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Statistical Modeling

Statistical Modeling. Matthew Dirk Wiers. Purpose.

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Statistical Modeling

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  1. Statistical Modeling Matthew Dirk Wiers

  2. Purpose Statistical modeling is a mathematical technique used to verify and quantify associations between one or more quantitative and/or qualitative predictor variables (x1, x2, …), and a single quantitative or qualitative response variable (y), or multiple multivariate normal response variables (y1, y2, …). E.g., the association between income (x1), whether or not someone at home cooks (x2), and the number of dinners in the last k eaten outside the home (y).

  3. Components • Probability Model: f (y, θ) Discrete: Bernoulli, Binomial, Poisson, Multinomial Continuous: Normal, Weibull, Multivariate Normal • Linear Model:β0 + β1x1i + β2x2i + … • Link:θi= g (β0 + β1x1i + β2x2i + …)

  4. Components • Maximum Likelihood Estimation: • Likelihood Ratio Tests:

  5. Probability Models Suppose there is a 6 week experiment with 15 animals in treatment group A and 15 animals in treatment group B. Consider the following measurements on each animal: • Whether or not there were malignant tumors. • The number of tumors that were malignant. • The number of tumors. • The average size of the tumors. • The time to the first tumor. • The number of tumors that were malignant, benign, or other. • The average size and average weight of the tumors. The corresponding probability models are Bernoulli, Binomial, Poisson, Normal, Weibull, Multinomial, and Multivariate Normal.

  6. Statistical Modeling • Bernoulli Modeling • Binomial Modeling • Binomial Probit Modeling • Binomial C-Log-Log Modeling • Poisson Modeling • Poisson Rate Modeling • Multinomial Modeling • Multinomial Ordinal Modeling

  7. Statistical Modeling • Normal Modeling • Weibull Modeling • Weibull Censor Modeling • Multivariate Normal Modeling • Multivariate Normal RM Modeling

  8. Bernoulli Modeling • Probability Model:

  9. Bernoulli Modeling • Link:

  10. Bernoulli Modeling • NLL:

  11. Bernoulli Modeling

  12. Bernoulli Modeling

  13. Bernoulli Modeling

  14. Bernoulli Modeling

  15. Bernoulli Modeling

  16. Binomial Modeling • Probability Model:

  17. Binomial Modeling • Link:

  18. Binomial Modeling • NLL:

  19. Binomial Modeling

  20. Binomial Modeling

  21. Binomial Modeling

  22. Binomial Modeling

  23. Binomial Probit Modeling • Link: • NLL:

  24. Binomial Probit Modeling

  25. Binomial Probit Modeling

  26. Binomial Probit Modeling

  27. Binomial C-Log-Log Modeling • Link: • NLL:

  28. Binomial C-Log-Log Modeling

  29. Binomial C-Log-Log Modeling

  30. Binomial C-Log-Log Modeling

  31. Poisson Modeling • Probability Model:

  32. Poisson Modeling • Link: • NLL:

  33. Poisson Modeling

  34. Poisson Modeling

  35. Poisson Modeling

  36. Poisson Modeling

  37. Poisson Modeling

  38. Poisson Modeling

  39. Poisson Modeling

  40. Poisson Modeling

  41. Poisson Modeling

  42. Poisson Rate Modeling • Link: • NLL:

  43. Poisson Rate Modeling

  44. Poisson Rate Modeling

  45. Poisson Rate Modeling

  46. Poisson Rate Modeling

  47. Poisson Rate Modeling

  48. Poisson Rate Modeling

  49. Poisson Rate Modeling

  50. Poisson Rate Modeling

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