Post-Calibration of Dual-Frame Telephone Surveys: Theory and Practice of the System-of-Equations Method





Published date: 

June, 2022


Chi-Lin Tsai


In response to the decline of landline households and the growth of cellphone-only users, more and more telephone surveys conduct interviews by cellphone as well as by landline. However, in the absence of a sampling frame that covers both landline households and cellphone users, a dual-frame sampling design is inevitable, that is, sampling from a landline frame and a cellphone frame separately, and then combining the two samples for the analysis. These two frames overlap in the subpopulation that uses both a landline and cellphone, and the sampling rates of them are usually different. Consequently, respondents in a dual-frame survey have unequal chances of being sampled. Several methods for correcting this problem have been proposed in the Western literature, but most of them are not suitable for Taiwan. A viable alternative referred to as the “System-of-Equations Method” is increasingly being adopted in the Taiwanese polling industry, but academic research has not considered it in much detail.

To fill this gap, this paper examines this method in three respects: 1) by elaborating its underlying assumptions and evaluating the consequences of assumption violation; 2) by examining the statistical properties of the method; and 3) by improving the procedure for applying the method. The results of this study establish the theoretical basis of the System-of-Equations Method, provide a practical guide for its proper use, and suggest directions for future research on dual-frame surveys.