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

Matrix Approach with no constraints (g=3)

Applying Constraint 1 – Part 1

Applying Constraint 1 – Part 2

Applying Constraint 1 – Part 3

Applying Constraint 1 – Part 4

Applying Constraint 2 – Part 1

Applying Constraint 2 – Part 2

Applying Constraint 2 – Part 3

Applying Constraint 2 – Part 4

Applying Constraint 3 – Part 1

Applying Constraint 3 – Part 2

Applying Constraint 3 – Part 3

Applying Constraint 4

S U M A R Y

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

Uniqueness of Estimates of Estimable Functions

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

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

Parameter Estimates – Constraint 1

Parameter Estimates – Constraint 2

Parameter Estimates – Constraint 3

Parameter Estimates – Constraint 4