BayesMfp {bfp}

Bayesian model inference for multiple fractional polynomial models

Description

Bayesian model inference for multiple fractional polynomial models is conducted by means of either exhaustive model space evaluation or posterior model sampling.

Usage

BayesMfp(formula = formula(data), data = parent.frame(), family =
gaussian, priorSpecs = list(a = 4, modelPrior = "flat"), method =
c("ask", "exhaustive", "sampling"), subset = NULL, na.action = na.omit,
verbose = TRUE, nModels = NULL, nCache=1e9L, chainlength = 1e5L)

bfp(x, max = 2, scale = TRUE, rangeVals=NULL)

uc(x)

Arguments

formula

model formula

data

optional data.frame for model variables (defaults to the parent frame)

family

distribution and link: only gaussian("identity") supported at the moment

priorSpecs

prior specifications, see details

method

which method should be used to explore the posterior model space? (default: ask the user)

subset

optional subset expression

na.action

default is to skip rows with missing data, and no other option supported at the moment

verbose

should information on computation progress be given? (default)

nModels

how many best models should be saved? (default: 1% of the explored models or the chainlength, 1 would mean only the maximum a posteriori [MAP] model)

nCache

maximum number of best models to be cached at the same time during the model sampling (only has an effect if sampling has been chosen as method)

chainlength

length of the model sampling chain (only has an effect if sampling has been chosen as method)

x

variable

max

maximum degree for this FP (default: 2)

scale

use pre-transformation scaling to avoid numerical problems? (default)

rangeVals

extra numbers if the scaling should consider values in this range. Use this argument if you have test data with larger range than the training range.

Details

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.

The prior specifications are a list:

a

hyperparameter for hyper-g prior which must be greater than 3 and is recommended to be not greater than 4 (default is 4)

modelPrior

choose if a flat model prior (default, "flat"), a model prior favoring sparse models explicitly ("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.

Value

Returns an object of class BayesMfp that inherits from list. It is essentially a list of models. Each model is a list and has the following components:

powers

a list of numeric vectors, where each vector contains the powers of the covariate that its name denotes.

ucTerms

an integer vector of the indices of uncertain fixed form covariates that are present in the model.

logM

log marginal likelihood

logP

log prior probability

posterior

normalized posterior probability, and if model sampling was done, the frequency of the model in the sampling algorithm

postExpectedg

posterior expected covariance factor g

postExpectedShrinkage

posterior expected shrinkage factor t=g/(g + 1)

R2

usual coefficient of determination for the linear model

Subsetting the object with [.BayesMfp returns again a BayesMfp object with the same attributes, which are

numVisited

the number of models that have been visited (exhaustive search) or cached (model sampling)

inclusionProbs

BMA inclusion probabilities for all uncertain covariates

linearInclusionProbs

BMA probabilities for exactly linear inclusion of FP covariates

logNormConst

the (estimated) log normalizing constant f (D)

chainlength

length of the Markov chain, only present if method = "sampling"

call

the original call

formula

the formula by which the appropriate untransformed design matrix can be extracted

x

the shifted and scaled design matrix for the data

xCentered

the column-wise centered x

y

the response vector

yMean

the mean of the response values

SST

sum of squares total

indices

a list with components that describe the positions of uncertain covariate groups, fractional polynomial terms and fixed variables in the design matrix

termNames

a list of character vectors containing the names of uncertain covariate groups, fractional polynomial terms and fixed variables

shiftScaleMax

matrix with 4 columns containing preliminary transformation parameters, maximum degrees and cardinalities of the powersets of the fractional polynomial terms

priorSpecs

the utilized prior specifications

randomSeed

if a seed existed at function call (get(".Random.seed", .GlobalEnv)), it is saved here

Note

logNormConst may be unusable due to necessary conversion from long double to double!

Various methods for posterior summaries are available.

See Also

BayesMfp Methods, BmaSamples

Examples

## generate some data
set.seed(19)

x1 <- rnorm(n=15)
x2 <- rbinom(n=15, size=20, prob=0.5) 
x3 <- rexp(n=15)

y <- rt(n=15, df=2)

## run an exhaustive model space evaluation with a flat model prior and
## a uniform prior (a = 4) on the shrinkage factor t = g/(1 + g):
test <- BayesMfp(y ~ bfp (x2, max = 4) + uc (x1 + x3), nModels = 100,
                 method="exhaustive")
test

## now the same with a *dependent* model prior:
test2 <- BayesMfp(y ~ bfp (x2, max = 4) + uc (x1 + x3), nModels = 100,
		 priorSpecs = list(a = 4, modelPrior = "dependent"),
                 method="exhaustive")
test2