Q2008 1

USE OF PROCESS DATA TO DETERMINE THE NUMBER OF CALL ATTEMPTS IN A TELEPHONE SURVEYAnnica IsakssonLinköping University, Sweden

Peter LundquistStatistics Sweden

Daniel Thorburn

Stockholm University, Sweden

Q2008 2

The ProblemConsider 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?

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

Ar Askk

kAy

yt ˆ

ˆ

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)

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

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

Q2008 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

Random interviewer effect with

expectation 0 and variance

bab 2

Random response error with

expectation 0 and variance

a2

True value for individual k

Q2008 7

Bias and Variance

s

h

hsAs

hhh

H

hA

sh p

H

hs ks k

Ask

sAsk

hpAycmp

Sn EnEtB

11

)(*RD 1)ˆ(

Bias if the RHG model does not hold:

s

h

hsAH

hA

shp

Ay

SnEtB

11)ˆ(

The variance of is derived in the paper

Sample covariance between response probabilities and

design weighted true values

Average response probability within

RHG Ayt̂

Q2008 8

Cost Function

sHh hh

nA CnC 1 start,,

1

nACnACnACCC ,,, 3210

sH

hAa

ahhh

nA nnCC 1 11

contact,,

2

sHh h

Ah

nA CmC 1 interview,,

3

nAC ,

Q2008 9

Optimum A for RHG h

hhh

Ayh

Ayh

Ayh

nEAVAB

tVtBtMSE hhh

)()(

)ˆ()ˆ()ˆ(

2

2

hhh nEACEnnECC 0

Assume: of the costs are allocated to RHG h nnE h

Q2008 10

Optimum A for RHG h: ResultThe optimum number of call attempts for RHG h is the number Ah that gives the lowest value on the function

)()())(( 02

hhhh ACEAVnnECCAB

Q2008 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: 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

t

hl

Ahl tt ˆˆ

Q2008 13

Relative Bias, Monthly Averages

- 5-4-3-2-10123456

1 6 11 16 21 26 31

N um ber o f W inD ati ev ents

Rel

ativ

e Bia

s (%

)

M aleF em ale

Q2008 14

= .002=

55,267,619,616=

110,979,155

.

2222

bUby S

2US

b

Measurement Error Model Parameters

y 1;0;1b0

Intraclass correlation, ICC (Biemer and Trewin, 1997):

Q2008 15

No Bias, ICC = .002

1 6 11 16 21 26 31

N um b er o f W in D ati E ven ts

N o m easurem enterro rsG am m a_ b = -1

G am m a_ b = 0

G am m a_ b = 1

Q2008 16

Bias, ICC = .002

1 6 11 16 21 26 31N um b er o f W in D ati E ven ts

N o m easurem enterro rsG am m a_ b = -1

G am m a_ b = 0

G am m a_ b = 1

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