influence.glmb: Bayesian Regression Diagnostics

In glmbayes: Bayesian Generalized Linear Models (IID Samples)

Bayesian Regression Diagnostics

Description

This function provides the basic quantities which are used in forming a wide variety of diagnostics for checking the quality of Bayesian regression fits. These methods delegate to influence, cooks.distance, dfbetas, and related functions in the stats package, applied to the fitted GLM component stored in the model object.

Usage

## S3 method for class 'glmb'
influence(model, ...)

Arguments

model	an object as returned by lm or glm.
...	further arguments passed to or from other methods.

Details

Cook's distance was introduced by \insertCiteCook1977glmbayes. The dfbetas, dffits, and covratio diagnostics follow the framework of \insertCiteBelsleyKuhWelsch1980glmbayes. Because glmb and lmb store coefficient draws rather than a single mode, these methods use the fitted fit component (from the underlying glm/lm fit at the posterior mode) for influence calculations.

Value

a list with components as returned by influence.

References

\insertAllCited

See Also

glmb, glmbayes-package; lmb, rglmb, rlmb; summary.glmb; influence, influence.measures, cooks.distance, dfbetas

Examples

set.seed(333)
## 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)

ps <- Prior_Setup(counts ~ outcome + treatment, family = poisson())
mu <- ps$mu
V0 <- ps$Sigma
glmb.D93 <- glmb(
  counts ~ outcome + treatment,
  family = poisson(),
  pfamily = dNormal(mu = mu, Sigma = V0)
)

## Start setup here [First output from earlier optim optimization]
betastar <- glmb.D93$coef.mode # Posterior mode from optim
x <- glmb.D93$x
y <- glmb.D93$y
# The fitted object does not currently store an offset, so use zeros here.
offset2 <- 0 * y # Should return this from lower level functions
weights2 <- glmb.D93$prior.weights

## Check influence measures for original model
fit <- glmb.wfit(x, y, weights2, offset2, family = poisson(), Bbar = mu, P = solve(V0), betastar)
influence.measures(fit)

print(fit)
print(glmb.D93$coef.mode)

### Now try a strong prior with poorly chosen intercept
mu1 <- 0 * mu
V1 <- 0.1 * V0
glmb2.D93 <- glmb(
  counts ~ outcome + treatment,
  family = poisson(),
  pfamily = dNormal(mu = mu1, Sigma = V1)
)

Bbar2 <- mu1 # Prior mean
betastar2 <- glmb2.D93$coef.mode # Posterior mode from optim
fit2 <- glmb.wfit(x, y, weights2, offset2, family = poisson(), Bbar2, P = solve(V1), betastar2)

influence.measures(fit2)

print(fit2)
print(glmb2.D93$coef.mode)



influence(glmb2.D93)
influence(glmb2.D93, do.coef = TRUE)
influence(glmb2.D93, do.coef = FALSE)

glmb.influence.measures(glmb2.D93, influence(glmb2.D93))


## Do not need method functions
dfbeta(glmb2.D93, influence(glmb2.D93))
dfbeta(glmb2.D93$fit, influence(glmb2.D93))
hatvalues(glmb2.D93, influence(glmb2.D93))
hatvalues(glmb2.D93$fit, influence(glmb2.D93))

# Implemented methods

rstandard(glmb2.D93, infl = influence(glmb2.D93))
rstandard(glmb2.D93)


# Methods requiring dedicated handling

## Needs a method function
dfbetas(glmb2.D93)
dfbetas(glmb2.D93, influence(glmb2.D93, do.coef = TRUE))
dfbetas(glmb2.D93$fit, influence(glmb2.D93))



# Needs a method function
cooks.distance(glmb2.D93)
cooks.distance(glmb2.D93$fit, influence(glmb2.D93))



# The rstandard method now works directly on glmb objects.


# Needs a method function
rstudent(glmb2.D93)
rstudent(glmb2.D93$fit, influence(glmb2.D93))


# Not a method, separate function
glmb.dffits(glmb2.D93)
dffits(glmb2.D93$fit, influence(glmb2.D93))

# Not a method - separate function
glmb.covratio(glmb2.D93)
covratio(glmb2.D93$fit, influence(glmb2.D93))



# Needs a method function but requires a different approach
# The influence function actually stores this measure
## This seems to require more work to create a method function

infl <- influence(glmb2.D93)
hat2 <- infl$hat
hat2

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