S.CARlocalised: Fit a spatial generalised linear mixed model to data, where a...

Description Usage Arguments Value Author(s) References Examples

View source: R/S.CARlocalised.R

Description

Fit a spatial generalised linear mixed model to areal unit data, where the response variable can be binomial or Poisson. Note, a Gaussian likelihood is not allowed because of a lack of identifiability among the parameters. The linear predictor is modelled by known covariates, a vector of random effects and a piecewise constant intercept process. The random effects are modelled by an intrinsic CAR prior, while the piecewise constant intercept process was proposed by Lee and Sarran (2015), and allow neighbouring areas to have very different values. Further details are given in the vignette accompanying this package. Inference is conducted in a Bayesian setting using Markov chain Monte Carlo (MCMC) simulation. Missing (NA) values are not allowed in this model. For a full model specification see the vignette accompanying this package.

Usage

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S.CARlocalised(formula, family, data=NULL, G, trials=NULL, W,
burnin, n.sample, thin=1, prior.mean.beta=NULL, prior.var.beta=NULL,
prior.tau2=NULL,prior.delta=NULL, MALA=TRUE, verbose=TRUE)

Arguments

formula

A formula for the covariate part of the model using the syntax of the lm() function. Offsets can be included here using the offset() function. The response, offset and each covariate is a vector of length K*1.The response cannot contain missing (NA) values.

family

One of either "binomial" or "poisson", which respectively specify a binomial likelihood model with a logistic link function, or a Poisson likelihood model with a log link function.

data

An optional data.frame containing the variables in the formula.

G

The maximum number of distinct intercept terms (groups) to allow in the model.

trials

A vector the same length as the response containing the total number of trials for each area. Only used if family="binomial".

W

A non-negative K by K neighbourhood matrix (where K is the number of spatial units). Typically a binary specification is used, where the jkth element equals one if areas (j, k) are spatially close (e.g. share a common border) and is zero otherwise. The matrix can be non-binary, but each row must contain at least one non-zero entry.

burnin

The number of MCMC samples to discard as the burn-in period.

n.sample

The number of MCMC samples to generate.

thin

The level of thinning to apply to the MCMC samples to reduce their temporal autocorrelation. Defaults to 1 (no thinning).

prior.mean.beta

A vector of prior means for the regression parameters beta (Gaussian priors are assumed). Defaults to a vector of zeros.

prior.var.beta

A vector of prior variances for the regression parameters beta (Gaussian priors are assumed). Defaults to a vector with values 100000.

prior.tau2

The prior shape and scale in the form of c(shape, scale) for an Inverse-Gamma(shape, scale) prior for tau2. Defaults to c(1, 0.01).

prior.delta

The prior maximum for the cluster smoothing parameter delta. Defaults to 10.

MALA

Logical, should the function use MALA (TRUE, default) or simple random walk (FALSE) updates for the random effects.

verbose

Logical, should the function update the user on its progress.

Value

summary.results

A summary table of the parameters.

samples

A list containing the MCMC samples from the model.

fitted.values

A vector of fitted values for each area.

residuals

A matrix with 2 columns where each column is a type of residual and each row relates to an area. The types are "response" (raw), and "pearson".

modelfit

Model fit criteria including the Deviance Information Criterion (DIC) and its corresponding estimated effective number of parameters (p.d), the Log Marginal Predictive Likelihood (LMPL), the Watanabe-Akaike Information Criterion (WAIC) and its corresponding estimated number of effective parameters (p.w), and the loglikelihood.

accept

The acceptance probabilities for the parameters.

localised.structure

A vector giving the posterior median of which intercept group each area is in.

formula

The formula (as a text string) for the response, covariate and offset parts of the model

model

A text string describing the model fit.

X

The design matrix of covariates.

Author(s)

Duncan Lee

References

Lee, D and Sarran, C (2015). Controlling for unmeasured confounding and spatial misalignment in long-term air pollution and health studies, Environmetrics, 26, 477-487.

Examples

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#################################################
#### Run the model on simulated data on a lattice
#################################################
#### Load other libraries required
library(MASS)

#### Set up a square lattice region
x.easting <- 1:10
x.northing <- 1:10
Grid <- expand.grid(x.easting, x.northing)
K <- nrow(Grid)

#### Split the area into two groups between which there will be a boundary.
groups <-rep(1, K) 
groups[Grid$Var1>5] <- 2

#### set up distance and neighbourhood (W, based on sharing a common border) matrices
distance <- as.matrix(dist(Grid))
W <-array(0, c(K,K))
W[distance==1] <-1 
	
#### Generate the response data
phi <- mvrnorm(n=1, mu=groups, Sigma=0.2 * exp(-0.1 * distance))
logit <- phi
prob <- exp(logit) / (1 + exp(logit))
trials <- rep(50,K)
Y <- rbinom(n=K, size=trials, prob=prob)


#### Run the localised smoothing model
formula <- Y ~ 1
## Not run: model <- S.CARlocalised(formula=formula, family="binomial", trials=trials,
G=2, W=W,burnin=20000, n.sample=100000)
## End(Not run)

#### Toy example for checking
model <- S.CARlocalised(formula=formula, family="binomial", trials=trials,
G=2, W=W,burnin=10, n.sample=50)

duncanplee/CARBayes documentation built on Sept. 23, 2018, 2 a.m.