1 / 75

Advancements in Finite Population Mixed Models: Insights from Gary Koch's Festschrift

This compilation honors Professor Gary Koch, showcasing innovative methodologies in finite population mixed models. Contributions from researchers across the globe emphasize the intersection of sampling, response error models, and mixed modeling to extract meaningful insights from limited data. Using a case study focused on measuring saturated fat intake, this work addresses fundamental questions in study design and model assumptions, offering a comprehensive overview of response error models and mixed effects modeling in practice.

flint
Download Presentation

Advancements in Finite Population Mixed Models: Insights from Gary Koch's Festschrift

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. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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- focus on 3 subjects SPH&HS, UMASS Amherst

  6. The Problem-Simplified • 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

  7. Population SPH&HS, UMASS Amherst

  8. Set Population 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 for Set SPH&HS, UMASS Amherst

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

  18. Re-parameterized RE Model Mean Latent Value: SPH&HS, UMASS Amherst

  19. Generating Response in the RE Model SPH&HS, UMASS Amherst

  20. Generating Response in the RE Model SPH&HS, UMASS Amherst

  21. Generating an Observed Response in the RE Model -1 1 -2 2 -2 -1 SPH&HS, UMASS Amherst

  22. 9 11 9 11 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) Latent Value SPH&HS, UMASS Amherst

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

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

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

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

  30. 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

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

  32. What are they (for Daisy)? Samples SPH&HS, UMASS Amherst

  33. What are they (for Rose)? Samples SPH&HS, UMASS Amherst

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

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

  36. MSE of BLUPs for True-Latent Values Samples Ave=32.06 Ave=32.06 SPH&HS, UMASS Amherst

  37. MSE of BLUPs |P=y Samples Ave=0.986 Ave=3.768 SPH&HS, UMASS Amherst

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

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

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

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

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

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

  44. 4 0 0 4 9 9 11 11 FPMM- Sample Space … SPH&HS, UMASS Amherst

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

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

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

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

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

  50. 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

More Related