q2008 1 use of process data to determine the number of call attempts in a telephone survey annica...
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Q2008 1
USE OF PROCESS DATA TO DETERMINE THE NUMBER OF CALL ATTEMPTS IN A TELEPHONE SURVEY
Annica IsakssonLinköping University, Sweden
Peter LundquistStatistics 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.
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
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)
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
hp
Aycmp
Sn E
nEtB
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
h
hh
Ayh
Ayh
Ayh
nEAV
AB
tVtBtMSE hhh
)()(
)ˆ()ˆ()ˆ(
2
2
hhh nEACE
nnE
CC 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
hhh
h ACEAVnnE
CCAB
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 B
ias
(%)
M aleF em ale
Q2008 14
= .002
= 55,267,619,616
= 110,979,155
.
222
2
bU
by
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 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 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, [email protected]
Peter Lundquist, [email protected]