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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.

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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

SPH&HS, UMASS Amherst

finite population mixed models research group
Finite Population Mixed Models Research Group

Luzmery Gonzalas, Columbia; Viviana Lencina, Argentina; Julio Singer, Brazil; Silvina San Martino, Argentina; Wenjun Li, US; and Ed Stanek US

slide3

How do we make up models to get better insight using limited information?

Study Design- Sampling

Response Error

Model Assumptions

An Example: What is a subject’s saturated fat intake?

SPH&HS, UMASS Amherst

seasons study umass worc
Seasons Study UMASS Worc

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seasons study umass worc1
Seasons Study UMASS Worc

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the problem simplified
The Problem-Simplified
  • 1 Measure of Sat. Fat on each Subject
  • Assume Response Error Variance known
  • How do we estimate Subject’s True Sat Fat intake?

Daisy

Lily

Rose

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Population

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Population

Set

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Response

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Response

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Response

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Response

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Response

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Response

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Response

0

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response error model
Response Error Model

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response error model1
Response Error Model

Latent Value

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slide19

Response Error Model

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slide20

Response Error Model

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slide21

Response Error Model

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sample space

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Sample Space
  • Response Error Model

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response error model2

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Response Error Model

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mixed model mm
Mixed Model (MM)

Random Effect

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mixed model mm1
Mixed Model (MM)

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mixed model mm2
Mixed Model (MM)

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mixed model mm3
Mixed Model (MM)

Who Are They?

?

?

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mixed model mm4
Mixed Model (MM)

??

??

What Does

it Mean?

?

?

SPH&HS, UMASS Amherst

sample space mm

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Sample Space (MM)

Artificial

Real

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mm latent values
MM Latent Values?

Samples

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blups of the mm latent value
BLUPs of the MM-Latent Value

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mse of blups for mm latent values
MSE of BLUPs for MM Latent Values?

Samples

Ave=0.986

Ave=3.768

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mse of blups vs true latent values
MSE of BLUPs vs True Latent Values?

Samples

Ave=32.06

Ave=32.06

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mse of blups vs true latent values1
MSE of BLUPs vs True Latent Values?

Samples

Ave=0.986

Ave=3.768

SPH&HS, UMASS Amherst

slide35

Finite Population Mixed Model (FPMM)

Population

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response error model3
Response Error Model

Latent Value

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fpmm sample space

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FPMM- Sample Space …

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FPMM- Sample Space …

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FPMM- Sample Space …

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FPMM- Sample Space …

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fpmm sample space4
FPMM- Sample Space …

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fpmm sample space5
FPMM- Sample Space …

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FPMM- Sample Space

All sample points are Potentially Observable

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fpmm blups of realized latent values3
FPMM- BLUPs of Realized Latent Values

Sample Sequence

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comparison of mm blup and fpmm blup
Comparison of MM-BLUP and FPMM-BLUP

MM-BLUP

FPMM-BLUP

Target Random Variable

MM-Latent Value

Latent Value

SPH&HS, UMASS Amherst

comparison of mm blup and fpmm blup1
Comparison of MM-BLUP and FPMM-BLUP

MM-BLUP

FPMM-BLUP

Predictor

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comparison of fpmm blup and mm blup sample space

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Comparison of FPMM-BLUP and MM-BLUP-Sample Space

Artificial

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to compare focus on this sample space

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To Compare, Focus on…THIS Sample Space

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sample space mm1

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sample space mm2

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Artificial

Real

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mse of blups vs true latent values2
MSE of BLUPs vs True Latent Values?

Samples

Ave=32.06

Ave=32.06

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mixed model mm5
Mixed Model (MM)

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blups of the mm latent value1
BLUPs of the MM-Latent Value

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fpmm sample space7

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sample space1

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Sample Space
  • Response Error Model

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sample space2

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Sample Space
  • Response Error Model

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response error model4
Response Error Model

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