HOW TO CHOOSE THE NUMBER OF CALL ATTEMPTS IN A TELEPHONE SURVEY IN THE PRESENCE OF NONRESPONSE AND MEASUREMENT ERRORS

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

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

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 aak
A random interviewer effect with expectation 0
and variance
A random response error with expectation 0 and
variance
True value for individual k
7
Bias and Variance
Bias only if the RHG model does not hold
Sample covariance between response probabilities
and design weighted true values
Average response probability within RHG
The variance, V(A), is derived in the paper.
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.
9
Choosing the Optimum A
Consider one RHG h. The optimum number of call
attempts is the number Ah that gives the lowest
value on the function
where is the marginal cost for RHG h.
10
A Case Study the Swedish LFS

• Target population Swedish residents 15-74 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

.
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 we do not know the number of call attempts,
only the number of WD events
.
12
Data Processing and Estimation

• Reduced target population Swedish residents
  16-64 years old
• Each monthly sample viewed as a SRS
• Process data are used to estimate
• Marginal costs
• Response and contact probabilities

.
13
Measurement Error Model Parameters
Estimated by 10-month- average sample variance

.002 (low) 55,267,619,616 110,979,155
.040 (high) 55,267,619,616 2,402,939,983
(ICC)
Biemer and Trewin (1997)
.
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

15
No Bias, Low ICC
16
Bias, Low ICC