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Quantitative Methods

Quantitative Methods. Checking the models II: the other three assumptions. TREATMNT Coef 1  1 BACAFTER = m + b  BACBEF + 2  2 + 

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Quantitative Methods

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  1. Quantitative Methods Checking the models II: the other three assumptions

  2. TREATMNT Coef 1 1 BACAFTER = m + bBACBEF + 2 2 +  3 -1 -2 TREATMNT Coef PREDICTED 1 -1.590 BACAFTER = -0.013 + 0.8831BACBEF + 2 -0.726 32.316 Checking the models II: the other 3 assumptions Assumptions of GLM BACAFTER = BACBEF+TREATMNT (Model Formula) (Model) (Fitted Value Equation or Best Fit Equation)

  3. TREATMNT Coef 1 1 BACAFTER = m + bBACBEF + 2 2 +  3 -1 -2 Checking the models II: the other 3 assumptions Assumptions of GLM (Model)

  4. TREATMNT Coef 1 1 BACAFTER = m + bBACBEF + 2 2 +  3 -1 -2 Checking the models II: the other 3 assumptions Assumptions of GLM (Model) Assumptions of GLM Independence Homogeneity of variance Normality of error Linearity/additivity

  5. TREATMNT Coef 1 1 BACAFTER = m + bBACBEF + 2 2 +  3 -1 -2 Checking the models II: the other 3 assumptions Assumptions of GLM (Model) Assumptions of GLM Independence Homogeneity of variance Normality of error Linearity/additivity

  6. TREATMNT Coef 1 1 BACAFTER = m + bBACBEF + 2 2 +  3 -1 -2 Checking the models II: the other 3 assumptions Assumptions of GLM (Model) Assumptions of GLM Independence Homogeneity of variance Normality of error Linearity/additivity

  7. TREATMNT Coef 1 1 BACAFTER = m + bBACBEF + 2 2 +  3 -1 -2 Checking the models II: the other 3 assumptions Assumptions of GLM (Model) Assumptions of GLM Independence Homogeneity of variance Normality of error Linearity/additivity

  8. TREATMNT Coef 1 1 BACAFTER = m + bBACBEF + 2 2 +  3 -1 -2 Checking the models II: the other 3 assumptions Assumptions of GLM (Model) Assumptions of GLM Independence Homogeneity of variance Normality of error Linearity/additivity

  9. TREATMNT Coef 1 1 BACAFTER = m + bBACBEF + 2 2 +  3 -1 -2 Checking the models II: the other 3 assumptions Assumptions of GLM (Model) Assumptions of GLM Independence Homogeneity of variance Normality of error Linearity/additivity

  10. TREATMNT Coef 1 1 BACAFTER = m + bBACBEF + 2 2 +  3 -1 -2 Checking the models II: the other 3 assumptions Assumptions of GLM (Model) Assumptions of GLM Independence Homogeneity of variance Normality of error Linearity/additivity

  11. TREATMNT Coef 1 1 BACAFTER = m + bBACBEF + 2 2 +  3 -1 -2 Checking the models II: the other 3 assumptions Assumptions of GLM (Model) Assumptions of GLM Independence Homogeneity of variance Normality of error Linearity/additivity

  12. TREATMNT Coef 1 1 BACAFTER = m + bBACBEF + 2 2 +  3 -1 -2 Checking the models II: the other 3 assumptions Assumptions of GLM (Model) Assumptions of GLM Independence Homogeneity of variance Normality of error Linearity/additivity

  13. Checking the models II: the other 3 assumptions Are the assumptions likely to be true? Assumptions of GLM Independence Homogeneity of variance Normality of error Linearity/additivity

  14. Checking the models II: the other 3 assumptions Model Criticism

  15. Checking the models II: the other 3 assumptions Model Criticism

  16. Checking the models II: the other 3 assumptions Model Criticism

  17. Checking the models II: the other 3 assumptions Transformations and Homogeneity

  18. Checking the models II: the other 3 assumptions Transformations and Homogeneity

  19. Checking the models II: the other 3 assumptions Transformations and Homogeneity

  20. Checking the models II: the other 3 assumptions Transformations and Homogeneity

  21. Checking the models II: the other 3 assumptions Transformations and Homogeneity

  22. Checking the models II: the other 3 assumptions Transformations and Homogeneity

  23. Checking the models II: the other 3 assumptions Transformations and Homogeneity

  24. Checking the models II: the other 3 assumptions Transformations and Homogeneity None, or linear Square root Log Negative inverse

  25. Checking the models II: the other 3 assumptions Non-linearity

  26. Checking the models II: the other 3 assumptions Non-linearity

  27. Checking the models II: the other 3 assumptions Non-linearity

  28. Checking the models II: the other 3 assumptions Non-linearity

  29. Checking the models II: the other 3 assumptions Example

  30. Checking the models II: the other 3 assumptions Example

  31. Checking the models II: the other 3 assumptions Example

  32. Checking the models II: the other 3 assumptions Example MTB > let LOGDEN=log(DENSITY)

  33. Checking the models II: the other 3 assumptions Hints

  34. Checking the models II: the other 3 assumptions Hints Don’t be too picky Morphometric data: log Count data: square root Proportional data: angular Survival data: negative inverse

  35. Continuous y-variable - varying strengths Increasing strength: none, square root, log, negative inverse Proportions - root arcsin Counts - square root Based on homogenising the error variance Checking the models II: the other 3 assumptions Selecting a transformation With covariates, consider transforming X too Go through the model criticism process again (and if necessary again and again)

  36. Checking the models II: the other 3 assumptions Last words… • You should always check assumptions as much as you can using the techniques of model criticism • Transformations can help to ‘cure’ failures to meet assumptions • Always repeat model criticism after transforming • Homogeneity of variance is the priority for transformations Model selection I: principles of model choice and designed experiments Read Chapter 10

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