibility of using model-based methods but there are concerns about the design being informative and potential misspecification of the model mean. An alternative approach termed Model-Over-Design (MOD)-Integration for a simplified problem is proposed under the joint design-model randomization when the purposive sample is available as a supplement to the core probability sample. A design-based estimate such as GREG for the population total is first constructed using the probability sample which uses the synthetic estimator based on the systematic part of the model mean containing fixed parameters, and then corrects it for the total model error corresponding to the random part of the model. Next, the above model-error correction is improved by using another estimator from the additional seen observations in the purposive sample. The initial probability sample is used for both estimation of model parameters to obtain a synthetic estimator and for estimation or prediction of the total model-error, the purposive supplement is used only to improve the model-error correction from the additional seen units. The MSE of the resulting estimator can be estimated under the joint randomization of man-made probability sample design, nature-made purposive sample design, and the model for the finite population.