Hw2sol - Stat 511 Homework 2 Solution(pts:20 Spring 2011 In the solution notice that you do have different choices of A and doesn’t affect the

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Unformatted text preview: Stat 511 Homework 2 Solution (pts:20) Spring 2011 In the solution, notice that you do have different choices of A and doesn’t affect the estimation. 1. Consider a factor effects model for a study with a balanced two-way factorial treatment design: Y ijk = μ + α i + β j + αβ ij + ijk , for i = 1 , 2, j = 1 , 2 , 3, and k = 1 , 2. The “LSMEANS” for the two row means are μ + α 1 + ( β 1 + β 2 + β 3 ) / 3 + ( αβ 11 + αβ 12 + αβ 13 ) / 3 and μ + α 2 + ( β 1 + β 2 + β 3 ) / 3 + ( αβ 21 + αβ 22 + αβ 23 ) / 3. The X matrix is: 1 1 0 1 0 0 1 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0 1 1 0 0 1 0 0 1 0 0 0 0 1 1 0 0 1 0 0 1 0 0 0 0 1 1 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 1 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 1 0 1 0 0 1 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0 1 Are the two LSMEANS estimable? If so, give vectors A (one for each LSMEANS) that demonstrate that each is estimable. Yes, they are estimable because they are linear function of E Y ijk . One set of possible A ’s are A 1 = (1 / 6 , 1 / 6 , 1 / 6 , 1 / 6 , 1 / 6 , 1 / 6 , , , , , , 0) A 2 = (0 , , , , , , 1 / 6 , 1 / 6 , 1 / 6 , 1 / 6 , 1 / 6 , 1 / 6) 2. I recently had to deal with a “two-way” factorial study where factor A was State: Iowa or Missouri, and factor B was a type of stream: Grazed, Buffered, or Grazed and Buffered. As it happened, the investigators could find all three types of streams in Iowa, but only two types...
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This note was uploaded on 02/11/2012 for the course STAT 511 taught by Professor Staff during the Spring '08 term at Iowa State.

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Hw2sol - Stat 511 Homework 2 Solution(pts:20 Spring 2011 In the solution notice that you do have different choices of A and doesn’t affect the

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