SPH&HS, UMASS Amherst SPH&HS, UMASS Amherst 1 Sampling, WLS, and Sampling, WLS, and Mixed Models Mixed Models Festschrift to Honor Festschrift to Honor Professor Gary Koch Professor Gary Koch Ed Stanek and Julio Ed Stanek and Julio Singer Singer U of Mass, Amherst, and U of Mass, Amherst, and U of Sao Paulo, Brazil U of Sao Paulo, Brazil
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Sampling, WLS, and Mixed Models Festschrift to Honor Professor Gary Koch
Sampling, WLS, and Mixed Models Festschrift to Honor Professor Gary Koch. Ed Stanek and Julio Singer U of Mass, Amherst, and U of Sao Paulo, Brazil. Finite Population Mixed Models Research Group. - PowerPoint PPT Presentation
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SPH&HS, UMASS AmherstSPH&HS, UMASS Amherst 11
Sampling, WLS, and Sampling, WLS, and Mixed Models Mixed Models
Festschrift to Honor Festschrift to Honor Professor Gary KochProfessor Gary Koch
Ed Stanek and Julio SingerEd Stanek and Julio SingerU of Mass, Amherst, and U of Mass, Amherst, and
U of Sao Paulo, BrazilU of Sao Paulo, Brazil
SPH&HS, UMASS AmherstSPH&HS, UMASS Amherst 22
Finite Population Mixed Models Finite Population Mixed Models Research GroupResearch Group
Luzmery Gonzalas, Columbia; Viviana Lencina, Argentina; Julio Singer, Brazil; Silvina San Martino, Argentina; Wenjun Li, US; and Ed Stanek US
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How do we make up models to get better insight using limited information?
Study Design- SamplingResponse ErrorModel Assumptions
An Example: What is a subject’s saturated fat intake?
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Seasons Study UMASS WorcSeasons Study UMASS Worc
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Seasons Study UMASS WorcSeasons Study UMASS Worc
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The Problem-SimplifiedThe Problem-Simplified 1 Measure of Sat. Fat on each Subject1 Measure of Sat. Fat on each Subject Assume Response Error Variance knownAssume Response Error Variance known How do we estimate Subject’s True Sat How do we estimate Subject’s True Sat
Fat intake?Fat intake?
Daisy Lily Rose
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Population
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PopulationSet
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11
Response
4
SPH&HS, UMASS AmherstSPH&HS, UMASS Amherst 1010
11
Response
0
SPH&HS, UMASS AmherstSPH&HS, UMASS Amherst 1111
9
Response
4
SPH&HS, UMASS AmherstSPH&HS, UMASS Amherst 1212
11
Response
4
SPH&HS, UMASS AmherstSPH&HS, UMASS Amherst 1313
9
Response
4
SPH&HS, UMASS AmherstSPH&HS, UMASS Amherst 1414
11
Response
0
SPH&HS, UMASS AmherstSPH&HS, UMASS Amherst 1515
11
Response
04
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Response Error ModelResponse Error Model jk R jk jkY E Y E
11 22
99 1111
0.50.5 0.50.5
1kY
k
1kP Y
R jk jE Y y
1 10y
11 22
00 44
0.50.5 0.50.5
2kY
k
2kP Y2 2y
jk j jkY y E
2varR jk jY
21 1
22 4
1j 2j
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Response Error ModelResponse Error Modelj j jY y E
1 1 1Y y E 2 2 2Y y E
21 1 2
2 4
Latent Value
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Mean Latent Value:Mean Latent Value:1
1 n
jj
yn
2 2 2
2 2 Y y E
E
1 1 1
1 1 Y y E
E
Response Error ModelResponse Error Model
SPH&HS, UMASS AmherstSPH&HS, UMASS Amherst 1919
2 1
11E 12E 21E 22E
Response Error ModelResponse Error Model
21 1 2
2 4
SPH&HS, UMASS AmherstSPH&HS, UMASS Amherst 2020
2 1
11E 12E 21E 22E
Response Error ModelResponse Error Model
1E1Y 2Y 2E
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6 4 6 4
-1 1 -2 2
Response Error ModelResponse Error Model
-1 -29 0
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Sample SpaceSample Space Response Error ModelResponse Error Model