Sampling wls and mixed models festschrift to honor professor gary koch
Download
1 / 75

Sampling, WLS, and Mixed Models Festschrift to Honor Professor Gary Koch - PowerPoint PPT Presentation


  • 46 Views
  • Uploaded on

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.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Sampling, WLS, and Mixed Models Festschrift to Honor Professor Gary Koch' - stuart-berry


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
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


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

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 information?

SPH&HS, UMASS Amherst


Seasons study umass worc focus on 3 subjects
Seasons Study UMASS Worc- focus on 3 subjects information?

SPH&HS, UMASS Amherst


The problem simplified
The Problem-Simplified information?

  • Observe:

    • 1 Measure of SFat on each Subject

  • Assume:

    • Response Error (RE) Variance known

  • Question:

    • How do we estimate Subject’s True Sat Fat intake?

  • Begin with a Response Error Model … which leads to….

    • Mixed Model

    • Finite Population Mixed Model

Daisy

Lily

Rose

SPH&HS, UMASS Amherst


Population

Population information?

SPH&HS, UMASS Amherst


Population1

Set information?

Population

SPH&HS, UMASS Amherst


Response information?

4

11

SPH&HS, UMASS Amherst


Response information?

0

11

SPH&HS, UMASS Amherst


Response information?

4

9

SPH&HS, UMASS Amherst


Response information?

4

11

SPH&HS, UMASS Amherst


Response information?

4

9

SPH&HS, UMASS Amherst


Response information?

0

11

SPH&HS, UMASS Amherst


Response…….. information?

0

11

4

SPH&HS, UMASS Amherst


Response error model for set
Response Error Model for Set information?

SPH&HS, UMASS Amherst


Summary response error model
Summary Response Error Model information?

Latent Value

SPH&HS, UMASS Amherst


Re parameterized re model
Re-parameterized RE Model information?

Mean Latent Value:

SPH&HS, UMASS Amherst


Generating response in the re model
Generating Response in the RE Model information?

SPH&HS, UMASS Amherst


Generating response in the re model1
Generating Response in the RE Model information?

SPH&HS, UMASS Amherst


Generating an observed response in the re model
Generating an Observed Response information?in the RE Model

-1

1

-2

2

-2

-1

SPH&HS, UMASS Amherst


Sample space

9 information?

11

9

11

4

4

0

0

Sample Space

  • Response Error Model

SPH&HS, UMASS Amherst


Response error model

9 information?

11

9

11

4

4

0

0

Response Error Model

SPH&HS, UMASS Amherst


Mixed model mm
Mixed Model (MM) information?

Random Effect

SPH&HS, UMASS Amherst


Mixed model mm1
Mixed Model (MM) information?

Latent Value

SPH&HS, UMASS Amherst


Mixed model mm in action
Mixed Model (MM) in action information?

SPH&HS, UMASS Amherst


Mixed model mm2
Mixed Model (MM) …. information?

SPH&HS, UMASS Amherst


Mixed model mm3
Mixed Model (MM) ….?? information?

Who Are They?

?

?

SPH&HS, UMASS Amherst


Mixed model mm4
Mixed Model (MM) information?

??

??

What Does

it Mean?

?

?

SPH&HS, UMASS Amherst


Sample space mm

8 information?

1

8

3

9

9

11

11

4

4

0

0

12

12

3

1

Sample Space (MM)

Artificial

Real

SPH&HS, UMASS Amherst


Mm latent values
MM-Latent Values? information?

Samples

SPH&HS, UMASS Amherst


What are they for daisy
What are they information?(for Daisy)?

Samples

SPH&HS, UMASS Amherst


What are they for rose
What are they information?(for Rose)?

Samples

SPH&HS, UMASS Amherst


Blups of the mm latent value
BLUPs of the MM-Latent Value information?

SPH&HS, UMASS Amherst


Mse of blups for mm latent values
MSE of BLUPs for MM-Latent Values information?

Samples

Ave=0.986

Ave=3.768

SPH&HS, UMASS Amherst


Mse of blups for true latent values
MSE of BLUPs for True-Latent Values information?

Samples

Ave=32.06

Ave=32.06

SPH&HS, UMASS Amherst


Mse of blups p y
MSE of BLUPs | information?P=y

Samples

Ave=0.986

Ave=3.768

SPH&HS, UMASS Amherst


Finite Population Mixed Model (FPMM) information?

Population

SPH&HS, UMASS Amherst


Response error model1
Response Error Model information?

Latent Value

SPH&HS, UMASS Amherst


Finite population mixed model fpmm
Finite Population Mixed Model (FPMM) information?

SPH&HS, UMASS Amherst


Finite population mixed model fpmm1
Finite Population Mixed Model (FPMM) information?

SPH&HS, UMASS Amherst


Finite population mixed model fpmm2
Finite Population Mixed Model (FPMM) information?

SPH&HS, UMASS Amherst


Finite population mixed model fpmm3
Finite Population Mixed Model (FPMM) information?

SPH&HS, UMASS Amherst


Fpmm sample space

4 information?

0

0

4

9

9

11

11

FPMM- Sample Space …

SPH&HS, UMASS Amherst


Fpmm sample space1
FPMM- Sample Space … information?

11

9

9

11

4

0

0

4

SPH&HS, UMASS Amherst


Fpmm sample space2
FPMM- Sample Space … information?

4

4

-7

13

0

0

13

-7

SPH&HS, UMASS Amherst


Fpmm sample space3
FPMM- Sample Space … information?

13

13

0

4

-7

-7

4

0

SPH&HS, UMASS Amherst


Fpmm sample space4
FPMM- Sample Space … information?

11

11

-7

13

9

9

13

-7

SPH&HS, UMASS Amherst


Fpmm sample space5
FPMM- Sample Space … information?

13

13

9

11

-7

-7

11

9

SPH&HS, UMASS Amherst


Fpmm sample space6

11 information?

4

0

9

11

9

9

9

0

4

4

0

13

13

11

4

11

4

13

13

0

11

11

11

-7

0

-7

13

13

4

11

4

0

-7

-7

-7

0

-7

9

13

11

4

13

9

9

0

-7

-7

FPMM- Sample Space

All sample points are Potentially Observable

SPH&HS, UMASS Amherst


Fpmm blups of realized latent values
FPMM- BLUPs of Realized Latent Values information?

SPH&HS, UMASS Amherst


Fpmm blups of realized latent values1
FPMM- BLUPs of Realized Latent Values information?

SPH&HS, UMASS Amherst


Fpmm blups of realized latent values2
FPMM- BLUPs of Realized Latent Values information?

SPH&HS, UMASS Amherst


Fpmm blups of realized latent values3
FPMM- BLUPs of Realized Latent Values information?

Sample Sequence

SPH&HS, UMASS Amherst


Comparison of mm blup and fpmm blup
Comparison of MM-BLUP and FPMM-BLUP information?

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 information?

MM-BLUP

FPMM-BLUP

Predictor

SPH&HS, UMASS Amherst


Comparison of fpmm blup and mm blup sample space

12 information?

3

8

1

11

0

9

9

4

11

9

4

9

0

0

4

12

8

1

3

4

11

13

13

13

4

13

11

11

0

11

11

-7

0

-7

13

11

4

4

13

0

-7

-7

0

-7

-7

9

13

13

4

11

9

-7

9

0

-7

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

Artificial

SPH&HS, UMASS Amherst


To compare focus on this sample space

12 information?

3

8

1

9

9

11

11

4

0

9

9

4

4

0

0

12

8

1

3

4

11

13

13

13

4

11

13

0

11

11

11

-7

-7

0

13

4

11

13

4

-7

0

-7

-7

0

-7

9

13

4

11

13

9

-7

9

-7

0

To Compare, Focus on…THIS Sample Space

SPH&HS, UMASS Amherst


Bigger Sample (n=3) Population (N=4) information?

SPH&HS, UMASS Amherst


N 3 what is lily s latent value
n=3, What is Lily’s Latent value? information?

4

4

11

11

0

0

13

3

9

11

-7

3

4

4

11

11

0

0

13

-7

9

11

-7

-7

  • Use n=3 subject effects for MM 1 possible sample set

SPH&HS, UMASS Amherst

60


N 3 what is lily s latent value1
n=3, What is Lily’s Latent value? information?

11

11

13

-7

11

11

13

-7

  • 8 sample points

SPH&HS, UMASS Amherst

61


N 3 what is lily s latent value2
n=3, What is Lily’s Latent value? information?

  • 8x(6 permutations)=48 sample points

SPH&HS, UMASS Amherst

62


N 3 what is lily s latent value3
n=3, What is Lily’s Latent value? information?

Combinations

SPH&HS, UMASS Amherst

63


N 3 what is lily s latent value4
n=3, What is Lily’s Latent value? information?

192 Sample Points

SPH&HS, UMASS Amherst

64


Select one sequence
Select one sequence information?

SPH&HS, UMASS Amherst

65


Select one sequence observe sample point
Select one sequence, information?Observe Sample Point

SPH&HS, UMASS Amherst

66


Fpmm average mse of predictor over permutations
FPMM-Average MSE of Predictor over Permutations information?

SPH&HS, UMASS Amherst

67


Ave mse
Ave MSE information?

13

11

11

11

11

11

-7

X

5.0

MM

4.6

16.2 FPMM

SPH&HS, UMASS Amherst

68


Ave mse1
Ave MSE information?

13

11

11

11

11

11

-7

X

29.4

MM

17.7

34.3 FPMM

SPH&HS, UMASS Amherst

69


Conclusions
Conclusions information?

FPMM-BLUP

13

11

11

11

11

11

-7

Population

Sample Space

Design Based

SPH&HS, UMASS Amherst

70


Conclusions1
Conclusions information?

FPMM-BLUP

13

11

11

11

11

11

-7

Population

Evaluate Performance Conditional on the Sample

Design Based

SPH&HS, UMASS Amherst

71


Conclusions2
Conclusions information?

MM-BLUP

13

11

11

-7

Conceptual “Priors”

Model Based

SPH&HS, UMASS Amherst

72


Conclusions3
Conclusions information?

MM-BLUP

13

11

11

-7

Evaluate Performance Conditional on the Sample

Model Based

SPH&HS, UMASS Amherst

73


Conclusions4
Conclusions information?

13

11

11

-7

  • Evaluate Performance Conditional on the Sample

  • MSE for BLUPs not evaluated Correctly

    • Extends to WLS estimate of mean

  • MM-BLUP not always best

  • Sample Design is relevant only for derivation- not performance

  • Prior Distributions relevant only for derivation- not performance

SPH&HS, UMASS Amherst

74


Thanks to gary
Thanks to Gary information?

For keeping the focus on “reality”

SPH&HS, UMASS Amherst

75


ad