~ Draft version ~ 1

HOW TO CHOOSE THE NUMBER OF CALL ATTEMPTS IN A TELEPHONE SURVEYIN THE PRESENCE OF NONRESPONSE AND

MEASUREMENT ERRORS Annica IsakssonLinköping University, Sweden

Peter LundquistStatistics 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

Ar Askk

kAyc

yt

ˆˆ *

t

Response set after A call attemptsInclusion

probability for individual k

Estimated response probability for

individual kafter A call attempts

Observed value for individual k (proxy for the true value µk)

~ 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 Hs response homogeneity groups (RHG) such that, for all A, given the sample,

Ask

~ Draft version ~ 6

Measurement Error ModelFor an individual k in RHG h, given the sample and that the individual responds at call attempt a,

A

aakakiakkk bvy

1,),(, )(

Indicates if individual k

responds at attempt a=ak

A random interviewer effect with expectation 0

and variance

bab 2

A random response error with

expectation 0 and variance

a2

True value for individual k

~ Draft version ~ 7

Bias and Variance

s

h

hsAs

hhh

H

hA

sh p

H

hs ks k

Ask

sAsk

hp

Aycmp

Sn E

nEtB

11

)(*RD 1)ˆ(

Bias only if the RHG model does not hold:

s

h

hsAH

hA

shp

SnEAB

11)(

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 ACCC 0

where is composed of… AC 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 AConsider 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.

)()())(( 02

hhh

h ACEAVnnE

CCAB

)( hAC

~ Draft version ~ 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

~ 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 16-64 years old

Each monthly sample viewed as a SRS

Process data are used to estimate: Marginal costs Response and contact probabilities

~ Draft version ~ 13

.

222

2

bU

by

S

Biemer and Trewin (1997):

2US b

Measurement Error Model Parameters

.002 (”low”) 55,267,619,616

110,979,155

.040 (”high”)

55,267,619,616

2,402,939,983

y

Estimated by 10-month- average sample

variance

1;0;1b0

(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

b

t

~ Draft version ~ 15

No Bias, Low ICC

1 6 11 16 21 26 31

# o f W D E v ents

m o p t_ P R Dm o p t_ 1_ lom o p t0_ lom o p t1_ lo

~ Draft version ~ 16

Bias, Low ICC

1 6 11 16 21 26 31

# o f W D E v ents

m o p t_ P R Dm o p t_ 1_ lom o p t0_ lom o p t1_ lo