Generalized additive mixed model analysis via slice sampling

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Description

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

Usage

1
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.

random

List describing random effects structure. This argument is optional.

family

Distribution family of the response variable. 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 (2012).

Value

nu

Matrix containing the MCMC samples for the combined fixed effects and random effects vectors. Each column of nu is a separate MCMC sample.

beta

Matrix containing the MCMC samples for the fixed effects vector.

u

Matrix containing the MCMC samples for the random effects vector. If the model contains smooth function components then u includes both random intercept and spline coefficient MCMC samples.

sigmaSquared

Matrix contain of variances.

scaledData

The scaled data set was used to fit in.

formulaInfor

Information obtained from the formula.

timeTaken

Time in seconds taken by the MCMC sampling.

Xmin

The minimum values of each predictor variable.

Xmax

The maximum values of each predictor variable.

Xrange

The difference between Xmax and Xmin.

Author(s)

Tung Pham tung.pham@epfl.ch and Matt Wand matt.wand@uts.edu.au

References

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

Pham, T. and Wand, M.P. (2012).
Generalized additive mixed model analysis via gammSlice.
Submitted.

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

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## Not run: 
library(mgcv)
dat0 <- gamSim(eg=1, n=500, scale = 0.2, dist = "poisson")
fit0 <- gSlc( y~s(x0) + s(x1) + s(x2) + s(x3), family = "poisson", data = dat0)
plot(fit0,pages = 1)
summary(fit0)

dat1 <- gamSim(eg=6, n = 400,scale = 0.1, dist = "poisson")
fit1 <- gSlc(y ~ s(x0) + s(x1) + s(x2) + s(x3), family = "poisson",
             data = dat1, random = list(fac=~1))
plot(fit1,pages=2)
summary(fit1)

dat2 <- gSlcSim(eg = 2, numGrp = 200, family = "poisson",
                randomFactor = FALSE)
fit2 <- gSlc(y~x1 + x2, family = "poisson", data = dat2)
summary(fit2)

dat3 <- gSlcSim(eg = 3,numGrp = 1000, family = "binomial",
                randomFactor = FALSE)
fit3 <- gSlc(y~s(x1),family = "binomial", data = dat3)
plot(fit3)
summary(fit3)

fit3a <- gSlc(y~s(x1,nBasis=10),family = "binomial",
                 data = dat3)
plot(fit3a)
summary(fit3a)


dat4 <- gSlcSim(eg = 4,  numGrp = 400, family = "poisson",
               randomFactor = FALSE)
fit4 <- gSlc(y~x1 + s(x2), family = "poisson", data = dat4)
plot(fit4)
summary(fit4)

dat5 <- gSlcSim(eg=6,family = "poisson", randomFactor = TRUE)
fit5 <- gSlc(y~x1 + x2 + s(x3) + s(x4), random = list(idnum=~1),
             family = "poisson", data = dat5)
plot(fit5)
summary(fit5)

## End(Not run)