Embed Size (px)
Citation preview
Self-rotating sampling design
Martins Liberts
University of LatviaCentral Statistical Bureau of Latvia
29/06/2010
Martins Liberts Self-rotating sampling design
Rotating Panel
The sampling with rotating panel it not simple procedure:
The units sampled for the first time have to be sampledmultiple times (positive coordination)The overlap of samples between waves have to be avoided(negative coordination)
We have to “remember” what we have sampled before
Martins Liberts Self-rotating sampling design
Rotating Panel
The sampling with rotating panel it not simple procedure:
The units sampled for the first time have to be sampledmultiple times (positive coordination)
The overlap of samples between waves have to be avoided(negative coordination)
We have to “remember” what we have sampled before
Martins Liberts Self-rotating sampling design
Rotating Panel
The sampling with rotating panel it not simple procedure:
The units sampled for the first time have to be sampledmultiple times (positive coordination)The overlap of samples between waves have to be avoided(negative coordination)
We have to “remember” what we have sampled before
Martins Liberts Self-rotating sampling design
Rotating Panel
The sampling with rotating panel it not simple procedure:
The units sampled for the first time have to be sampledmultiple times (positive coordination)The overlap of samples between waves have to be avoided(negative coordination)
We have to “remember” what we have sampled before
Martins Liberts Self-rotating sampling design
Sampling Design
We want to have a sampling design with following features:
Probabilistic sampling design
Rotation of units according to the specific rotation pattern
Uniform distribution of sampled units over space
Uniform distribution of sampled units over time
Easy management of sampled units in a sample
Martins Liberts Self-rotating sampling design
Sampling Design
We want to have a sampling design with following features:
Probabilistic sampling design
Rotation of units according to the specific rotation pattern
Uniform distribution of sampled units over space
Uniform distribution of sampled units over time
Easy management of sampled units in a sample
Martins Liberts Self-rotating sampling design
Sampling Design
We want to have a sampling design with following features:
Probabilistic sampling design
Rotation of units according to the specific rotation pattern
Uniform distribution of sampled units over space
Uniform distribution of sampled units over time
Easy management of sampled units in a sample
Martins Liberts Self-rotating sampling design
Sampling Design
We want to have a sampling design with following features:
Probabilistic sampling design
Rotation of units according to the specific rotation pattern
Uniform distribution of sampled units over space
Uniform distribution of sampled units over time
Easy management of sampled units in a sample
Martins Liberts Self-rotating sampling design
Sampling Design
We want to have a sampling design with following features:
Probabilistic sampling design
Rotation of units according to the specific rotation pattern
Uniform distribution of sampled units over space
Uniform distribution of sampled units over time
Easy management of sampled units in a sample
Martins Liberts Self-rotating sampling design
Sampling Design
We want to have a sampling design with following features:
Probabilistic sampling design
Rotation of units according to the specific rotation pattern
Uniform distribution of sampled units over space
Uniform distribution of sampled units over time
Easy management of sampled units in a sample
Martins Liberts Self-rotating sampling design
Sampling Design
We are using two stage sampling design (common to severalhousehold surveys in Latvia):
Stratified systematic πps sampling of census counting areas(PSUs)
Simple random sampling of dwellings (SSUs) in each sampledPSU
All eligible households are selected in sampled dwelling
All eligible persons are selected in sampled dwelling
Martins Liberts Self-rotating sampling design
Sampling Design
We are using two stage sampling design (common to severalhousehold surveys in Latvia):
Stratified systematic πps sampling of census counting areas(PSUs)
Simple random sampling of dwellings (SSUs) in each sampledPSU
All eligible households are selected in sampled dwelling
All eligible persons are selected in sampled dwelling
Martins Liberts Self-rotating sampling design
Sampling Design
We are using two stage sampling design (common to severalhousehold surveys in Latvia):
Stratified systematic πps sampling of census counting areas(PSUs)
Simple random sampling of dwellings (SSUs) in each sampledPSU
All eligible households are selected in sampled dwelling
All eligible persons are selected in sampled dwelling
Martins Liberts Self-rotating sampling design
Sampling Design
We are using two stage sampling design (common to severalhousehold surveys in Latvia):
Stratified systematic πps sampling of census counting areas(PSUs)
Simple random sampling of dwellings (SSUs) in each sampledPSU
All eligible households are selected in sampled dwelling
All eligible persons are selected in sampled dwelling
Martins Liberts Self-rotating sampling design
Sampling Design
We are using two stage sampling design (common to severalhousehold surveys in Latvia):
Stratified systematic πps sampling of census counting areas(PSUs)
Simple random sampling of dwellings (SSUs) in each sampledPSU
All eligible households are selected in sampled dwelling
All eligible persons are selected in sampled dwelling
Martins Liberts Self-rotating sampling design
Serpentine of PSUs
Figure: Serpentine of PSUs in stratum “Rural areas”
Martins Liberts Self-rotating sampling design
Sampling Design
We are using rotation scheme 2− (2)− 2 for dwellings (inLabour Force Survey)
A dwelling is sampled for the two quartersA dwelling is not sampled for the next two quartersA dwelling is sampled again for the next two quarters
The rotation scheme is good to have overlap for quarterly(50%) and annual (56%) samples
Martins Liberts Self-rotating sampling design
Sampling Design
We are using rotation scheme 2− (2)− 2 for dwellings (inLabour Force Survey)
A dwelling is sampled for the two quarters
A dwelling is not sampled for the next two quartersA dwelling is sampled again for the next two quarters
The rotation scheme is good to have overlap for quarterly(50%) and annual (56%) samples
Martins Liberts Self-rotating sampling design
Sampling Design
We are using rotation scheme 2− (2)− 2 for dwellings (inLabour Force Survey)
A dwelling is sampled for the two quartersA dwelling is not sampled for the next two quarters
A dwelling is sampled again for the next two quarters
The rotation scheme is good to have overlap for quarterly(50%) and annual (56%) samples
Martins Liberts Self-rotating sampling design
Sampling Design
We are using rotation scheme 2− (2)− 2 for dwellings (inLabour Force Survey)
A dwelling is sampled for the two quartersA dwelling is not sampled for the next two quartersA dwelling is sampled again for the next two quarters
The rotation scheme is good to have overlap for quarterly(50%) and annual (56%) samples
Martins Liberts Self-rotating sampling design
Sampling Design
We are using rotation scheme 2− (2)− 2 for dwellings (inLabour Force Survey)
A dwelling is sampled for the two quartersA dwelling is not sampled for the next two quartersA dwelling is sampled again for the next two quarters
The rotation scheme is good to have overlap for quarterly(50%) and annual (56%) samples
Martins Liberts Self-rotating sampling design
The Rotation Pattern of PSUs
The rotation pattern [2− (2)− 2] is unevenly distributed overtime
[2− (2)− 2] is equivalent to
[2− (2)− 2− (2)][(2)− 2− (2)− 2]
[2− (2)− 2− (2)] + [(2)− 2− (2)− 2] = [8]
The rotation pattern [8] is evenly distributed over time
Martins Liberts Self-rotating sampling design
The Rotation Pattern of PSUs
The rotation pattern [2− (2)− 2] is unevenly distributed overtime
[2− (2)− 2] is equivalent to
[2− (2)− 2− (2)][(2)− 2− (2)− 2]
[2− (2)− 2− (2)] + [(2)− 2− (2)− 2] = [8]
The rotation pattern [8] is evenly distributed over time
Martins Liberts Self-rotating sampling design
The Rotation Pattern of PSUs
The rotation pattern [2− (2)− 2] is unevenly distributed overtime
[2− (2)− 2] is equivalent to
[2− (2)− 2− (2)]
[(2)− 2− (2)− 2]
[2− (2)− 2− (2)] + [(2)− 2− (2)− 2] = [8]
The rotation pattern [8] is evenly distributed over time
Martins Liberts Self-rotating sampling design
The Rotation Pattern of PSUs
The rotation pattern [2− (2)− 2] is unevenly distributed overtime
[2− (2)− 2] is equivalent to
[2− (2)− 2− (2)][(2)− 2− (2)− 2]
[2− (2)− 2− (2)] + [(2)− 2− (2)− 2] = [8]
The rotation pattern [8] is evenly distributed over time
Martins Liberts Self-rotating sampling design
The Rotation Pattern of PSUs
The rotation pattern [2− (2)− 2] is unevenly distributed overtime
[2− (2)− 2] is equivalent to
[2− (2)− 2− (2)][(2)− 2− (2)− 2]
[2− (2)− 2− (2)] + [(2)− 2− (2)− 2] = [8]
The rotation pattern [8] is evenly distributed over time
Martins Liberts Self-rotating sampling design
The Rotation Pattern of PSUs
The rotation pattern [2− (2)− 2] is unevenly distributed overtime
[2− (2)− 2] is equivalent to
[2− (2)− 2− (2)][(2)− 2− (2)− 2]
[2− (2)− 2− (2)] + [(2)− 2− (2)− 2] = [8]
The rotation pattern [8] is evenly distributed over time
Martins Liberts Self-rotating sampling design
The Rotation Pattern
PSU waves W1 W2 W3 W4 W5 W6 W7 W8
Dwelling waves (sample 1) w1 w2 w3 w4Dwelling waves (sample 2) w1 w2 w3 w4
Table: Rotation Scheme of Dwellings in One PSU
Martins Liberts Self-rotating sampling design
Weekly Sample Size
I will show an example where sample size is 8 PSUs per week
Martins Liberts Self-rotating sampling design
Sampling for the 1st week
b1,1 = ξ; ξ ∼ U [0, 1]
Martins Liberts Self-rotating sampling design
Sampling for the 1st week
b1,1 = ξ b1,2 ={ξ + 1+δ
8
}
Martins Liberts Self-rotating sampling design
Sampling for the 1st week
b1,1 = ξ b1,2 ={ξ + 1+δ
8
}b1,3 =
{ξ + 21+δ
8
}
Martins Liberts Self-rotating sampling design
Sampling for the 1st week
b1,i ={ξ + (i − 1) 1+δ
8
}
Martins Liberts Self-rotating sampling design
Sampling for 2 weeks
b1,i ={ξ + (i − 1) 1+δ
8
}b2,i =
{ξ + (i − 1) 1+δ
8 + 1+δ8·13
}
Martins Liberts Self-rotating sampling design
Sampling for 3 weeks
b1,i ={ξ + (i − 1) 1+δ
8
}· · · b3,i =
{ξ + (i − 1) 1+δ
8 + 2 1+δ8·13
}
Martins Liberts Self-rotating sampling design
Sampling for 13 weeks
bj ,i ={ξ + (i − 1) 1+δ
8 + (j − 1) 1+δ8·13
}
Martins Liberts Self-rotating sampling design
Sampling for 14 weeks
bj ,i ={ξ + (i − 1) 1+δ
8 + (j − 1) 1+δ8·13
}
Martins Liberts Self-rotating sampling design
Sampling for 15 weeks
bj ,i ={ξ + (i − 1) 1+δ
8 + (j − 1) 1+δ8·13
}
Martins Liberts Self-rotating sampling design
Sampling for 26 weeks
bj ,i ={ξ + (i − 1) 1+δ
8 + (j − 1) 1+δ8·13
}
Martins Liberts Self-rotating sampling design
Sampling for 39 weeks
bj ,i ={ξ + (i − 1) 1+δ
8 + (j − 1) 1+δ8·13
}
Martins Liberts Self-rotating sampling design
Sampling for 1 weeks (q=6)
b1,i ={ξ + (i − 1) 1+δ
8
}
Martins Liberts Self-rotating sampling design
Sampling for 2 weeks (q=6)
b1,i ={ξ + (i − 1) 1+δ
8
}b2,i =
{ξ + (i − 1) 1+δ
8 + q13 + 1+δ
8·13
}
Martins Liberts Self-rotating sampling design
Sampling for 3 weeks (q=6)
· · · b3,i ={ξ + (i − 1) 1+δ
8 + 2( q
13 + 1+δ8·13
)}
Martins Liberts Self-rotating sampling design
Sampling for 13 weeks (q=6)
bj ,i ={ξ + (i − 1) 1+δ
8 + (j − 1)( q
13 + 1+δ8·13
)}
Martins Liberts Self-rotating sampling design
Sampling for 14 weeks (q=6)
bj ,i ={ξ + (i − 1) 1+δ
8 + (j − 1)( q
13 + 1+δ8·13
)}
Martins Liberts Self-rotating sampling design
Sampling for 15 weeks (q=6)
bj ,i ={ξ + (i − 1) 1+δ
8 + (j − 1)( q
13 + 1+δ8·13
)}
Martins Liberts Self-rotating sampling design
Sampling for 26 weeks (q=6)
bj ,i ={ξ + (i − 1) 1+δ
8 + (j − 1)( q
13 + 1+δ8·13
)}
Martins Liberts Self-rotating sampling design
Sampling for 39 weeks (q=6)
bj ,i ={ξ + (i − 1) 1+δ
8 + (j − 1)( q
13 + 1+δ8·13
)}
Martins Liberts Self-rotating sampling design
Optimisation of design
We have seen that each sampling point can be computedusing the formulabj ,i =
{ξ + (i − 1) 1+δ
8 + (j − 1)( q
13 + 1+δ8·13
)}
We can define sampling point separately for each stratum
bh,j ,i ={ξh + (i − 1) 1+δh
8 + (j − 1)(
qh13 + 1+δh
8·13
)}The design can be optimised by two parameters for eachstratum
δh ∈(
maxk (Nhk )Pk Nhk
; 18
), where Nhk is the size of PSU (number of
households in PSU) – the parameter of “skewness”qh ∈ [0; 13] and qh ∈ Z – the “speed” of rotation
Martins Liberts Self-rotating sampling design
Optimisation of design
We have seen that each sampling point can be computedusing the formulabj ,i =
{ξ + (i − 1) 1+δ
8 + (j − 1)( q
13 + 1+δ8·13
)}We can define sampling point separately for each stratum
bh,j ,i ={ξh + (i − 1) 1+δh
8 + (j − 1)(
qh13 + 1+δh
8·13
)}
The design can be optimised by two parameters for eachstratum
δh ∈(
maxk (Nhk )Pk Nhk
; 18
), where Nhk is the size of PSU (number of
households in PSU) – the parameter of “skewness”qh ∈ [0; 13] and qh ∈ Z – the “speed” of rotation
Martins Liberts Self-rotating sampling design
Optimisation of design
We have seen that each sampling point can be computedusing the formulabj ,i =
{ξ + (i − 1) 1+δ
8 + (j − 1)( q
13 + 1+δ8·13
)}We can define sampling point separately for each stratum
bh,j ,i ={ξh + (i − 1) 1+δh
8 + (j − 1)(
qh13 + 1+δh
8·13
)}The design can be optimised by two parameters for eachstratum
δh ∈(
maxk (Nhk )Pk Nhk
; 18
), where Nhk is the size of PSU (number of
households in PSU) – the parameter of “skewness”qh ∈ [0; 13] and qh ∈ Z – the “speed” of rotation
Martins Liberts Self-rotating sampling design
Optimisation of design
We have seen that each sampling point can be computedusing the formulabj ,i =
{ξ + (i − 1) 1+δ
8 + (j − 1)( q
13 + 1+δ8·13
)}We can define sampling point separately for each stratum
bh,j ,i ={ξh + (i − 1) 1+δh
8 + (j − 1)(
qh13 + 1+δh
8·13
)}The design can be optimised by two parameters for eachstratum
δh ∈(
maxk (Nhk )Pk Nhk
; 18
), where Nhk is the size of PSU (number of
households in PSU) – the parameter of “skewness”
qh ∈ [0; 13] and qh ∈ Z – the “speed” of rotation
Martins Liberts Self-rotating sampling design
Optimisation of design
We have seen that each sampling point can be computedusing the formulabj ,i =
{ξ + (i − 1) 1+δ
8 + (j − 1)( q
13 + 1+δ8·13
)}We can define sampling point separately for each stratum
bh,j ,i ={ξh + (i − 1) 1+δh
8 + (j − 1)(
qh13 + 1+δh
8·13
)}The design can be optimised by two parameters for eachstratum
δh ∈(
maxk (Nhk )Pk Nhk
; 18
), where Nhk is the size of PSU (number of
households in PSU) – the parameter of “skewness”qh ∈ [0; 13] and qh ∈ Z – the “speed” of rotation
Martins Liberts Self-rotating sampling design
Weighting
The probability of inclusion for any dwelling can be computedas
πhkl =nhNhk
Nh
mh
Mhk
where nh – the number of PSUs sampled in the stratum h (inspecific period – for example one quarter)Nhk – the size of PSU hk (the number of dwellings in thepopulation of PSU hk)Nh – the number of dwellings in the stratum hmh – the number of dwellings sampled in the 2nd stage in thestratum hMhk – the number of dwellings in the population of PSU hk
Nhk = Mhk ⇒ πhkl = nhmhNh
– we have achieved self-weightingsampling in each stratum
Martins Liberts Self-rotating sampling design
Weighting
The probability of inclusion for any dwelling can be computedas
πhkl =nhNhk
Nh
mh
Mhk
where nh – the number of PSUs sampled in the stratum h (inspecific period – for example one quarter)Nhk – the size of PSU hk (the number of dwellings in thepopulation of PSU hk)Nh – the number of dwellings in the stratum h
mh – the number of dwellings sampled in the 2nd stage in thestratum hMhk – the number of dwellings in the population of PSU hk
Nhk = Mhk ⇒ πhkl = nhmhNh
– we have achieved self-weightingsampling in each stratum
Martins Liberts Self-rotating sampling design
Weighting
The probability of inclusion for any dwelling can be computedas
πhkl =nhNhk
Nh
mh
Mhk
where nh – the number of PSUs sampled in the stratum h (inspecific period – for example one quarter)Nhk – the size of PSU hk (the number of dwellings in thepopulation of PSU hk)Nh – the number of dwellings in the stratum hmh – the number of dwellings sampled in the 2nd stage in thestratum hMhk – the number of dwellings in the population of PSU hk
Nhk = Mhk ⇒ πhkl = nhmhNh
– we have achieved self-weightingsampling in each stratum
Martins Liberts Self-rotating sampling design
Weighting
The probability of inclusion for any dwelling can be computedas
πhkl =nhNhk
Nh
mh
Mhk
where nh – the number of PSUs sampled in the stratum h (inspecific period – for example one quarter)Nhk – the size of PSU hk (the number of dwellings in thepopulation of PSU hk)Nh – the number of dwellings in the stratum hmh – the number of dwellings sampled in the 2nd stage in thestratum hMhk – the number of dwellings in the population of PSU hk
Nhk = Mhk ⇒ πhkl = nhmhNh
– we have achieved self-weightingsampling in each stratum
Martins Liberts Self-rotating sampling design
Weighting
Nhk 6= Mhk in reality because of a population migration
Nhk has to be fixed for self-rotating design to workMhk normally is not fixed; it is updated each time the secondstage sampling is done
The difference between Nhk and Mhk is increasing thevariance of design weights in stratum h
Statistician has to monitor the difference between Nhk andMhk
When the difference has reached a “critical” level
The frame of PSUs has to be updated – update of Nhk
New sample of PSUs has to be selected (we have done it forLFS 2010)
Martins Liberts Self-rotating sampling design
Weighting
Nhk 6= Mhk in reality because of a population migration
Nhk has to be fixed for self-rotating design to workMhk normally is not fixed; it is updated each time the secondstage sampling is done
The difference between Nhk and Mhk is increasing thevariance of design weights in stratum h
Statistician has to monitor the difference between Nhk andMhk
When the difference has reached a “critical” level
The frame of PSUs has to be updated – update of Nhk
New sample of PSUs has to be selected (we have done it forLFS 2010)
Martins Liberts Self-rotating sampling design
Weighting
Nhk 6= Mhk in reality because of a population migration
Nhk has to be fixed for self-rotating design to workMhk normally is not fixed; it is updated each time the secondstage sampling is done
The difference between Nhk and Mhk is increasing thevariance of design weights in stratum h
Statistician has to monitor the difference between Nhk andMhk
When the difference has reached a “critical” level
The frame of PSUs has to be updated – update of Nhk
New sample of PSUs has to be selected (we have done it forLFS 2010)
Martins Liberts Self-rotating sampling design
Weighting
Nhk 6= Mhk in reality because of a population migration
Nhk has to be fixed for self-rotating design to workMhk normally is not fixed; it is updated each time the secondstage sampling is done
The difference between Nhk and Mhk is increasing thevariance of design weights in stratum h
Statistician has to monitor the difference between Nhk andMhk
When the difference has reached a “critical” level
The frame of PSUs has to be updated – update of Nhk
New sample of PSUs has to be selected (we have done it forLFS 2010)
Martins Liberts Self-rotating sampling design
Conclusions
We have found a way how to compute sampling units for LFSand other continuous surveys according to the rotation pattern
Sampling units can be computed for long period (5 years forexample). It allows timely planning of the work forinterviewers
The possibility to use simple approximation methods forvariance estimation (re-sampling techniques)
Martins Liberts Self-rotating sampling design
Conclusions
We have found a way how to compute sampling units for LFSand other continuous surveys according to the rotation pattern
Sampling units can be computed for long period (5 years forexample). It allows timely planning of the work forinterviewers
The possibility to use simple approximation methods forvariance estimation (re-sampling techniques)
Martins Liberts Self-rotating sampling design
Conclusions
We have found a way how to compute sampling units for LFSand other continuous surveys according to the rotation pattern
Sampling units can be computed for long period (5 years forexample). It allows timely planning of the work forinterviewers
The possibility to use simple approximation methods forvariance estimation (re-sampling techniques)
Martins Liberts Self-rotating sampling design
The work has been supported by:
Central Statistical Bureau of Latvia
University of Latvia
The ESF project “1DP/1.1.2.1.2./09/IPIA/VIAA/004”
Martins Liberts Self-rotating sampling design
Thank you!
Martins Liberts Self-rotating sampling design
