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Last data update: 2014.03.03

R: Gaussian Markov Random Field fitting within GAMLSS

gamlss.gmrf

R Documentation

Gaussian Markov Random Field fitting within GAMLSS

Description

The function gmrf() can be used to fit Markov Random Field additive terms within GAMLSS.

Usage

gamlss.gmrf(x, y, w, xeval = NULL, ...)
gmrf(x, precision, neighbour, polys, area, adj.weight,  df, start, method, 
control = gmrf.control(...), ...)

Arguments

`x`	a factor containing the areas
`precision`	the precision matrix if set
`neighbour`	an object containing the neighbour information for the area if set
`polys`	the polygon information if set
`area`	this argument is here to allow more areas than the levels of the factor `x`, see example below
`start`	starting value for the smoothing parameter `lambda`
`df`	degrees of freedom for fitting if required, only for `method="A"`
`method`	"Q" for Q-function, or "A" for alternating mehtod
`adj.weight`	a value to adjust the iterative weight if necessary
`y`	working response variable
`w`	iterative weights
`xeval`	whether to predict or not
`control`	to be use for some of the srgument of `MRF()`.
`...`	for extra arguments

Details

The function gmrf() is to support the function MRF() and MRFA() within GAMLSS. It is intended to be called within a GAMLSS formula. The function gmrf() is not intended to be used directly. It is calling the function MRFA() and MRF() within the GAMLSS fitting algorithm. The results using the option method="Q" or method="A" should produce identical results.

Value

a fitted gamlss object

Author(s)

Fernanda De Bastiani, Mikis Stasinopoulos, Robert Rigby and Vlasios Voudouris.

Maintainer: Fernanda <fernandadebastiani@gmail.com>

References

Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion), Appl. Statist., 54, part 3, pp 507-554.

Rue and Held (2005) Gaussian markov random fields: theory and applications, Chapman & Hall, USA.

Stasinopoulos D. M., Rigby R.A. and Akantziliotou C. (2006) Instructions on how to use the GAMLSS package in R. Accompanying documentation in the current GAMLSS help files, (see also http://www.gamlss.org/).

Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R. Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, http://www.jstatsoft.org/v23/i07.

Examples

library(gamlss)
library(mgcv)
data(columb)
data(columb.polys)
vizinhos=polys2nb(columb.polys)
precisionC <- nb2prec(vizinhos,x=columb$district)
# MRFA
 m1<- gamlss(crime~ gmrf(district, polys=columb.polys, method="Q"), data=columb)
 m2<- gamlss(crime~ gmrf(district, polys=columb.polys, method="A"), data=columb)
AIC(m1,m2, k=0)
draw.polys(columb.polys, getSmo(m2), scheme="topo")