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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 on theme: "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."— Presentation transcript:

1 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 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

3 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?

4 SPH&HS, UMASS Amherst4 Seasons Study UMASS Worc

5 SPH&HS, UMASS Amherst5 Seasons Study UMASS Worc

6 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

7 SPH&HS, UMASS Amherst 7 Population

8 SPH&HS, UMASS Amherst 8 PopulationSet

9 SPH&HS, UMASS Amherst 9 11 Response 4

10 SPH&HS, UMASS Amherst 10 11 Response 0

11 SPH&HS, UMASS Amherst 11 9 Response 4

12 SPH&HS, UMASS Amherst 12 11 Response 4

13 SPH&HS, UMASS Amherst 13 9 Response 4

14 SPH&HS, UMASS Amherst 14 11 Response 0

15 SPH&HS, UMASS Amherst 15 11 Response 0 4

16 SPH&HS, UMASS Amherst16 Response Error Model 12911 0.50.5 1204 0.50.5

17 SPH&HS, UMASS Amherst17 Response Error Model Latent Value

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

19 SPH&HS, UMASS Amherst19 Response Error Model

20 SPH&HS, UMASS Amherst20 Response Error Model

21 SPH&HS, UMASS Amherst21 1 -22 Response Error Model -2

22 SPH&HS, UMASS Amherst22 Sample Space Response Error Model Response Error Model 9 4 11 4 9 0 0 9 4 4 9 0 0

23 SPH&HS, UMASS Amherst23 Response Error Model 9 4 11 4 9 0 0

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

25 SPH&HS, UMASS Amherst25 Mixed Model (MM)

26 SPH&HS, UMASS Amherst26 Mixed Model (MM)

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

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

29 SPH&HS, UMASS Amherst29 Sample Space (MM) 3 12 9 4 11 4 9 0 0 1 8 3 8 1 12 Real Artificial

30 SPH&HS, UMASS Amherst30 MM Latent Values? Daisy (j=1) Rose (j=2) 11101422 910422 1110102-2 91002-2 32112102 1212102 321810-2 12810-2 Samples

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

32 SPH&HS, UMASS Amherst32 MSE of BLUPs for MM Latent Values? Daisy (j=1) Rose (j=2) MSEMSE 10.90100.814.4125.79 8.93101.154.2925.24 10.84100.710.6421.86 8.87101.280.5222.19 3.1321.2811.48102.19 1.1620.7111.36101.86 3.0721.157.71105.24 1.1020.817.59105.79 Samples Ave=0.986Ave=3.768

33 SPH&HS, UMASS Amherst33 MSE of BLUPs vs True Latent Values? Daisy (j=1) Rose (j=2) MSEMSE 10.90100.814.4125.79 8.93101.154.2925.24 10.84100.710.6421.86 8.87101.280.5222.19 3.131047.1911.481089.84 1.161078.1611.361087.65 3.071047.997.711032.61 1.101079.187.591031.30 Samples Ave=32.06

34 SPH&HS, UMASS Amherst34 MSE of BLUPs vs True Latent Values? Daisy (j=1) Rose (j=2) MSEMSE 10.90100.814.4125.79 8.93101.154.2925.24 10.84100.710.6421.86 8.87101.280.5222.19 Samples Ave=0.986 Ave=3.768

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

36 SPH&HS, UMASS Amherst36 Response Error Model Latent Value

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

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

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

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

41 SPH&HS, UMASS Amherst41 FPMM- Sample Space … 9 4 11 4 9 0 0

42 SPH&HS, UMASS Amherst42 FPMM- Sample Space … 0 11 4 0 9 4 9

43 SPH&HS, UMASS Amherst43 FPMM- Sample Space … -7 4 13 4 -7 0 13 0

44 SPH&HS, UMASS Amherst44 FPMM- Sample Space … 0 13 4 0 -7 4

45 SPH&HS, UMASS Amherst45 FPMM- Sample Space … -7 11 13 11 -7 9 13 9

46 SPH&HS, UMASS Amherst46 FPMM- Sample Space … 9 13 11 13 9 -7 11 -7

47 SPH&HS, UMASS Amherst47 FPMM- Sample Space 11 13 11 13 9 -7 11 -7 11 13 11 -7 9 13 9 9 4 11 4 9 0 0 0 4 0 9 4 9 0 13 4 0 -7 4 4 13 4 -7 0 13 0 All sample points are Potentially Observable

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

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

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

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

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

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

54 SPH&HS, UMASS Amherst54 Comparison of FPMM-BLUP and MM-BLUP-Sample Space 11 13 11 13 9 -7 11 -7 11 13 11 -7 9 13 9 0 11 4 0 9 4 9 0 13 4 0 -7 4 4 13 4 -7 0 13 0 9 4 11 4 9 0 0 1 12 3 1 8 3 8 Artificial

55 SPH&HS, UMASS Amherst55 To Compare, Focus on …THIS Sample Space 11 13 11 13 9 -7 11 -7 11 13 11 -7 9 13 9 0 11 4 0 9 4 9 0 13 4 0 -7 4 4 13 4 -7 0 13 0 9 4 11 4 9 0 0 1 12 3 1 8 3 8

56 SPH&HS, UMASS Amherst56 Sample Space (MM) 3 12 9 4 11 4 9 0 0 1 8 3 8 1 12 Real Artificial

57 SPH&HS, UMASS Amherst57 Sample Space (MM) 1 12 3 1 8 3 8 Real Artificial 9 4 11 4 9 0 0

58 SPH&HS, UMASS Amherst58 MSE of BLUPs vs True Latent Values? Daisy (j=1) Rose (j=2) MSEMSE 10.90100.814.4125.79 8.93101.154.2925.24 10.84100.710.6421.86 8.87101.280.5222.19 3.131047.1911.481089.84 1.161078.1611.361087.65 3.071047.997.711032.61 1.101079.187.591031.30 Samples Ave=32.06

59 SPH&HS, UMASS Amherst59 Mixed Model (MM)

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

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

62 SPH&HS, UMASS Amherst62 FPMM- Sample Space … -7 4 13 4 -7 0 13 0

63 SPH&HS, UMASS Amherst63 FPMM- Sample Space … 0 13 4 0 -7 4

64 SPH&HS, UMASS Amherst64 FPMM- Sample Space … 0 11 4 0 9 4 9

65 SPH&HS, UMASS Amherst65 FPMM- Sample Space … 9 4 11 4 9 0 0

66 SPH&HS, UMASS Amherst66 FPMM- Sample Space … -7 11 13 11 -7 9 13 9

67 SPH&HS, UMASS Amherst67

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

69 SPH&HS, UMASS Amherst69

70 SPH&HS, UMASS Amherst70 Sample Space Response Error Model Response Error Model 4 911 0

71 SPH&HS, UMASS Amherst71 Sample Space Response Error Model Response Error Model 4 911 0

72 SPH&HS, UMASS Amherst72 Response Error Model

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