arm (version 1.9-1)

sim: Functions to Get Posterior Distributions

Description

This generic function gets posterior simulations of sigma and beta from a lm object, or simulations of beta from a glm object, or simulations of beta from a merMod object

Usage

sim(object, ...)
"sim"(object, n.sims = 100)
"sim"(object, n.sims = 100)
"sim"(object, n.sims = 100)
"sim"(object, n.sims = 100)
"coef"(object,...)
"coef"(object, slot=c("ALL", "coef", "zeta"),...)
"coef"(object,...)
"fixef"(object,...)
"ranef"(object,...)
"fitted"(object, regression,...)

Arguments

object

the output of a call to lm with n data points and k predictors.

slot

return which slot of sim.polr, available options are coef, zeta, ALL.

...

further arguments passed to or from other methods.

n.sims

number of independent simulation draws to create.

regression

the orginial mer model

Value

References

Andrew Gelman and Jennifer Hill. (2006). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press.

See Also

display, lm, glm, lmer

Examples

#Examples of "sim"
 set.seed (1)
 J <- 15
 n <- J*(J+1)/2
 group <- rep (1:J, 1:J)
 mu.a <- 5
 sigma.a <- 2
 a <- rnorm (J, mu.a, sigma.a)
 b <- -3
 x <- rnorm (n, 2, 1)
 sigma.y <- 6
 y <- rnorm (n, a[group] + b*x, sigma.y)
 u <- runif (J, 0, 3)
 y123.dat <- cbind (y, x, group)
# Linear regression
 x1 <- y123.dat[,2]
 y1 <- y123.dat[,1]
 M1 <- lm (y1 ~ x1)
 display(M1)
 M1.sim <- sim(M1)
 coef.M1.sim <- coef(M1.sim)
 sigma.M1.sim <- sigma.hat(M1.sim)
 ## to get the uncertainty for the simulated estimates
 apply(coef(M1.sim), 2, quantile)
 quantile(sigma.hat(M1.sim))

# Logistic regression
 u.data <- cbind (1:J, u)
 dimnames(u.data)[[2]] <- c("group", "u")
 u.dat <- as.data.frame (u.data)
 y <- rbinom (n, 1, invlogit (a[group] + b*x))
 M2 <- glm (y ~ x, family=binomial(link="logit"))
 display(M2)
 M2.sim <- sim (M2)
 coef.M2.sim <- coef(M2.sim)
 sigma.M2.sim <- sigma.hat(M2.sim)

# Ordered Logistic regression
house.plr <- polr(Sat ~ Infl + Type + Cont, weights = Freq, data = housing)
display(house.plr)
M.plr <- sim(house.plr)
coef.sim <- coef(M.plr, slot="coef")
zeta.sim <- coef(M.plr, slot="zeta")
coefall.sim <- coef(M.plr)

# Using lmer:
# Example 1
 E1 <- lmer (y ~ x + (1 | group))
 display(E1)
 E1.sim <- sim (E1)
 coef.E1.sim <- coef(E1.sim)
 fixef.E1.sim <- fixef(E1.sim)
 ranef.E1.sim <- ranef(E1.sim)
 sigma.E1.sim <- sigma.hat(E1.sim)
 yhat <- fitted(E1.sim, E1)

# Example 2
 u.full <- u[group]
 E2 <- lmer (y ~ x + u.full + (1 | group))
 display(E2)
 E2.sim <- sim (E2)
 coef.E2.sim <- coef(E2.sim)
 fixef.E2.sim <- fixef(E2.sim)
 ranef.E2.sim <- ranef(E2.sim)
 sigma.E2.sim <- sigma.hat(E2.sim)
 yhat <- fitted(E2.sim, E2)

# Example 3
 y <- rbinom (n, 1, invlogit (a[group] + b*x))
 E3 <- glmer (y ~ x + (1 | group), family=binomial(link="logit"))
 display(E3)
 E3.sim <- sim (E3)
 coef.E3.sim <- coef(E3.sim)
 fixef.E3.sim <- fixef(E3.sim)
 ranef.E3.sim <- ranef(E3.sim)
 sigma.E3.sim <- sigma.hat(E3.sim)
 yhat <- fitted(E3.sim, E3)