SPH&HS, UMASS Amherst 1 Sampling, WLS, and Mixed Models Festschrift to Honor Professor Gary Koch Ed Stanek and Julio Singer U of Mass, Amherst, and U of.

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Presentation transcript:

SPH&HS, UMASS Amherst 1 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

2 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

SPH&HS, UMASS Amherst 3 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 Amherst4 Seasons Study UMASS Worc

SPH&HS, UMASS Amherst5 Seasons Study UMASS Worc

SPH&HS, UMASS Amherst6 The Problem-Simplified 1 Measure of Sat. Fat on each Subject 1 Measure of Sat. Fat on each Subject Assume Response Error Variance known Assume Response Error Variance known How do we estimate Subject’s True Sat Fat intake? How do we estimate Subject’s True Sat Fat intake? DaisyLilyRose

SPH&HS, UMASS Amherst 7 Population

SPH&HS, UMASS Amherst 8 PopulationSet

SPH&HS, UMASS Amherst 9 11 Response 4

SPH&HS, UMASS Amherst Response 0

SPH&HS, UMASS Amherst 11 9 Response 4

SPH&HS, UMASS Amherst Response 4

SPH&HS, UMASS Amherst 13 9 Response 4

SPH&HS, UMASS Amherst Response 0

SPH&HS, UMASS Amherst Response 0 4

SPH&HS, UMASS Amherst16 Response Error Model

SPH&HS, UMASS Amherst17 Response Error Model Latent Value

SPH&HS, UMASS Amherst18 Mean Latent Value: Response Error Model

SPH&HS, UMASS Amherst19 Response Error Model

SPH&HS, UMASS Amherst20 Response Error Model

SPH&HS, UMASS Amherst Response Error Model -2

SPH&HS, UMASS Amherst22 Sample Space Response Error Model Response Error Model

SPH&HS, UMASS Amherst23 Response Error Model

SPH&HS, UMASS Amherst24 Mixed Model (MM) Random Effect

SPH&HS, UMASS Amherst25 Mixed Model (MM)

SPH&HS, UMASS Amherst26 Mixed Model (MM)

SPH&HS, UMASS Amherst27 Mixed Model (MM) Who Are They? ??

SPH&HS, UMASS Amherst28 Mixed Model (MM) What Does it Mean? ?? ??

SPH&HS, UMASS Amherst29 Sample Space (MM) Real Artificial

SPH&HS, UMASS Amherst30 MM Latent Values? Daisy (j=1) Rose (j=2) Samples

SPH&HS, UMASS Amherst31 BLUPs of the MM-Latent Value

SPH&HS, UMASS Amherst32 MSE of BLUPs for MM Latent Values? Daisy (j=1) Rose (j=2) MSEMSE Samples Ave=0.986Ave=3.768

SPH&HS, UMASS Amherst33 MSE of BLUPs vs True Latent Values? Daisy (j=1) Rose (j=2) MSEMSE Samples Ave=32.06

SPH&HS, UMASS Amherst34 MSE of BLUPs vs True Latent Values? Daisy (j=1) Rose (j=2) MSEMSE Samples Ave=0.986 Ave=3.768

SPH&HS, UMASS Amherst 35 Population Finite Population Mixed Model (FPMM)

SPH&HS, UMASS Amherst36 Response Error Model Latent Value

SPH&HS, UMASS Amherst37 Finite Population Mixed Model (FPMM)

SPH&HS, UMASS Amherst38 Finite Population Mixed Model (FPMM)

SPH&HS, UMASS Amherst39 Finite Population Mixed Model (FPMM)

SPH&HS, UMASS Amherst40 Finite Population Mixed Model (FPMM)

SPH&HS, UMASS Amherst41 FPMM- Sample Space …

SPH&HS, UMASS Amherst42 FPMM- Sample Space …

SPH&HS, UMASS Amherst43 FPMM- Sample Space …

SPH&HS, UMASS Amherst44 FPMM- Sample Space …

SPH&HS, UMASS Amherst45 FPMM- Sample Space …

SPH&HS, UMASS Amherst46 FPMM- Sample Space …

SPH&HS, UMASS Amherst47 FPMM- Sample Space All sample points are Potentially Observable

SPH&HS, UMASS Amherst48 FPMM- BLUPs of Realized Latent Values

SPH&HS, UMASS Amherst49 FPMM- BLUPs of Realized Latent Values

SPH&HS, UMASS Amherst50 FPMM- BLUPs of Realized Latent Values

SPH&HS, UMASS Amherst51 FPMM- BLUPs of Realized Latent Values Sample Sequence

SPH&HS, UMASS Amherst52 Comparison of MM-BLUP and FPMM-BLUP MM-BLUPFPMM-BLUP Target Random Variable MM-Latent Value Latent Value

SPH&HS, UMASS Amherst53 Comparison of MM-BLUP and FPMM-BLUP MM-BLUPFPMM-BLUP Predictor

SPH&HS, UMASS Amherst54 Comparison of FPMM-BLUP and MM-BLUP-Sample Space Artificial

SPH&HS, UMASS Amherst55 To Compare, Focus on …THIS Sample Space

SPH&HS, UMASS Amherst56 Sample Space (MM) Real Artificial

SPH&HS, UMASS Amherst57 Sample Space (MM) Real Artificial

SPH&HS, UMASS Amherst58 MSE of BLUPs vs True Latent Values? Daisy (j=1) Rose (j=2) MSEMSE Samples Ave=32.06

SPH&HS, UMASS Amherst59 Mixed Model (MM)

SPH&HS, UMASS Amherst60 BLUPs of the MM-Latent Value

SPH&HS, UMASS Amherst61 Finite Population Mixed Model (FPMM)

SPH&HS, UMASS Amherst62 FPMM- Sample Space …

SPH&HS, UMASS Amherst63 FPMM- Sample Space …

SPH&HS, UMASS Amherst64 FPMM- Sample Space …

SPH&HS, UMASS Amherst65 FPMM- Sample Space …

SPH&HS, UMASS Amherst66 FPMM- Sample Space …

SPH&HS, UMASS Amherst67

SPH&HS, UMASS Amherst68 Finite Population Mixed Model (FPMM)

SPH&HS, UMASS Amherst69

SPH&HS, UMASS Amherst70 Sample Space Response Error Model Response Error Model

SPH&HS, UMASS Amherst71 Sample Space Response Error Model Response Error Model

SPH&HS, UMASS Amherst72 Response Error Model