x1 <- c("a", "b")
x2 <- c("c", "d")
dat <- expand.grid(id = 1:20, x1 = x1, x2 = x2)
contrasts(dat$x1) <- c(-0.5, 0.5)
contrasts(dat$x2) <- c(-0.5, 0.5)
dat$y <- rnorm(nrow(dat))
# grand mean (intercept)
gm <- mean(aggregate(y ~ x1 + x2, data = dat, mean)$y)
# main effect x1
mx1 <- diff(aggregate(y ~ x1, data = dat, mean)$y)
# main effect x2
mx2 <- diff(aggregate(y ~ x2, data = dat, mean)$y)
# plot
interaction.plot(dat$x1, dat$x2, dat$y, fun = mean)
# interaction x1:x2
int <- aggregate(y ~ x1 + x2, data = dat, mean)
int <- tidyr::pivot_wider(int, names_from = c(x1, x2), values_from = y)
intx1x2 <- (int$a_c - int$a_d) - (int$b_c - int$b_d)
# model
fit <- lm(y ~ x1 * x2, data = dat)
car::Anova(fit, type = "3")
Anova Table (Type III tests)
Response: y
Sum Sq Df F value Pr(>F)
(Intercept) 0.011 1 0.0119 0.9134
x1 0.117 1 0.1207 0.7292
x2 0.064 1 0.0660 0.7980
x1:x2 0.046 1 0.0478 0.8275
Residuals 73.364 76
rbind("model" = coef(fit),
"manual" = c(gm, mx1, mx2, intx1x2))
(Intercept) x11 x21 x11:x21
model 0.01197932 -0.07633766 -0.05642767 0.09607497
manual 0.01197932 -0.07633766 -0.05642767 0.09607497
