mgcv (version 1.8-5)

smooth.construct.mrf.smooth.spec: Markov Random Field Smooths

Description

For data observed over discrete spatial units, a simple Markov random field smoother is sometimes appropriate. These functions provide such a smoother class for mgcv. See details for how to deal with regions with missing data.

Usage

## S3 method for class 'mrf.smooth.spec':
smooth.construct(object, data, knots)
## S3 method for class 'mrf.smooth':
Predict.matrix(object, data)

Arguments

object

For the smooth.construct method a smooth specification object, usually generated by a term s(x,...,bs="mrf",xt=list(polys=foo)). x is a factor variable giving labels for geographic districts, and the xt

data

a list containing just the data (including any by variable) required by this term, with names corresponding to object$term (and object$by). The by variable is the last element.

knots

If there are more geographic areas than data were observed for, then this argument is used to provide the labels for all the areas (observed and unobserved).

Value

• An object of class "mrf.smooth" or a matrix mapping the coefficients of the MRF smooth to the predictions for the areas listed in data.

Details

A Markov random field smooth over a set of discrete areas is defined using a set of area labels, and a neighbourhood structure for the areas. The covariate of the smooth is the vector of area labels corresponding to each obervation. This covariate should be a factor, or capable of being coerced to a factor.

The neighbourhood structure is supplied in the xt argument to s. This must contain at least one of the elements polys, nb or penalty. [object Object],[object Object],[object Object]

If no basis dimension is supplied then the constructor produces a full rank MRF, with a coefficient for each geographic area. Otherwise a low rank approximation is obtained based on truncation of the parameterization given in Wood (2006) Section 4.10.4.

Note that smooths of this class have a built in plot method, and that the utility function in.out can be useful for working with discrete area data. The plot method has two schemes, scheme==0 is colour, scheme==1 is grey scale.

The situation in which there are areas with no data requires special handling. You should set drop.unused.levels=FALSE in the model fitting function, gam, bam or gamm, having first ensured that any fixed effect factors do not contain unobserved levels. Also make sure that the basis dimension is set to ensure that the total number of coefficients is less than the number of observations.

References

Wood S.N. (2006) Generalized additive models: an introduction with R. CRC.

See Also

in.out, polys.plot

Examples

library(mgcv)
## Load Columbus Ohio crime data (see ?columbus for details and credits)
data(columb)       ## data frame
data(columb.polys) ## district shapes list
xt <- list(polys=columb.polys) ## neighbourhood structure info for MRF
par(mfrow=c(2,2))
## First a full rank MRF...
b <- gam(crime ~ s(district,bs="mrf",xt=xt),data=columb,method="REML")
plot(b,scheme=1)
## Compare to reduced rank version...
b <- gam(crime ~ s(district,bs="mrf",k=20,xt=xt),data=columb,method="REML")
plot(b,scheme=1)
## An important covariate added...
b <- gam(crime ~ s(district,bs="mrf",k=20,xt=xt)+s(income),
         data=columb,method="REML")
plot(b,scheme=c(0,1))

## plot fitted values by district
par(mfrow=c(1,1))
fv <- fitted(b)
names(fv) <- as.character(columb$district)
polys.plot(columb.polys,fv)