# Fit a GRaF model to binary data

### Description

Sets up and fits a GRaF model, returning an object of class `graf`

for which functions are available to visualise, compare and make predictions from models.

### Usage

1 2 3 |

### Arguments

`y` |
A vector denoting presence (1) and absence (0) records. |

`x` |
A dataframe of covariates which may contain factors as well as continuous variables. Factor covariates can still interact with other covariates, but they are not infuenced by either the mean function or the length-scale parameters and therefore give a maximum-likelihood estimate. |

`error` |
An optional matrix of standard deviations associated with x. If this is missing, covariates are assumed to be measured without error. |

`weights` |
An optional vector of weights to be used in the fitting process. Weights must be positive or zero. Observations with a weight of zero will be ignored. |

`prior` |
An optional R function providing an |

`l` |
An optional vector of lengthscales for each dimension of the Gaussian field. The lengthscale controls the smoothness of the fitted function, with a higher value giving a flatter curve
If |

`opt.l` |
Whether to optimise the lengthscale parameters with respect to the model marginal likelihood using |

`theta.prior.pars` |
If |

`hessian` |
If |

`opt.control` |
If |

`verbose` |
Logical, whether to display (limited) progress information for the fitting algorithms. |

`method` |
The approximation method used to fit model. Currently only |

### Details

In addition to the dataframe of covariates `x`

a matrix of corresponding standard deviations, describing the measurement error, may be specified via the `error`

argument.

If prior knowledge about the species' ecology is available (e.g. environmental thresholds beyond which the species cannot persist), this may be incorporated into the GRaF model by providing an R function via the `prior`

argument.

The smoothness of the fitted random field is controlled by a vector of lengthscales which is used to parameterise a squared exponential covariance function, with one lengthscale for each covariate. `graf`

centres and standardises covariates before fitting and the lengthscales therefore relate to these scaled covariates.
Lengthscales can be specified by the user via the the `l`

argument, roughly approximated by `graf`

by setting `l = NULL`

or optimised by setting `opt.l = TRUE`

.

### Value

A `graf`

object which can be viewed and manipulated using `print`

, `plot`

and `predict`

functions.

### References

Golding & Purse (2013) GRaF: Fast and Flexible Bayesian Species Distribution Modelling Using Gaussian Random Fields. Manuscript in preparation, preprint available here: http://dx.doi.org/10.6084/m9.figshare.767289

Rasmussen & Williams(2006) Gaussian Processes for Machine Learning. http://www.gaussianprocess.org/gpml/chapters/

### See Also

`print.graf`

, `plot.graf`

, `predict.graf`

, `plot3d`

, `DIC`

, `optim`

.

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 | ```
# load Anguilla data from the dismo package
data(Anguilla_train)
# get the first 100 presence-absence records
y <- Anguilla_train$Angaus[1:100]
# get covariates, removing LocSed (contains NAs) and make DSDam a factor
x <- Anguilla_train[1:100, 3:13]
x$DSDam <- factor(x$DSDam)
# fit a presence-absence model to the data
m1 <- graf(y, x)
#print a brief summary of the model
m1 # print(m1)
# plot the (conditional) effect of each term
par(mfrow = c(3, 4))
plot(m1)
# visualise the interaction between SegTSeas and SegLowFlow
par(mfrow = c(2, 2), mar = rep(2, 4))
plot3d(m1, dims = c(2, 3), theta = -110)
# fit another model with flatter responses
m2 <- graf(y, x, l = m1$ls * 2)
# compare the two models by DIC
DIC(m1)
DIC(m2)
# m2 has lower DIC so could be considered preferable
# predict back to dataset
pred <- predict(m2, x)
head(pred)
``` |

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