gSlc {gammSlice}

Generalized additive mixed model analysis via slice sampling

Description

Use slice sampling-based Markov chain Monte Carlo to fit a generalized additive mixed model.

Usage

gSlc(formula, data = NULL, random = NULL, family, control = gSlc.control())

Arguments

formula

Formula describing the generalized additive mixed model.

data

Data frame containing the input data. This argument is optional.

random

List describing random effects structure.This argument is optional.

family

Distribution family of the response variable. The options are "binomial" and "poisson".

control

Control options specified by gSlc.control.

Details

A Bayesian generalized additive mixed model is fitted to the input data according to specified formula. Such models are special cases of the general design generalized linear mixed models of Zhao, Staudenmayer, Coull and Wand (2003). Markov chain Monte Carlo, with slice sampling for the fixed and random effects, is used to obtain samples from the posterior distributions of the model parameters. Full details of the sampling scheme are in the appendix of Pham and Wand (2018).

Value

An object of class "gScl". The functions summary() and plot() are used to obtain a summary and plot of the fits. The object is a list with the following components:

nu

Matrix containing Markov chain Monte Carlo samples of the entire nu=(beta,u) vector. The rows correspond to Markov chain Monte Carlo replicates and the columns correspond to entries of the nu=(beta,u) vector.

beta

Matrix containing Markov chain Monte Carlo samples of the beta vector corresponding to the linear components of the model. The rows correspond to Markov chain Monte Carlo replicates and the columns correspond to entries of the beta vector.

sigmaSquared

Matrix containing Markov chain Monte Carlo samples of the entire sigma squared vector. The rows correspond to Markov chain Monte Carlo replicates and the columns correspond to entries of the sigmaSquared vector.

y

Response data vector.

XlinPreds

Matrix containing predictors that are purely linear components of the model.

linPredNames

Names of XlinPreds.

XsplPreds

Matrix containing predictors that are penalised spline components of the model.

splPredNames

Names of XsplPreds.

Zspl

Horizontal concatenation of each of the spline basis "Z" matrices used for smooth function components.

ncZspl

Vector giving the numbers of columns in the horizontal partition of Zspl corresponding to each smooth function component.

range.x.list

List containing values of the range.x input to the internal ZOSull() function.

intKnots.list

List containing values of the intKnots input to the internal ZOSull() function.

family

Character string indicating the family of the fitted model; either "binomial" or "poisson".

modelType

Charater string indicating the type of model fitted.

Author(s)

Tung Pham [e-mail] and Matt Wand [e-mail]

References

Neal, R.M. (2003).
Slice sampling (with discussion).
The Annals of Statistics, 31, 705-767.

Pham, T. and Wand, M.P. (2018).
Generalized additive mixed model analysis via gammSlice.
Australian and New Zealand Journal of Statistics, 60, 279-300.

Zhao, Y., Staudenmayer, J., Coull, B.A. and Wand, M.P. (2003).
General design Bayesian generalized linear mixed models.
Statistical Science, 21, 35-51.

See Also

gSlc.control, plot.gSlc, summary.gSlc

Examples

## Not run: 
# Example 1 of Pham & Wand (2018):

set.seed(39402)
m <- 100 ; n <- 2
beta0True <- 0.5 ; betaxTrue <- 1.7 
sigsqTrue <- 0.8 ; idnum <- rep(1:m,each=n)
x <- runif(m*n)
U <- rep(rnorm(m,0,sqrt(sigsqTrue)),each=n)
mu <- 1/(1+exp(-(beta0True+betaxTrue*x+U)))
y <- rbinom((m*n),1,mu)
fit1 <- gSlc(y ~ x,random = list(idnum = ~1),family = "binomial")
summary(fit1)

## End(Not run)

## Not run: 
# Example 2 of Pham & Wand (2018):

set.seed(53902)
n <- 400 ; x <- runif(n)
fTrue <- function(x) return(cos(4*pi*x) + 2*x - 1)
mu <- exp(fTrue(x)) ; y <- rpois(n,mu)
fit2 <- gSlc(y~s(x),family="poisson")
summary(fit2)
plot(fit2)

## End(Not run)

## Not run: 
# Example 3 of Pham & Wand (2018):

set.seed(981127)
n <- 500 ; betax1True <- 0.5;  x1 <- sample(c(0,1),n,replace=TRUE) 
x2 <- runif(n) ; fTrue <- function(x) return(sin(2*pi*x))
mu <- 1/(1+exp(-(betax1True*x1+fTrue(x2)))) ; y <- rpois(n,mu)
y <- rbinom(n,1,mu)
fit3 <- gSlc(y ~ x1 + s(x2),family="binomial")
summary(fit3)
plot(fit3)

## End(Not run)

## Not run: 
# Example 4 of Pham & Wand (2018):

set.seed(2966703)
m <- 100 ; n <- 10;  x1 <- runif(m*n);   x2 <- runif(m*n)
idnum <- rep(1:m,each=n) ; sigsqTrue <- 1
U <- rep(rnorm(m,0,sqrt(sigsqTrue)),each=n)
mu <- exp(U + cos(4*pi*x1) + 2*x1 + sin(2*pi*x2^2)) ; y <- rpois(m*n,mu)
fit4 <- gSlc(y ~ s(x1) + s(x2),random = list(idnum=~1),family = "poisson")
summary(fit4)
plot(fit4)

## End(Not run)