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Neighborhood Factor= s and Children: Small Area Statistics

Outline

Objectives<= /font>

Description of Data= sets

Problems with data<= /a>

Methodology=

SAE: Area Level Mod= el

SAE: Area level mod= el

MSE of

Voc. Score: HT vs. = GREG

Voc. Score: HT vs. = GREG

Voc. Score: HT vs. = SAE

Voc. Score: HT vs. SAE

Example: CMA=3D12 (Kitchener)

Injuries: HT vs. SA= E

Injuries: HT vs. SA= E

Chronic Disease: HT= vs. SAE

Chronic Disease: HT= vs. SAE

Average Errors: HT = vs. SAE

Conclusions=

Acknowledgement=

Slide 22

Slide 23

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Neighborhood Factor= s and Children: Small Area Statistics
Longyang Wu, Xu Wang and Xianlin Ma
Dept. of Statistics & Act= uarial Science
University of Waterloo=

Outline
Introduction
Data preparation
Methodology
Results
Conclusions

Objectives<= /font>
Design-based methods (HT and = GREG) to estimate population mean
Small area estimation (SAE) m= ethod to estimate population mean
Compare the results of two me= thods

Description of Data= sets
Area level data: five variabl= es
Individual level data: 13 var= iables
Response Variables

Problems with data<= /a>
Sample size
7 CMAs > 50 - 2 CMAs > 160
Most (15) 30
Small A= rea Estimation (SAE)
Variables dont match in two = level data sets
Area level model
2nd order inclusion probability unavailable
Missing data

Methodology=
Design-based (direct ) estima= tors
Horvitz Thompson (HT)
Generalized regression (GREG)=
estimated by combining adjacent area data

SAE: Area Level Mod= el
Model: (Rao J. Small area estimation)
Zi is area level c= ovariates,
EBLUP ( unknown )
b estimated by:

SAE: Area level mod= el
ML estimation
Where

MSE of
Where

Voc. Score: HT vs. = GREG

Voc. Score: HT vs. = GREG

Voc. Score: HT vs. = SAE

Voc. Score: HT vs. SAE

Example: CMA=3D12 (Kitchener)

Injuries: HT vs. SA= E

Injuries: HT vs. SA= E

Chronic Disease: HT= vs. SAE

Chronic Disease: HT= vs. SAE

Average Errors: HT = vs. SAE

Conclusions=
Average errors from SAE are s= maller than those from HT
SAE increases precision

Acknowledgement=
Prof. Changbao Wu, for superv= ising the
case study
Prof. Hugh Chipman and Prof. = Will Welch,
for financial support<= /td>

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Case Study II
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<= /td> =
Neighborhood Factors and
Children: Small Area Statistics
<= /td> <= /td> = <= /td>
Longyang Wu, Xu Wang and Xianlin Ma
Dept. of Statistics & Actuarial Science
University of Waterloo
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Outline
<= /td> <= /td> <= /td>
Introduction
Data preparation
Methodology
Res= ults
Conclusions
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Objectives
<= /td> <= /td> = <= /td> <= /td>
Design-based methods (HT and
GR= EG) to estimate population mean
Small area estimation (SAE) method
to estimate po= pulation mean
Compare the results of two methods
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Description of Data sets
<= /td> <= /td> = <= /td>
n Ar= ea level data: five variables
n In= dividual level data: 13 variables
= Response Variables
Variable Names
Property=
Level
Missing data
Chronic health=
Categorical
3
0.00%
Child injury
Binary
2
1.48%
<= /td>
Cognitive
Com= petence
Continuous
40:160
22.2%
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Problems with data
<= /td> <= /td> <= /td> <= /td> = <= /td> <= /td> <= /td>
Sa= mple size
- 7 = CMA= s > 50 - 2 CMAs > 160
- Mo= st (15) 30<= /font>
Small= Area Estimation (SAE)
V= ariables don= t match in two level data sets
Area level model
2nd order inclusion probability unavailable
Mi= ssing data
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Methodology
<= /td> = <= /td> <= /td>
Design-based (direct ) estimators
- Ho= rvitz = Thompson (HT)
- Ge= neralized regression (GREG)
estimated by combining adjac= ent area data
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Voc. Score: HT vs. GREG
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Voc. Score: HT vs. GREG
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Voc. Score: HT vs. SAE
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Voc. Score: HT vs. SAE
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Example: CMA=3D12 (Kitchener)
Voc. Score
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Mean
Variance=
HT
107.42
212.30
EBLUP
103.24
68.93
=
Ki= tchener has the second smallest sample
size (13) with= an extreme value (160)
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Injuries: HT vs. SAE
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Injuries: HT vs. SAE
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Chronic Disease: HT vs. SAE
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Chronic Disease: HT vs. SAE
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charset="windows-1252" PowerPoint Presentation
Average Errors: HT vs. SAE
Method
Voc.score
Injuries=
Chronic<= br>
SAE
18.69
0.00294
0.0116
HT
22.50
0.00554<= br>
0.0190
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Conclusions
<= /td> = <= /td>
Average errors from SAE are smaller
than those fro= m HT
SAE increases precision
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Acknowledgement
= <= /td> =
Pr= of. Changbao Wu, for supervising the
case study
Pr= of. Hugh Chipman and Prof. Will Welch,
fo= r financial support
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3D"Thank
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3D"Questions?"
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Content-Type: text/html; charset="us-ascii" PowerPoint Presentation
7/15/2003
1
Neig= hborhood Factors and Children: Small Area Statistics=
Longyang Wu, &= nbsp; Xu Wang and Xianlin Ma
Dept. of Statistics & Actuarial Science
University of Waterloo
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7/15/2003
2
Outline
3D"*"Introduction = ;
3D"*"
3D"*"Data preparation=
3D"*"
3D"*"Methodology =
3D"*"
3D"*"Results
3D"*"
3D"*"Conclusions
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Objectives
3D"*"Design-based methods (HT and <= span style=3D'position:absolute;top:48.27%;left:7.36%;width:92.63%;height:51.72= %'>GREG) to estimate population mean
w
3D"*"Small area estimation (SAE) method to estimate popu= lation mean
w
3D"*"Compare the results of two methods
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7/15/2003
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Description of Data sets
3D"*"
nArea level data: five variables
n
nIndividual level data: 13 variables
n
n Response Variables
22.2%
1.48%
0.00%
Missing data
40:160
 2
 3
Level
Continuous
Binary
Categorical
Property
Cognitive Co= mpetence
Child injury
Chronic health
 Variable Names
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7/15/2003
5
Problems with data
§Sa= mple size
-7 = CMAs > 50        = ;  -   2 CMA<= span style=3D'font-family:"Times New Roman";mso-ascii-font-family:Tahoma;mso-ha= nsi-font-family: "Times New Roman";font-size:86%'>’s > 160 <= /div>
-Mo= st (15) » 30       
- Þ   Small Area Estimation (SAE)=
§
§Va= riables dont = match in two level data sets
§ Þ A= rea level model
§=
§2<= /span>nd order inclusion probability unavailable
§=
§Mi= ssing data
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7/15/2003
6
Methodology
<= span style=3D'font-size:88%'>3D"*"De= sign-based (direct ) estimators
<= span style=3D'font-size:88%'>-Ho= rvitz Thompson (HT)
-
-
<= span style=3D'font-size:88%'>-Ge= neralized regression (GREG)
w
w
w
w
w         estimated by combining adjacent area data
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7/15/2003
7
SAE: Area Level Model
3D"*"Model:  (Rao J. Small area estimation)
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wZi is area level covariates,
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3D"*"EB= LUP (      un= known )
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wb<= span style=3D'font-family:Tahoma;mso-ascii-font-family:Tahoma;font-size:75%'> estimated by:=
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7/15/2003
8
SAE: Area level model
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7/15/2003
10
Voc. Score: HT vs. GREG=
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7/15/2003
11
Voc. Score: HT vs. GREG=
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7/15/2003
12
Voc. Score: HT vs. SAE<= /div>
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7/15/2003
13
 Vo= c. Score: HT vs. SAE
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7/15/2003
14
Example: CMA=3D12 (Kitchener)<= /span>
68.93
103.24
EBLUP
212.30
107.42
HT
Variance
Mean
Estimator
Voc. Score
Kitchener has the second smallest sample size (13) with an extreme value (160)
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7/15/2003
15
Injuries: HT vs. SAE
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7/15/2003
16
Injuries: HT vs. SAE
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7/15/2003
17
Chronic Disease: HT vs. SAE
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7/15/2003
18
Chronic Disease: HT vs. SAE
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7/15/2003
19
Average Errors: HT vs. SAE
0.0190
0.00554
22.50
HT
 0.0116
 0.00294
18.69
SAE
Chronic