[R] Crossed factorial design with 2 random factors

[Hans Ole Ørka]

Hello, I have a balanced factorial crossed design with 2 random factors; boars and farms, the response are number of piglets (2 replicates). In Minitab I analyze the experiment with ANOVA->GLM where both factors and the interaction are included. In addition I get the expexded mean squares and the variance components printed out (For Minitab output see bellow).

I have not yet figured out how to get the same results from R. I have tried both aov and lme, but I can figure out how to reproduce the result output from Minitab in a right manner. All help are appreciated. The data is:

#Data for R
Boar<-factor(c(rep(1,10),rep(2,10),rep(3,10),rep(4,10),rep(5,10),rep(6,10)))
Farm<-factor(c(rep(seq(1,5,1),12)))
Replicates<-factor(rep(c(rep(1,5),rep(2,5)),6))
Piglets<-c(8,8,6,8,7,7,6,6,8,9,8,7,7,9,9,8,8,9,8,8,8,8,9,9,11,9,
9,9,9,9,8,9,10,11,11,9,8,10,11,10,9,8,9,12,13,8,9,10,10,13,9,10,12,13,12,8,9,11,12,12)

The minitab output:

General Linear Model: Piglets versus Boar; Farm

Factor  Type    Levels  Values
Boar    random       6  1; 2; 3; 4; 5; 6
Farm    random       5  1; 2; 3; 4; 5


Analysis of Variance for Piglets, using Adjusted SS for Tests

Source     DF    Seq SS   Adj SS   Adj MS      F      P
Boar        5   84.7333  84.7333  16.9467  11.92  0.000
Farm        4   45.1667  45.1667  11.2917   7.94  0.001
Boar*Farm  20   28.4333  28.4333   1.4217   2.37  0.016
Error      30   18.0000  18.0000   0.6000
Total      59  176.3333


S = 0.774597   R-Sq = 89.79%   R-Sq(adj) = 79.92%


Expected Mean Squares, using Adjusted SS

   Source     Expected Mean Square for Each Term
1  Boar       (4) + 2.0000 (3) + 10.0000 (1)
2  Farm       (4) + 2.0000 (3) + 12.0000 (2)
3  Boar*Farm  (4) + 2.0000 (3)
4  Error      (4)


Error Terms for Tests, using Adjusted SS

                                  Synthesis
   Source     Error DF  Error MS  of Error MS
1  Boar          20.00    1.4217  (3)
2  Farm          20.00    1.4217  (3)
3  Boar*Farm     30.00    0.6000  (4)


Variance Components, using Adjusted SS

           Estimated
Source         Value
Boar          1.5525
Farm          0.8225
Boar*Farm     0.4108
Error         0.6000

Thanks
Hans Ole Oerka