summary.glmb: Summarizing Bayesian Generalized Linear Model Fits

In glmbayes: Bayesian Generalized Linear Models (IID Samples)

Summarizing Bayesian Generalized Linear Model Fits

Description

These functions are all methods for class glmb or summary.glmb objects.

Usage

## S3 method for class 'glmb'
summary(object, ...)

## S3 method for class 'summary.glmb'
print(x, digits = max(3, getOption("digits") - 3), ...)

Arguments

object	an object of class "glmb" for which a summary is desired.
x	an object of class "summary.glmb" for which a printed output is desired.
digits	the number of significant digits to use when printing.
...	Additional optional arguments

Details

The summary.glmb function summarizes the output from the glmb function. Key output includes mean residuals, information related to the prior, mean coefficients with associated stats, percentiles for the coefficients, as well as the effective number of parameters and the DIC statistic. The dir_tail component reports the directional tail diagnostic; see directional_tail and \insertCiteglmbayesChapterA04glmbayes for interpretation.

Value

summary.glmb returns a object of class "summary.glmb", a list with components:

call	the component from object
n	number of draws generated
residuals	vector of mean deviance residuals
coefficients1	Matrix with the prior mean and maximum likelihood coefficients with associated standard deviations
coefficients	Matrix with columns for the posterior mode, posterior mean, posterior standard deviation, monte carlo error, and tail probabilities (posterior probability of observing a value for the coefficient as extreme as the prior mean)
dir_tail	List containing information related to the directional tail relative to the Prior
dir_tail_null	List containing information related to the directional tail relative to the Null Model
Percentiles	Matrix with estimated percentiles associated with the posterior density
pD	Estimated effective number of parameters
deviance	Vector with draws for the deviance
DIC	Estimated DIC statistic
iters	Average number of candidates per generated draws

References

\insertAllCited

See Also

directional_tail, glmb, glmbayes-package, lmb, rglmb, rlmb, summary, summary.lm, summary.glm

Examples

###########################  Example for lmb function

## Annette Dobson (1990) "An Introduction to Generalized Linear Models".
## Page 9: Plant Weight Data.
ctl <- c(4.17,5.58,5.18,6.11,4.50,4.61,5.17,4.53,5.33,5.14)
trt <- c(4.81,4.17,4.41,3.59,5.87,3.83,6.03,4.89,4.32,4.69)
group <- gl(2, 10, 20, labels = c("Ctl","Trt"))
weight <- c(ctl, trt)

ps <- Prior_Setup(weight ~ group, family = gaussian())

lmb.D9 <- lmb(
  weight ~ group,
  pfamily = dNormal_Gamma(
    ps$mu,
    Sigma_0 = ps$Sigma_0,
    shape = ps$shape,
    rate  = ps$rate
  )
)
summary(lmb.D9)

###########################  Example for glmb function

## Dobson (1990) Page 93: Randomized Controlled Trial :
counts <- c(18,17,15,20,10,20,25,13,12)
outcome <- gl(3,1,9)
treatment <- gl(3,3)
print(d.AD <- data.frame(treatment, outcome, counts))

ps <- Prior_Setup(counts ~ outcome + treatment, family = poisson(), data = d.AD)

glmb.D93 <- glmb(
  counts ~ outcome + treatment,
  family  = poisson(),
  pfamily = dNormal(mu = ps$mu, Sigma = ps$Sigma)
)
summary(glmb.D93)

## Menarche logit model with default (non-informative) Prior_Setup prior
data(menarche, package = "MASS")
Age2 <- menarche$Age - 13

ps_m <- Prior_Setup(
  cbind(Menarche, Total - Menarche) ~ Age2,
  family = binomial(logit),
  data = menarche
)

glmb.out1 <- glmb(
  cbind(Menarche, Total - Menarche) ~ Age2,
  family  = binomial(logit),
  pfamily = dNormal(mu = ps_m$mu, Sigma = ps_m$Sigma),
  data    = menarche
)
summary(glmb.out1)

## Posterior mean fitted probabilities on response scale
require(graphics)
pred1 <- predict(glmb.out1, type = "response")
pred1_m <- colMeans(pred1)
plot(
  Menarche / Total ~ Age,
  data = menarche,
  main = "Proportion with menarche (data and posterior mean fit)"
)
lines(menarche$Age, pred1_m, col = "blue", lwd = 2)

glmbayes documentation built on Aug. 5, 2026, 1:07 a.m.