1. Solution Copy files from f:\edwin\solution

2.  21  11  22 1  2 BMD  1 exercise 1 y 3 Hip  11  22  33  44  55 1 42 52 y 5 Arm y 4 Spine y 2 Duration y 1 Intensity

4.  21  11  22 1  2 BMD  1 exercise  j or  y j 1 y 3 Hip  11  22  33  44  55  42 52 y 5 Arm y 4 Spine y 2 Duration y 1 Intensity Genetic + Stratification effects  k or  y k

5. 0 0 0 0 0  2(1)  2(2)  2(3)  2(4)  2(5)  j =,  k =    2(1)  2(2) Common pathway model

6.  0 0 0 3(1) 3(2) 4(1) 4(2) 5(1) 5(2)  0 0 0 3(1) 3(2) 4(1) 4(2) 5(1) 5(2)  0 0 0 3(3) 3(4) 4(3) 4(4) 5(3) 5(4)  0 3(5) 4(5) 5(5)  j =,  k = Independent pathway

7. Common pathway model Model fitDifference test -2ll# parameters 22 df.p. Full 14481.329 37 No genetic 14486.732 355.40320.067 No admixture 14483.339 322.0095 No genetic + no admixture 14489.726 30 Vs Full8.39770.299 Vs no admixture 6.38820.041

8. Independent pathway Model fitDifference test -2ll# parameters 22 df.p. Full 14468.534 51 No genetic 14477.966 459.43160.151 No admixture 14481.836 3613.30150.579 No genetic + no admixture 14489.726 30 Vs Full21.19210.447 Vs no admixture 7.8960.246 Independent pathway

9. Difference test 22 df.p. Full 12.795140.543 No admixture 1.50340.826 Common versus independent