Random effects and nested models with SAS

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1 Random effects and nested models with SAS /************* classical2.sas ********************* Three levels of factor A, four levels of B Both fixed Both random A fixed, B random B nested within A ***************************************************/ options linesize = 79 pagesize=100 noovp formdlim='-'; data mixedup; infile 'mixedup.data'; input ID Y A B; proc glm; title 'Default proc glm: Both Fixed'; model y = a b; means a*b; proc glm; title 'Both Random with proc glm'; model y = a b; random a b a*b / test ; /* Have to specify interaction random too, and explicitly ask for tests */ proc glm; title 'A Fixed, B Random'; model y = a b; random b a*b / test; proc glm; title 'A fixed, B random and nested within A'; model y = a b(a); random b(a) / test; proc mixed cl; title 'A fixed, B random and nested within A'; title2 'Using proc mixed'; model y = a ; random b(a); proc glm; title 'Both random, B nested within A'; model y = a b(a); random a b(a) / test; proc sort; by A B; /* Data must be sorted in order of nesting*/ proc nested; title 'Nested random effects with proc nested'; class A B; var Y; proc mixed cl; title 'Pure nested with proc mixed'; model y = ; random a b(a); Page 1 of 11

2 Default proc glm: Both Fixed 1 Default proc glm: Both Fixed 2 Sum of Source DF Squares Mean Square F Value Pr > F Model <.0001 Error Corrected Total R-Square Coeff Var Root MSE Y Mean Source DF Type I SS Mean Square F Value Pr > F Page 2 of 11

3 Both Random with proc glm 4 Both Random with proc glm 5 Sum of Source DF Squares Mean Square F Value Pr > F Model <.0001 Error Corrected Total R-Square Coeff Var Root MSE Y Mean Source DF Type I SS Mean Square F Value Pr > F Source A B A*B Type III Expected Mean Square Var(Error) + 3 Var(A*B) + 12 Var(A) Var(Error) + 3 Var(A*B) + 9 Var(B) Var(Error) + 3 Var(A*B) Page 3 of 11

4 Both Random with proc glm 7 Tests of Hypotheses for Random Model Analysis of Variance A B Error: MS(A*B) A*B Error: MS(Error) A Fixed, B Random 8 A Fixed, B Random 9 Sum of Source DF Squares Mean Square F Value Pr > F Model <.0001 Error Corrected Total R-Square Coeff Var Root MSE Y Mean Page 4 of 11

5 Source DF Type I SS Mean Square F Value Pr > F A Fixed, B Random 10 Source A B A*B Type III Expected Mean Square Var(Error) + 3 Var(A*B) + Q(A) Var(Error) + 3 Var(A*B) + 9 Var(B) Var(Error) + 3 Var(A*B) A Fixed, B Random 11 Tests of Hypotheses for Mixed Model Analysis of Variance A B Error: MS(A*B) A*B Error: MS(Error) Page 5 of 11

6 A fixed, B random and nested within A 12 A fixed, B random and nested within A 13 Sum of Source DF Squares Mean Square F Value Pr > F Model <.0001 Error Corrected Total R-Square Coeff Var Root MSE Y Mean Source DF Type I SS Mean Square F Value Pr > F B(A) B(A) A fixed, B random and nested within A 14 Source A B(A) Type III Expected Mean Square Var(Error) + 3 Var(B(A)) + Q(A) Var(Error) + 3 Var(B(A)) Page 6 of 11

7 A fixed, B random and nested within A 15 Tests of Hypotheses for Mixed Model Analysis of Variance A Error: MS(B(A)) B(A) Error: MS(Error) A fixed, B random and nested within A 16 Using proc mixed The Mixed Procedure Model Information Data Set Dependent Variable Covariance Structure Estimation Method Residual Variance Method Fixed Effects SE Method Degrees of Freedom Method WORK.MIXEDUP Y Variance Components REML Profile Model-Based Containment Dimensions Covariance Parameters 2 Columns in X 4 Columns in Z 12 Subjects 1 Max Obs Per Subject 36 Number of Observations Number of Observations Not Used 0 Page 7 of 11

8 Iteration History Iteration Evaluations -2 Res Log Like Criterion Convergence criteria met. Covariance Parameter Estimates Cov Parm Estimate Alpha Lower Upper B(A) Residual Fit Statistics -2 Res Log Likelihood AIC (smaller is better) AICC (smaller is better) BIC (smaller is better) Type 3 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F A Page 8 of 11

9 Both random, B nested within A 17 Both random, B nested within A 18 Sum of Source DF Squares Mean Square F Value Pr > F Model <.0001 Error Corrected Total R-Square Coeff Var Root MSE Y Mean Source DF Type I SS Mean Square F Value Pr > F B(A) B(A) Both random, B nested within A 19 Source A B(A) Type III Expected Mean Square Var(Error) + 3 Var(B(A)) + 12 Var(A) Var(Error) + 3 Var(B(A)) Page 9 of 11

10 Both random, B nested within A 20 Tests of Hypotheses for Random Model Analysis of Variance A Error: MS(B(A)) B(A) Error: MS(Error) Nested random effects with proc nested 21 The NESTED Procedure Coefficients of Expected Mean Squares Source A B Error A B Error Nested Random Effects Analysis of Variance for Variable Y Variance Sum of Error Source DF Squares F Value Pr > F Term Total A B B Error Error Nested Random Effects Analysis of Variance for Variable Y Variance Variance Percent Source Mean Square Component of Total Total A B Error Y Mean Standard Error of Y Mean Page 10 of 11

11 Pure nested with proc mixed 22 The Mixed Procedure Model Information Data Set Dependent Variable Covariance Structure Estimation Method Residual Variance Method Fixed Effects SE Method Degrees of Freedom Method WORK.MIXEDUP Y Variance Components REML Profile Model-Based Containment Dimensions Covariance Parameters 3 Columns in X 1 Columns in Z 15 Subjects 1 Max Obs Per Subject 36 Number of Observations Number of Observations Not Used 0 Iteration History Iteration Evaluations -2 Res Log Like Criterion Convergence criteria met. Covariance Parameter Estimates Cov Parm Estimate Alpha Lower Upper A B(A) Residual Page 11 of 11

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