Dealing with multiple list frames to improve population coverage: a simulation study

Multiple frame surveys are powerful tools for dealing with a number of non-standard sampling designs, especially for improving population coverage and response rates by controlling survey costs. In an overlap design, the probability for units in the overlap domain to be included in the final sample is increased, and as a consequence this multiplicity must be accounted for at the estimation stage. In this paper we focus on an application issue tipical of modern telephone surveys. We assume a Dual Frame set up as extensively applied in large scale surveys and official statistics and assume that the variable of interest has a Bernuolli distribu- tion. The two frames available are the frame of landline telephone numbers (frame A) and the frame of the cellular telephone numbers (frame B) which are typically overlapping. A first sample is selected from frame A and then an indipendent sample is selected from B. It is a popular device in practice to overcome the overlap issue by dropping from interviewing any unit eventually re-selected from B. However since that would regard selected units only, it appears as not sufficient in order to deal with the actual dual frame design configured. In this paper empirical evidence will be provided of the bias and increased estimators instability/loss of accuracy that may result from the practical device above of actually ignoring the overlap versus the aknowledging of the overlap between frames as in a dual frames design implying a correction to the estimators. Empirical results include a comparison of bias and efficiency with special attention to the multiplicity dual frame estimator. Different estimators will be also considered, requiring more information at the estimation stage to be collected besides the study variable(s). Simulations are carried out at different overlapping rate ranging up to the special case where one frame is a sub- set of the other. The simulation is conducted with different success probabilities and assuming units are selected with simple random sampling as well as with more complex sampling designs.