Q.lCAR {ar.matrix}

Precision matrix for a pCAR process

Description

Functions for creating precision matricies and observations of a Leroux CAR(lCAR) process as defined in MacNab 2011. The matrix defines the precision of estimates when observations share connections which are conditionally auto-regressive(CAR).

Usage

Q.lCAR(graph, sigma, rho, sparse=FALSE, vcov=FALSE)

r.lCAR(n, graph, sigma, rho)

Arguments

graph

matrix, square matrix indicating where two observations are connected (and therefore conditionally auto-regressive).

sigma

float > 0, process standard derviation see MacNab 2011.

rho

float >= 0 & < 1, how correlated neighbors are. The function will still run with values outside of the range [0,1) however the stability of the simulation results are not gaurunteed. see MacNab 2011.

sparse

bool Should the matrix be of class 'dsCMatrix'

vcov

bool If the vcov matrix should be returned instead of the precision matrix.

n

int > 0, number of observations to simulate from the GMRF.

Value

Q.lCAR returns either a precision or variance-covariance function with a lCAR structure.

r.lCAR retrurns a matrix with n rows which are the n observations of a Gaussian Markov random field lCAR process.

References

Y.C. MacNab On Gaussian Markov random fields and Bayesian disease mapping. Statistical Methods in Medical Research. 2011.

Examples

require("leaflet")
require("sp")

# simulate lCAR data and attach to spatial polygons data frame
US.df@data$data <- c(r.lCAR(1, graph=US.graph, sigma=1, rho=.99))

# color palette of data
pal <- colorNumeric(palette="YlGnBu", domain=US.df@data$data)

# see map
map1<-leaflet() %>%
    addProviderTiles("CartoDB.Positron") %>%
    addPolygons(data=US.df, fillColor=~pal(data), color="#b2aeae",
                fillOpacity=0.7, weight=0.3, smoothFactor=0.2) %>%
    addLegend("bottomright", pal=pal, values=US.df$data, title="", opacity=1)
map1