The use of sampling weights for survey data analysis

The use of the sampling weights when fitting models to complex survey data is considered. It is shown that when the sample is selected with unequal selection probabilities that are related to the values of the response variables even after conditioning on all the available design information, ignoring the sample selection scheme in the inference process, can yield misleading results. Probability weighting of the sample observations yields consistent estimators of the model parameters and protects against model misspecification, although in a limited sense. Other methods of incorporating the sampling weights in the inference process are discussed and compared to the use of probability weighting.