Exam2.B.5.RdExam2.B.5 is related to multi batch regression data assuming different forms of linear models.
Stroup, W. W. (2012). Generalized Linear Mixed Models: Modern Concepts, Methods and Applications. CRC Press.
#----------------------------------------------------------------------------------- ## Nested Model with no intercept #----------------------------------------------------------------------------------- data(Table1.2) Table1.2$Batch <- factor(x = Table1.2$Batch) Exam2.B.5.lm1 <- lm( formula = Y~0+Batch+ Batch/X , data = Table1.2 # , subset # , weights # , na.action , method = "qr" , model = TRUE # , x = FALSE # , y = FALSE , qr = TRUE , singular.ok = TRUE , contrasts = NULL # , offset # , ... ) DesignMatrix.lm1 <- model.matrix (object = Exam2.B.5.lm1) DesignMatrix.lm1#> Batch1 Batch2 Batch3 Batch4 Batch1:X Batch2:X Batch3:X Batch4:X #> 1 1 0 0 0 0 0 0 0 #> 2 1 0 0 0 3 0 0 0 #> 3 1 0 0 0 6 0 0 0 #> 4 1 0 0 0 9 0 0 0 #> 5 1 0 0 0 12 0 0 0 #> 6 1 0 0 0 18 0 0 0 #> 7 1 0 0 0 24 0 0 0 #> 8 1 0 0 0 36 0 0 0 #> 9 1 0 0 0 48 0 0 0 #> 10 0 1 0 0 0 0 0 0 #> 11 0 1 0 0 0 3 0 0 #> 12 0 1 0 0 0 6 0 0 #> 13 0 1 0 0 0 9 0 0 #> 14 0 1 0 0 0 12 0 0 #> 15 0 1 0 0 0 18 0 0 #> 16 0 1 0 0 0 24 0 0 #> 17 0 1 0 0 0 36 0 0 #> 18 0 1 0 0 0 48 0 0 #> 19 0 0 1 0 0 0 0 0 #> 20 0 0 1 0 0 0 3 0 #> 21 0 0 1 0 0 0 6 0 #> 22 0 0 1 0 0 0 9 0 #> 23 0 0 1 0 0 0 12 0 #> 24 0 0 1 0 0 0 18 0 #> 25 0 0 1 0 0 0 24 0 #> 26 0 0 1 0 0 0 36 0 #> 27 0 0 1 0 0 0 48 0 #> 28 0 0 0 1 0 0 0 0 #> 29 0 0 0 1 0 0 0 3 #> 30 0 0 0 1 0 0 0 6 #> 31 0 0 0 1 0 0 0 9 #> 32 0 0 0 1 0 0 0 12 #> 33 0 0 0 1 0 0 0 18 #> 34 0 0 0 1 0 0 0 24 #> 35 0 0 0 1 0 0 0 36 #> 36 0 0 0 1 0 0 0 48 #> attr(,"assign") #> [1] 1 1 1 1 2 2 2 2 #> attr(,"contrasts") #> attr(,"contrasts")$Batch #> [1] "contr.treatment" #>#----------------------------------------------------------------------------------- ## Interaction Model with intercept #----------------------------------------------------------------------------------- Exam2.B.5.lm2 <- lm( formula = Y~Batch +X+ Batch*X , data = Table1.2 # , subset # , weights # , na.action , method = "qr" , model = TRUE # , x = FALSE # , y = FALSE , qr = TRUE , singular.ok = TRUE , contrasts = NULL # , offset # , ... ) DesignMatrix.lm2 <- model.matrix (object = Exam2.B.5.lm2) DesignMatrix.lm2#> (Intercept) Batch2 Batch3 Batch4 X Batch2:X Batch3:X Batch4:X #> 1 1 0 0 0 0 0 0 0 #> 2 1 0 0 0 3 0 0 0 #> 3 1 0 0 0 6 0 0 0 #> 4 1 0 0 0 9 0 0 0 #> 5 1 0 0 0 12 0 0 0 #> 6 1 0 0 0 18 0 0 0 #> 7 1 0 0 0 24 0 0 0 #> 8 1 0 0 0 36 0 0 0 #> 9 1 0 0 0 48 0 0 0 #> 10 1 1 0 0 0 0 0 0 #> 11 1 1 0 0 3 3 0 0 #> 12 1 1 0 0 6 6 0 0 #> 13 1 1 0 0 9 9 0 0 #> 14 1 1 0 0 12 12 0 0 #> 15 1 1 0 0 18 18 0 0 #> 16 1 1 0 0 24 24 0 0 #> 17 1 1 0 0 36 36 0 0 #> 18 1 1 0 0 48 48 0 0 #> 19 1 0 1 0 0 0 0 0 #> 20 1 0 1 0 3 0 3 0 #> 21 1 0 1 0 6 0 6 0 #> 22 1 0 1 0 9 0 9 0 #> 23 1 0 1 0 12 0 12 0 #> 24 1 0 1 0 18 0 18 0 #> 25 1 0 1 0 24 0 24 0 #> 26 1 0 1 0 36 0 36 0 #> 27 1 0 1 0 48 0 48 0 #> 28 1 0 0 1 0 0 0 0 #> 29 1 0 0 1 3 0 0 3 #> 30 1 0 0 1 6 0 0 6 #> 31 1 0 0 1 9 0 0 9 #> 32 1 0 0 1 12 0 0 12 #> 33 1 0 0 1 18 0 0 18 #> 34 1 0 0 1 24 0 0 24 #> 35 1 0 0 1 36 0 0 36 #> 36 1 0 0 1 48 0 0 48 #> attr(,"assign") #> [1] 0 1 1 1 2 3 3 3 #> attr(,"contrasts") #> attr(,"contrasts")$Batch #> [1] "contr.treatment" #>#----------------------------------------------------------------------------------- ## Interaction Model with no intercept #----------------------------------------------------------------------------------- Exam2.B.5.lm3 <- lm( formula = Y~0 + Batch + Batch*X , data = Table1.2 # , subset # , weights # , na.action , method = "qr" , model = TRUE # , x = FALSE # , y = FALSE , qr = TRUE , singular.ok = TRUE , contrasts = NULL # , offset # , ... ) DesignMatrix.lm3 <- model.matrix(object = Exam2.B.5.lm3) #----------------------------------------------------------------------------------- ## Interaction Model with intercept but omitting X term as main effect #----------------------------------------------------------------------------------- Exam2.B.5.lm4 <- lm( formula = Y~Batch + Batch*X , data = Table1.2 # , subset # , weights # , na.action , method = "qr" , model = TRUE # , x = FALSE # , y = FALSE , qr = TRUE , singular.ok = TRUE , contrasts = NULL # , offset # , ... ) DesignMatrix.lm4 <- model.matrix(object = Exam2.B.5.lm4) DesignMatrix.lm4#> (Intercept) Batch2 Batch3 Batch4 X Batch2:X Batch3:X Batch4:X #> 1 1 0 0 0 0 0 0 0 #> 2 1 0 0 0 3 0 0 0 #> 3 1 0 0 0 6 0 0 0 #> 4 1 0 0 0 9 0 0 0 #> 5 1 0 0 0 12 0 0 0 #> 6 1 0 0 0 18 0 0 0 #> 7 1 0 0 0 24 0 0 0 #> 8 1 0 0 0 36 0 0 0 #> 9 1 0 0 0 48 0 0 0 #> 10 1 1 0 0 0 0 0 0 #> 11 1 1 0 0 3 3 0 0 #> 12 1 1 0 0 6 6 0 0 #> 13 1 1 0 0 9 9 0 0 #> 14 1 1 0 0 12 12 0 0 #> 15 1 1 0 0 18 18 0 0 #> 16 1 1 0 0 24 24 0 0 #> 17 1 1 0 0 36 36 0 0 #> 18 1 1 0 0 48 48 0 0 #> 19 1 0 1 0 0 0 0 0 #> 20 1 0 1 0 3 0 3 0 #> 21 1 0 1 0 6 0 6 0 #> 22 1 0 1 0 9 0 9 0 #> 23 1 0 1 0 12 0 12 0 #> 24 1 0 1 0 18 0 18 0 #> 25 1 0 1 0 24 0 24 0 #> 26 1 0 1 0 36 0 36 0 #> 27 1 0 1 0 48 0 48 0 #> 28 1 0 0 1 0 0 0 0 #> 29 1 0 0 1 3 0 0 3 #> 30 1 0 0 1 6 0 0 6 #> 31 1 0 0 1 9 0 0 9 #> 32 1 0 0 1 12 0 0 12 #> 33 1 0 0 1 18 0 0 18 #> 34 1 0 0 1 24 0 0 24 #> 35 1 0 0 1 36 0 0 36 #> 36 1 0 0 1 48 0 0 48 #> attr(,"assign") #> [1] 0 1 1 1 2 3 3 3 #> attr(,"contrasts") #> attr(,"contrasts")$Batch #> [1] "contr.treatment" #>