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Matrix Approach to 1-Way ANOVA

Matrix Approach to 1-Way ANOVA. Comparison of Sexual Side Effects in 4 Antidepressants JG Modell, et al (1997). "Comparative Sexual Side Effects of Bupropion, Fluoxetine, Paroxetine, and Sertraline ", Clinical Pharmacology and Therapeutics, Vol.61(4),pp476-487. Model.

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Matrix Approach to 1-Way ANOVA

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  1. Matrix Approach to 1-Way ANOVA Comparison of Sexual Side Effects in 4 Antidepressants JG Modell, et al (1997). "Comparative Sexual Side Effects of Bupropion, Fluoxetine, Paroxetine, and Sertraline ", Clinical Pharmacology and Therapeutics, Vol.61(4),pp476-487.

  2. Model

  3. Matrix Approach with no constraints (g=3)

  4. Applying Constraint 1 – Part 1

  5. Applying Constraint 1 – Part 2

  6. Applying Constraint 1 – Part 3

  7. Applying Constraint 1 – Part 4

  8. Applying Constraint 2 – Part 1

  9. Applying Constraint 2 – Part 2

  10. Applying Constraint 2 – Part 3

  11. Applying Constraint 2 – Part 4

  12. Applying Constraint 3 – Part 1

  13. Applying Constraint 3 – Part 2

  14. Applying Constraint 3 – Part 3

  15. Applying Constraint 4

  16. S U M M A R Y

  17. Estimable Functions • A linear function of the parameter vector b, h’b is said to be estimable if h’=t’X. That is, if h’ can be written as a linear function of the rows of X

  18. Uniqueness of Estimates of Estimable Functions

  19. Application: Comparison of g=4 Antidepressants • Response: Y = Change in libido scores for patients on antidepressants • Treatments: g=4 Brands of antidepressants • Prozac (n1 = 37) • Paxil (n2 = 21) • Zoloft (n3 = 27) • Wellbutrin (n4 = 22) • N=107, g=4, Prozac, Paxil, Zoloft are SSRI’s, Wellbutrin not • Will make generalizations of case g=3

  20. Data and Analysis of Variance H0 : Brand Means are all equal Conclude brand means are not all equal Note: s2 = MSE = 0.96

  21. Parameter Estimates – Constraint 1

  22. Parameter Estimates – Constraint 2

  23. Parameter Estimates – Constraint 3

  24. Parameter Estimates – Constraint 4

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