Optimum Number of Call Attempts in Telephone Survey Design

1. USE OF PROCESS DATA TO DETERMINE THE NUMBER OF CALL ATTEMPTS IN A TELEPHONE SURVEY Annica Isaksson Linköping University, Sweden Peter Lundquist Statistics Sweden Daniel Thorburn Stockholm University, Sweden Q2008

2. The Problem Consider a telephone survey of individuals, in which a maximum number A of call attempts is to be made to sampled individuals. HOW SHALL A BE CHOSEN? Part of a larger problem of designing efficient call scheduling algorithms. Q2008

3. Prerequisites • (Single-occasion survey) • Direct sampling from a frame with good population coverage • Estimation of a population total by the direct weighting estimator Observed value for individual k (proxy for the true value µk) Response set after A call attempts Estimated response probability for individual k after A call attempts Inclusion probability for individual k Q2008

4. The Survey as a Three-Stage Process • Stage 1: Sample selection • Stage 2: Contact and response Maximally A call attempts are made. Individuals respond in accordance with an unknown response distribution. • Stage 3: Measurement Observed values are related to the true values according to a measurement error model. Q2008

5. Response Model The sample can be divided into Hs response homogeneity groups (RHG) such that, for all A, given the sample, • all individuals within the same group have the same probability of responding • individuals respond independently of each other • individuals respond independently of each other after different numbers of call attempts Q2008

6. Measurement Error Model For an individual k in RHG h, given the sample and that the individual responds at call attempt a, Indicates if individual k responds at attempt a=ak Random interviewer effect with expectation 0 and variance True value for individual k Random response error with expectation 0 and variance Q2008

7. Bias and Variance Bias if the RHG model does not hold: Sample covariance between response probabilities and design weighted true values Average response probability within RHG The variance of is derived in the paper Q2008

8. Cost Function Q2008

9. Optimum A for RHG h Assume: of the costs are allocated to RHG h Q2008

10. Optimum A for RHG h: Result The optimum number of call attempts for RHG h is the number Ah that gives the lowest value on the function Q2008

11. Our Data LFS data from March-Dec. 2007, supplemented with: • Annual salary 2006 according to the Swedish Tax Register (our y) • Process data from WinDati (WD) . Note: not all WD events are call attempts Q2008

12. Data Processing and Estimation • Each monthly sample viewed as a SRS • Parameter: = total annual salary 2006 • Bias within RHG h and month l estimated by . Q2008

13. Relative Bias, Monthly Averages Q2008

14. Measurement Error Model Parameters Intraclass correlation, ICC (Biemer and Trewin, 1997): = .002 = 55,267,619,616 = 110,979,155 . Q2008

15. No Bias, ICC = .002 Q2008

16. Bias, ICC = .002 Q2008

17. Tentative Results • Efficient planning requires high-quality data on processes and costs • Perhaps the choice of A should be based on variance rather than MSE Q2008

18. Discussion and Future Work • Do the results hold for other study variables, other survey settings? • Improved models for measurement errors, response and costs? • Develop a planning tool? Q2008

19. Thank you for your attention! Annica Isaksson, annica.isaksson@liu.se Peter Lundquist, peter.lundquist@scb.se Q2008