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Enhancing Model Insights Through Sampling: A Festschrift for Professors Koch and Singer

This publication celebrates the contributions of Professors Gary Koch and Julio Singer, focusing on advanced sampling methods, response error models, and mixed models within the context of finite populations. It explores the design of studies aimed at understanding complex dietary assessments, particularly saturated fat intake. Contributions by international researchers highlight various model assumptions, improving insights into data limitations and enhancing our understanding of latent values. This work serves as a critical resource for statisticians and epidemiologists in the field.

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Enhancing Model Insights Through Sampling: A Festschrift for Professors Koch and Singer

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  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 SPH&HS, UMASS Amherst

  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. 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

  4. Seasons Study UMASS Worc SPH&HS, UMASS Amherst

  5. Seasons Study UMASS Worc SPH&HS, UMASS Amherst

  6. 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 SPH&HS, UMASS Amherst

  7. Population SPH&HS, UMASS Amherst

  8. Population Set SPH&HS, UMASS Amherst

  9. Response 4 11 SPH&HS, UMASS Amherst

  10. Response 0 11 SPH&HS, UMASS Amherst

  11. Response 4 9 SPH&HS, UMASS Amherst

  12. Response 4 11 SPH&HS, UMASS Amherst

  13. Response 4 9 SPH&HS, UMASS Amherst

  14. Response 0 11 SPH&HS, UMASS Amherst

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

  16. Response Error Model SPH&HS, UMASS Amherst

  17. Response Error Model Latent Value SPH&HS, UMASS Amherst

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

  19. Response Error Model SPH&HS, UMASS Amherst

  20. Response Error Model SPH&HS, UMASS Amherst

  21. Response Error Model -1 1 -2 2 -2 -1 SPH&HS, UMASS Amherst

  22. 11 9 9 11 11 9 11 9 0 4 4 0 4 4 0 0 Sample Space • Response Error Model SPH&HS, UMASS Amherst

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

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

  25. Mixed Model (MM) SPH&HS, UMASS Amherst

  26. Mixed Model (MM) SPH&HS, UMASS Amherst

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

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

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

  30. MM Latent Values? Samples SPH&HS, UMASS Amherst

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

  32. MSE of BLUPs for MM Latent Values? Samples Ave=0.986 Ave=3.768 SPH&HS, UMASS Amherst

  33. MSE of BLUPs vs True Latent Values? Samples Ave=32.06 Ave=32.06 SPH&HS, UMASS Amherst

  34. MSE of BLUPs vs True Latent Values? Samples Ave=0.986 Ave=3.768 SPH&HS, UMASS Amherst

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

  36. Response Error Model Latent Value SPH&HS, UMASS Amherst

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

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

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

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

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

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

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

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

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

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

  47. 11 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

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

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

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

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