# gamlss.gmrf: Gaussian Markov Random Field fitting within GAMLSS In gamlss.spatial: Spatial Terms in Generalized Additive Models for Location Scale and Shape Models

## Description

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

## Usage

 ```1 2 3 4 5``` ```gamlss.gmrf(x, y, w, xeval = NULL, ...) gmrf(x, precision = NULL, neighbour = NULL, polys = NULL, area = NULL, adj.weight = 1000, df = NULL, lambda = NULL, start = 10, method = c("Q", "A"), 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 `adj.weight` a value to adjust the iterative weight if necessary `df` degrees of freedom for fitting if required, only for `method="A"` `lambda` The smoothing parameter `lambda` if known, only for `method="A"` `start` starting value for the smoothing parameter `lambda` `method` "Q" for Q-function, or "A" for alternating method `y` working response variable `w` iterative weights `xeval` whether to predict or not `control` to be use for some of the argument 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 <[email protected]>

## References

Stasinopoulos, D. M., Rigby, R. A., Heller, G. Z., Voudouris, V. and De Bastiani, F. (2017) Flexible Regression and Smoothing: Using GAMLSS in R. Chapman and Hall, Boca Raton. (see also http://www.gamlss.org/)

De Bastiani, F. Rigby, R. A., Stasinopoulos, D. M., Cysneiros, A. H. M. A. and Uribe-Opazo, M. A. (2016) Gaussian Markov random spatial models in GAMLSS. Journal of Applied Statistics, pp 1-19.

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. (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.

`MRF`, `MRFA`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```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") ```

### Example output

```Loading required package: gamlss.dist
**********   GAMLSS Version 5.0-2  **********
For more on GAMLSS look at http://www.gamlss.org/
Type gamlssNews() to see new features/changes/bug fixes.

This is mgcv 1.8-20. For overview type 'help("mgcv-package")'.

Attaching package: 'nnet'

The following object is masked from 'package:mgcv':

multinom

Spam version 2.1-1 (2017-07-02) is loaded.
Type 'help( Spam)' or 'demo( spam)' for a short introduction
and overview of this package.
Help for individual functions is also obtained by adding the
suffix '.spam' to the function name, e.g. 'help( chol.spam)'.

Attaching package: 'spam'

The following objects are masked from 'package:base':

backsolve, forwardsolve

GAMLSS-RS iteration 1: Global Deviance = 326.4786
GAMLSS-RS iteration 2: Global Deviance = 326.4786
Warning message:
In sqrt(diag(shes)) : NaNs produced
GAMLSS-RS iteration 1: Global Deviance = 326.4786
GAMLSS-RS iteration 2: Global Deviance = 326.4786
df      AIC
m2 24.46858 326.4786
m1 24.46858 326.4786
```

gamlss.spatial documentation built on May 24, 2018, 5:04 p.m.