bayes_wfit: Bayesian Weighted Fitting Engines

In glmbayes: Bayesian Generalized Linear Models (IID Samples)

Bayesian Weighted Fitting Engines

Description

These functions provide the Bayesian analogue of lm.wfit. They implement the core weighted least squares step used inside Bayesian linear linear models, incorporating prior precision and posterior mode information.

Usage

rNormal_reg.wfit(
  x,
  y,
  P,
  mu,
  w,
  offset = NULL,
  method = "qr",
  tol = 1e-07,
  singular.ok = TRUE,
  ...
)

glmb.wfit(
  x,
  y,
  weights = rep.int(1, nobs),
  offset = rep.int(0, nobs),
  family = gaussian(),
  Bbar,
  P,
  betastar,
  method = "qr",
  tol = 1e-07,
  singular.ok = TRUE,
  ...
)

Arguments

x	design matrix of dimension n * p.
y	vector of observations of length n, or a matrix with n rows.
P	Prior precision matrix of dimension p * p.
mu	Prior mean vector of length p.
w	vector of weights (length n) to be used in the fitting process for the wfit functions. Weighted least squares is used with weights w, i.e., sum(w * e^2) is minimized.
offset	(numeric of length n). This can be used to specify an a priori known component to be included in the linear predictor during fitting.
method	currently, only method = "qr" is supported.
tol	tolerance for the qr decomposition. Default is 1e-7.
singular.ok	logical. If FALSE, a singular model is an error.
...	currently disregarded.
weights	an optional vector of prior weights to be used in the fitting process. Should be NULL or a numeric vector.
family	a description of the error distribution and link function to be used in the model. Should be a family function. (see family for details of family functions.)
Bbar	Prior mean vector of length p.
betastar	Posterior mode vector of length p which has already been estimated.

Details

rNormal_reg.wfit performs the Bayesian weighted least squares update for linear models under a Normal prior.

glmb.wfit performs the corresponding update for generalized linear models, reconstructing the weighted least squares step using the posterior mode and the GLM family functions.

Value

a list with components:

a list wih components:

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.