# Example 8.3 from Generalized Linear Mixed Models: Modern Concepts, Methods and Applications by Walter W. Stroup (p-255) Exam8.3 explains Response surface design with incomplete blocking ## Examples ```r ## Response Surface Design with incomplete blocking (page 255) data(DataSet8.3) DataSet8.3$block <- factor(x = DataSet8.3$block) DataSet8.3$aa <- factor(x = DataSet8.3$a) DataSet8.3$bb <- factor(x = DataSet8.3$b) DataSet8.3$cc <- factor(x = DataSet8.3$c) library(lmerTest) library(lattice) Exam8.3.fm1 <- lmer( y ~ aa:bb:cc + a + b + c + I(a^2) + I(b^2) + I(c^2) + a*b + a*c + b*c + (1|block) , data = DataSet8.3 ) ##--- page 256 anova(Exam8.3.fm1, ddf = "Kenward-Roger", type = 1) Exam8.3.fm2 <- lmer( y ~ a + b + c + I(a^2) + I(b^2) + I(c^2) + a*b + a*c + b*c + (1|block) , data = DataSet8.3 ) ##--- page 257 anova(Exam8.3.fm2, ddf = "Kenward-Roger", type = 1) ##--- page 257 Exam8.3.fm3 <- lmer( y ~ a + b + c + I(a^2) + I(b^2) + a*c + b*c + (1|block) , DataSet8.3 ) anova(Exam8.3.fm3, ddf = "Kenward-Roger", type = 1) ##--- scatter plot with regression plane by using Hoerl function ( page#233) a <- seq(from = -1, to = 1, by = 1) b <- seq(from = -1, to = 1, by = 1) c <- seq(from = -1, to = 1, by = 1) abc <- expand.grid(a = a, b = b, c = c) Yhat <- NULL for(i in 1:nrow(abc)) { Yhat[i] <- 50.08500 + 1.6*abc$a[i] + 1.69375*abc$b[i] + 0.51875*abc$c[i]- 3.30250*I((abc$a[i])^2)-3.51500*I((abc$b)^2)[i] - 0.52500*(abc$a)[i]*(abc$c)[i]-1.16250*(abc$b)[i]*(abc$c)[i] } Newdata <- data.frame(abc, Yhat) Plot1 <- wireframe(Yhat ~ b*a, data = subset(Newdata,c==-1), xlab = "b", ylab = "a", main = "Predicte response surface at C=-1", colorkey = FALSE, drape = TRUE, scales = list(arrows = FALSE),xlim=c(max(b),(min(b))), screen = list(z = -50, x =-70) ) Plot2 <- wireframe(Yhat ~ b*a, data = subset(Newdata,c==0), xlab = "b", ylab = "a", main = "Predicte response surface at C=0", colorkey = FALSE , drape = TRUE, scales = list(arrows = FALSE),xlim=c(max(b),(min(b))), screen = list(z = -50, x =-70) ) Plot3 <- wireframe(Yhat ~ b*a, data = subset(Newdata,c==1), xlab = "b", ylab = "a", main = "Predicte response surface at C=1", colorkey = FALSE, drape = TRUE, scales = list(arrows = FALSE),xlim=c(max(b),(min(b))), screen = list(z = -50, x =-70) ) print(Plot1) print(Plot2) print(Plot3) ``` ## References 1. Stroup, W. W. (2012). **Generalized Linear Mixed Models: Modern Concepts, Methods and Applications**. CRC Press. ## See Also `DataSet8.3` ## Author(s) 1. Muhammad Yaseen (myaseen208@gmail.com ) 2. Adeela Munawar (adeela.uaf@gmail.com )

Exam8.3 function