sim: Functions to Get Posterior Distributions

In arm: Data Analysis Using Regression and Multilevel/Hierarchical Models

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, ...)

## S4 method for signature 'lm'
sim(object, n.sims = 100)
## S4 method for signature 'glm'
sim(object, n.sims = 100)
## S4 method for signature 'polr'
sim(object, n.sims = 100)
## S4 method for signature 'merMod'
sim(object, n.sims = 100)

## S3 method for class 'sim'
coef(object,...)
## S3 method for class 'sim.polr'
coef(object, slot=c("ALL", "coef", "zeta"),...)
## S3 method for class 'sim.merMod'
coef(object,...)
## S3 method for class 'sim.merMod'
fixef(object,...)
## S3 method for class 'sim.merMod'
ranef(object,...)
## S3 method for class 'sim.merMod'
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

coef	matrix (dimensions n.sims x k) of n.sims random draws of coefficients.
zeta	matrix (dimensions n.sims x k) of n.sims random draws of zetas (cut points in polr).
fixef	matrix (dimensions n.sims x k) of n.sims random draws of coefficients of the fixed effects for the merMod objects. Previously, it is called unmodeled.
sigma	vector of n.sims random draws of sigma (for glm's, this just returns a vector of 1's or else of the square root of the overdispersion parameter if that is in the model)

Author(s)

Andrew Gelman [e-mail]; Yu-Sung Su [e-mail]; Vincent Dorie [e-mail]

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)

arm documentation built on April 1, 2024, 3:01 p.m.