~ Draft version ~ 1 HOW TO CHOOSE THE NUMBER OF CALL ATTEMPTS IN A TELEPHONE SURVEY IN THE PRESENCE OF NONRESPONSE AND MEASUREMENT ERRORS Annica Isaksson Linköping University, Sweden Peter Lundquist Statistics Sweden Daniel Thorburn Stockholm University, Sweden

~ Draft version ~ 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. Part of a larger problem of designing efficient call scheduling algorithms. HOW SHALL A BE CHOSEN?

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

~ Draft version ~ 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.

~ Draft version ~ 5 Response Model 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 The sample can be divided into H s response homogeneity groups (RHG) such that, for all A, given the sample,

~ Draft version ~ 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=a k A random interviewer effect with expectation 0 and variance A random response error with expectation 0 and variance True value for individual k

~ Draft version ~ 7 Bias and Variance Bias only if the RHG model does not hold: The variance, V(A), is derived in the paper. Sample covariance between response probabilities and design weighted true values Average response probability within RHG

~ Draft version ~ 8 Cost Function where is composed of… Starting costs (tracking, letter of introduction…) Contact costs (making calls without an answer, talking to other individuals than the one selected, booking an interview for another time…) Interview costs (interviewing, editing…) All costs are assumed to be constant within RHG.

~ Draft version ~ 9 Choosing the Optimum A Consider one RHG h. The optimum number of call attempts is the number A h that gives the lowest value on the function where is the marginal cost for RHG h.

~ Draft version ~ 10 A Case Study: the Swedish LFS. Target population: Swedish residents years old Frame: the Swedish Population Register Monthly panel survey of ~21,500 individuals. An individual is observed every quarter for two years. Stratified SRS with stratification by gender, age and county (144 strata in all) Data collected by telephone

~ Draft version ~ 11 Our Data Annual salary 2006 according to the Swedish Tax Register (our y) Process data from WinDati (WD). LFS data from March-Dec. 2007, supplemented with: Note: we do not know the number of call attempts, only the number of ‘WD events’

~ Draft version ~ 12 Data Processing and Estimation. Reduced target population: Swedish residents years old Each monthly sample viewed as a SRS Process data are used to estimate:  Marginal costs  Response and contact probabilities

~ Draft version ~ 13. Biemer and Trewin (1997): Measurement Error Model Parameters.002 (”low”)55,267,619,616110,979, (”high”)55,267,619,6162,402,939,983 Estimated by 10-month- average sample variance (ICC)

~ Draft version ~ 14 Illustrations One RHG (women), one ICC level (low) Unbiased or biased estimator of = total annual salary 2006 Three curves representing different values on One curve for no measurement errors Each curve represents a 10-month-average The optimum A (optimum number of WD events) is the one for which the curve is at its minimum

~ Draft version ~ 15 No Bias, Low ICC

~ Draft version ~ 16 Bias, Low ICC