mcmcsae (version 0.7.4)

reg: Create a model component object for a regression (fixed effects) component in the linear predictor

Description

This function is intended to be used on the right hand side of the formula argument to create_sampler or generate_data. It creates an additive regression term in the model's linear predictor. By default, the prior for the regression coefficients is improper uniform. If b0 or Q0 are specified the prior becomes normal with mean b0 (default 0) and variance (matrix) sigma_^2 Q0^-1 where sigma_^2 is the overall scale parameter of the model, if any.

Usage

reg(
  formula = ~1,
  remove.redundant = FALSE,
  sparse = NULL,
  X = NULL,
  Q0 = NULL,
  b0 = NULL,
  R = NULL,
  r = NULL,
  S = NULL,
  s = NULL,
  lower = NULL,
  upper = NULL,
  name = "",
  perm = NULL,
  debug = FALSE,
  e = parent.frame()
)

Value

an object with precomputed quantities and functions for sampling from prior or conditional posterior distributions for this model component. Intended for internal use by other package functions.

Arguments

formula

a formula specifying the predictors to be used in the model, in the same way as the right hand side of the formula argument of R's lm function. Variable names are looked up in the data frame passed as data argument to create_sampler or generate_data, or in environment(formula).

remove.redundant

whether redundant columns should be removed from the design matrix. Default is FALSE. But note that treatment contrasts are automatically applied to all factor variables in formula.

sparse

whether the model matrix associated with formula should be sparse. The default is to base this on a simple heuristic.

X

a (possibly sparse) design matrix can be specified directly, as an alternative to the creation of one based on formula. If X is specified formula is ignored.

Q0

prior precision matrix for the regression effects. The default is a zero matrix corresponding to a noninformative improper prior. It can be specified as a scalar value, as a numeric vector of appropriate length, or as a matrix object.

b0

prior mean for the regression effect. Defaults to a zero vector. It can be specified as a scalar value or as a numeric vector of appropriate length.

R

optional constraint matrix for equality restrictions R'x = r where x is the vector of regression effects.

r

right hand side for the equality constraints.

S

optional constraint matrix for inequality constraints S'x >= s where x is the vector of regression effects.

s

right hand side for the inequality constraints.

lower

as an alternative to s, lower and upper may be specified for two-sided constraints lower <= S'x <= upper.

upper

as an alternative to s, lower and upper may be specified for two-sided constraints lower <= S'x <= upper.

name

the name of the model component. This name is used in the output of the MCMC simulation function MCMCsim. By default the name will be 'reg' with the number of the model term attached.

perm

whether permutation should be used in the Cholesky decomposition used for updating the model component's coefficient. Default is based on a simple heuristic.

debug

if TRUE a breakpoint is set at the beginning of the posterior draw function associated with this model component. Mainly intended for developers.

e

for internal use only.

Examples

# \donttest{
data(iris)
# default: flat priors on regression coefficients
sampler <- create_sampler(Sepal.Length ~
    reg(~ Petal.Length + Species, name="beta"),
  data=iris
)
sim <- MCMCsim(sampler, burnin=100, n.iter=400)
summary(sim)
# (weakly) informative normal priors on regression coefficients
sampler <- create_sampler(Sepal.Length ~
    reg(~ Petal.Length + Species, Q0=1e-2, name="beta"),
  data=iris
)
sim <- MCMCsim(sampler, burnin=100, n.iter=400)
summary(sim)
# binary regression
sampler <- create_sampler(Species == "setosa" ~
    reg(~ Sepal.Length, Q=0.1, name="beta"),
  family="binomial", data=iris)
sim <- MCMCsim(sampler, burnin=100, n.iter=400)
summary(sim)
pred <- predict(sim)
str(pred)
# example with equality constrained regression effects
n <- 500
df <- data.frame(x=runif(n))
df$y <- rnorm(n, 1 + 2*df$x)
R <- matrix(1, 2, 1)
r <- 3
sampler <- create_sampler(y ~ reg(~ 1 + x, R=R, r=r, name="beta"), data=df)
sim <- MCMCsim(sampler)
summary(sim)
plot(sim, "beta")
summary(transform_dc(sim$beta, fun=function(x) crossprod_mv(R, x) - r))
# }