Bayesian model inference for fractional polynomial models from the generalized linear model family or the Cox model is conducted by means of either exhaustive model space evaluation or posterior model sampling. The approach is based on analytical marginal likelihood approximations, using integrated Laplace approximation. Alternatively, test-based Bayes factors (TBFs) are used.
glmBayesMfp(
formula = formula(data),
censInd = NULL,
data = parent.frame(),
weights,
offset,
family,
phi = 1,
tbf = FALSE,
empiricalBayes = FALSE,
fixedg = NULL,
priorSpecs = list(gPrior = HypergPrior(), modelPrior = "sparse"),
method = c("ask", "exhaustive", "sampling"),
subset,
na.action = na.omit,
verbose = TRUE,
debug = FALSE,
nModels,
nCache = 1e+09,
chainlength = 10000,
nGaussHermite = 20,
useBfgs = FALSE,
largeVariance = 100,
useOpenMP = TRUE,
higherOrderCorrection = FALSE,
fixedcfactor = FALSE,
empiricalgPrior = FALSE,
centerX = TRUE
)model formula
censoring indicator. Default is NULL, but if
a non-NULL vector is supplied, this is assumed to be logical
(TRUE = observed, FALSE = censored) and Cox regression is
performed.
optional data.frame for model variables (defaults to the parent frame)
optionally a vector of positive weights (if not provided, a vector of one's)
this can be used to specify an _a priori_ known component to be included in the linear predictor during fitting. This must be a numeric vector of length equal to the number of cases (if not provided, a vector of zeroes)
distribution and link (as in the glm function). Needs to be explicitly specified for all models except the Cox model.
value of the dispersion parameter (defaults to 1)
Use TBF methodology to compute the marginal likelihood? (not
default) Must be TRUE if Cox regression is done.
rank the models in terms of conditional
marginal likelihood, using an empirical Bayes estimate of g? (not default)
Due to coding structure, the prior on g must be given in priorSpecs
although it does not have an effect when empiricalBayes==TRUE.
If this is a number, then it is taken as a fixed value of g,
and as with the empiricalBayes option, the models are ranked in terms
of conditional marginal likelihood. By default, this option is NULL,
which means that g is estimated in a fully or empirical Bayesian way.
prior specifications, see details
which method should be used to explore the posterior model space? (default: ask the user)
optional subset expression
default is to skip rows with missing data, and no other option supported at the moment
should information on computation progress be given? (default)
print debugging information? (not default)
how many best models should be saved? (default: 1% of the
total number of (cached) models). Must not be larger than nCache if
method == "sampling".
maximum number of best models to be cached at the same time during the model sampling, only has effect if method = sampling
length of the model sampling chain (only has an effect if sampling has been chosen as method)
number of quantiles used in Gauss Hermite quadrature
for marginal likelihood approximation (and later in the MCMC sampler for the
approximation of the marginal covariance factor density). If
empiricalBayes or a fixed g is used, this option has no effect.
Shall the BFGS algorithm be used in the internal maximization
(not default)? Else, the default Brent optimize routine is used, which seems
to be more robust. If empiricalBayes or a fixed g is used, this
option has no effect and always the Brent optimize routine is used.
When should the BFGS variance estimate be considered
“large”, so that a reestimation of it is computed? (Only has an
effect if useBfgs == TRUE, default: 100)
shall OpenMP be used to accelerate the computations? (default)
should a higher-order correction of the Laplace approximation be used, which works only for canonical GLMs? (not default)
If TRUE sets the c factor assuming alpha is set to 0. Otherwise take alpha=mean(y)
If TRUE uses the the observed isnformation matrix instead of X'X in the g prior. (Experimental)
Center the data before fitting (FALSE)
An object of S3 class GlmBayesMfp.
The formula is of the form y ~ bfp (x1, max = 4) + uc (x2 + x3), that
is, the auxiliary functions bfp and uc must be
used for defining the fractional polynomial and uncertain fixed form
covariates terms, respectively. There must be an intercept, and no other
fixed covariates are allowed. All max arguments of the
bfp terms must be identical. y is the response vector
for GLMs or the vector of survival times for Cox regression. Note that Cox
regression is only implemented with TBFs.
The prior specifications are a list:
A g-prior class object. Defaults to a hyper-g prior. See
'>GPrior for more information.
choose if a flat model prior ("flat"), a
model prior favoring sparse models explicitly (default, "sparse"),
or a dependent model prior ("dependent") should be used.
If method = "ask", the user is prompted with the maximum
cardinality of the model space and can then decide whether to use
posterior sampling or the exhaustive model space evaluation.
Note that if you specify only one FP term, the exhaustive model search must be done, due to the structure of the model sampling algorithm. However, in reality this will not be a problem as the model space will typically be very small.