group <- rep(1:10, rep(10,10))
mu.a <- 0
sigma.a <- 2
mu.b <- 3
sigma.b <- 4
rho <- 0
Sigma.ab <- array (c(sigma.a^2, rho*sigma.a*sigma.b,
rho*sigma.a*sigma.b, sigma.b^2), c(2,2))
sigma.y <- 1
ab <- mvrnorm (10, c(mu.a,mu.b), Sigma.ab)
a <- ab[,1]
b <- ab[,2]
x <- rnorm (100)
y1 <- rnorm (100, a[group] + b[group]*x, sigma.y)
y2 <- rbinom(100, 1, prob=invlogit(a[group] + b*x))
M1 <- lm (y1 ~ x)
sigma.hat(M1)
M2 <- bayesglm (y1 ~ x, prior.scale=Inf, prior.df=Inf)
sigma.hat(M2) # should be same to sigma.hat(M1)
M3 <- glm (y2 ~ x, family=binomial(link="logit"))
sigma.hat(M3)
M4 <- lmer (y1 ~ (1+x|group))
sigma.hat(M4)
M5 <- glmer (y2 ~ (1+x|group), family=binomial(link="logit"))
sigma.hat(M5)
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