Q.mBYM {ar.matrix}

Modified Precision matrix for a BYM process

Description

EXPIREMENTAL. Functions for creating precision matricies and observations of a modified BYM process as defined in MacNab 2011. The matrix defines the precision of estimates when observations share connections which are conditionally auto-regressive(CAR). Because the precision matrix is not symetric the process is not a true GMRF.

Usage

Q.mBYM(graph, sigma, rho, vcov=FALSE)

r.mBYM(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.

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.mBYM returns either a precision or variance-covariance function with a modified BYM structure.

r.mBYM retrurns a matrix with n rows which are the n observations of a pseudo Gaussian Markov random field of a modified BYM process.

References

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

Examples

## Not run: 
require("leaflet")
require("sp")

# simulate mBYM data and attach to spatial polygons data frame
US.df@data$data <- c(r.mBYM(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

## End(Not run)