Skip to contents

Running SALSA for a spatial smooth with a CReSS basis

Source: R/runSALSA2D.R
runSALSA2D.Rd

This function fits a spatially adaptive two dimensional smooth of spatial coordinates with knot number and location selected by SALSA.

Usage

runSALSA2D(
  model,
  salsa2dlist,
  d2k,
  k2k,
  splineParams = NULL,
  chooserad = FALSE,
  panels = NULL,
  suppress.printout = FALSE,
  tol = 0,
  plot = FALSE,
  basis = "gaussian",
  initialise = TRUE,
  initialKnots = NULL,
  initialKnPos = NULL,
  logfile = FALSE
)

Arguments

model

A model with no spatial smooth

salsa2dlist

Vector of objects required for runSALSA2D: fitnessMeasure, knotgrid, startKnots, minKnots, codemaxKnots, r_seq, gap, interactionTerm.

d2k

(n x k) Matrix of distances between all data points in model and all valid knot locations specified in knotgrid

k2k

(k x k) Matrix of distances between all valid knot locations specified in knotgrid

splineParams

(default =NULL) List object containng output from runSALSA (e.g. knot locations for continuous covariates)

chooserad

logical flag. If FALSE (default) then the range parameter of the basis is chosen after the knot location and number. If TRUE, the range is assessed at every iteration of a knot move/add/drop.

panels

Vector denoting the panel identifier for each data point (if robust standard errors are to be calculated). Defaults to data order index if not given.

suppress.printout

(Default: FALSE. Logical stating whether to show the analysis printout.

tol

Numeric stating the tolerance for the fitness Measure. e.g. tol=2 with AIC would only allow changes to be made if the AIC score improves by 2 units.

plot

logical stating whether to print out the chosen knot locations at each iteration. default = FALSE.

basis

One of 'gaussian' (default) or 'exponential'. Specifys what kind of local radial function to use (LRF.g or LRF.e)

initialise

(Defauls: FALSE). Logical stating whether to allow the runSALSA2D function to find some starting knot locations. If FALSE, one of initialKnots or initialKnPos must be specified.

initialKnots

c x 2 dataframe or matrix specifying the coordinates of the starting locations of knots. c is the number of initial knots (should match what is specified in SALSA2dlist)

initialKnPos

vector of length c denoting the rows of the knotgrid to use as the initial starting locations of knots.

logfile

(Default: FALSE). Logical stating whether to store a log file of the analysis printout.

Value

This function returns the best model bestModel and the fitness statistic for this model fitStat

The spline paramater object that is returned as part of the model object now contains a list in the first element (previously reserved for the spatial component). This list contains the objects required for the SALSA2D fitting process:

knotDist

Matrix of knot to knot distances (k x k). May be Euclidean or geodesic distances. Must be square and the same dimensions as nrows(na.omit(knotgrid)). Created using makeDists.

radii

Sequence of range parameters for the CReSS basis from local (small) to global (large). Determines the range of the influence of each knot.

dist

Matrix of distances between data locations and knot locations (n x k). May be Euclidean or geodesic distances. Euclidean distances created using makeDists.

datacoords

Coordinates of the data locations

response

Vector of response data for the modelling process

knotgrid

Grid of legal knot locations.

minKnots

Minimum number of knots to be tried.

maxKnots

Maximum number of knots to be tried.

gap

Minimum gap between knots (in unit of measurement of datacoords)

radiusIndices

Vector of length startKnots identifying which radii (splineParams[[1]]$radii) will be used for each knot location (splineParams[[1]]$knotPos)

knotPos

Index of knot locations. The index identifies which knots (i.e. which rows) from knotgrid were selected by SALSA

Details

The object salsa2dlist contains parameters for the runSALSA2D function.

fitnessMeasure. The criterion for selecting the `best' model. Available options: AIC, AIC_c, BIC, QIC_b, cv.gamMRSea (use cv.opts in salsa2dlist to specify seed, folds, cost function (Defaults: cv.opts=list(cv.gamMRSea.seed=357, K=10, cost=function(y, yhat) mean((y - yhat)^2)))

knotgrid. A set of 'k' knot locations (k x 2 matrix or dataframe of coordinates). May be made using getKnotgrid.

startknots. Starting number of knots (initialised as spaced filled locations).

minKnots. Minimum number of knots to be tried.

maxKnots. Maximum number of knots to be tried.

gap. The minimum gap between knots (in unit of measurement of coordinates). interactionTerm. Specifies which term in baseModel the spatial smooth will interact with. If NULL no interaction term is fitted. cv.opts Used if fitnessMeasure = cv.gamMRSea. See above for specification.

References

Scott-Hayward, L.; M. Mackenzie, C.Donovan, C.Walker and E.Ashe. Complex Region Spatial Smoother (CReSS). Journal of computational and Graphical Statistics. 2013. doi: 10.1080/10618600.2012.762920

Scott-Hayward, L.. Novel Methods for species distribution mapping including spatial models in complex regions: Chapter 5 for SALSA2D methods. PhD Thesis, University of St Andrews. 2013

Author

Lindesay Scott-Hayward (University of St Andrews), Cameron Walker (University of Auckland)

Examples

# load data
data(ns.data.re)
# load prediction data
data(ns.predict.data.re)
# load knot grid data
data(knotgrid.ns)

#set some input info for SALSA
ns.data.re$response<- ns.data.re$birds

# make distance matrices for datatoknots and knottoknots
distMats<-makeDists(cbind(ns.data.re$x.pos, ns.data.re$y.pos), na.omit(knotgrid.ns))

# set initial model without the spatial term
# (so all other non-spline terms)
initialModel<- glm(response ~ 1 + offset(log(area)),
                   family='quasipoisson', data=ns.data.re)

# make parameter set for running salsa2d
# I have chosen a gap parameter of 1000 (in metres) to speed up the process.
# Note that this means there cannot be two knots within 1000m of each other.

salsa2dlist<-list(fitnessMeasure = 'QICb', 
                  knotgrid = na.omit(knotgrid.ns),
                  startKnots = 6,
                  minKnots = 2, 
                  maxKnots = 20, 
                  gap=1000)

salsa2dOutput<-runSALSA2D(initialModel, 
                          salsa2dlist, 
                          d2k=distMats$dataDist,
                          k2k=distMats$knotDist)
#> [1] "initialDispersion 20.4447417001531"
#> [1] "******************************************************************************"
#> [1] "Initialising..."
#> [1] "******************************************************************************"
#> [1] "Space-filling knots...."
#> [1] "Initialising model..."
#> [1] "Initial model fitted..."
#> [1] "Fitting Initial Radii"
#> [1] "initialising complete"
#> [1] "******************************************************************************"
#> [1] "Exchanging..."
#> [1] "******************************************************************************"
#> [1] "******************************************************************************"
#> [1] "Moving knot..."
#> [1] "******************************************************************************"
#> [1] "Adding knot..."
#> [1] "knot added ***********************************"
#> [1] "******************************************************************************"
#> [1] "Moving knot..."
#> [1] "******************************************************************************"
#> [1] "move ***********************************"
#> [1] "move ***********************************"
#> [1] "Adding knot..."
#> [1] "******************************************************************************"
#> [1] "Moving knot..."
#> [1] "******************************************************************************"
#> [1] "Adding knot..."
#> [1] "Improving..."
#> [1] "******************************************************************************"
#> [1] "improve *************************************"
#> [1] "improve *************************************"
#> [1] "improve *************************************"
#> [1] "improve *************************************"
#> [1] "improve *************************************"
#> [1] "improve *************************************"
#> [1] "improve *************************************"
#> [1] "improve *************************************"
#> [1] "improve *************************************"
#> [1] "improve *************************************"
#> [1] "improve *************************************"
#> [1] "improve *************************************"
#> [1] "improve *************************************"
#> [1] "improve *************************************"
#> [1] "improve *************************************"
#> [1] "improve *************************************"
#> [1] "improve *************************************"
#> [1] "improve *************************************"
#> [1] "improve *************************************"
#> [1] "improve *************************************"
#> [1] "improve *************************************"
#> [1] "improve *************************************"
#> [1] "improve *************************************"
#> [1] "******************************************************************************"
#> [1] "Simplifying model..."
#> [1] "******************************************************************************"
#> [1] "e"
#> [1] "******************************************************************************"
#> [1] "Exchanging..."
#> [1] "******************************************************************************"
#> [1] "******************************************************************************"
#> [1] "Moving knot..."
#> [1] "******************************************************************************"
#> [1] "Adding knot..."
#> [1] "Improving..."
#> [1] "******************************************************************************"
#> [1] "******************************************************************************"
#> [1] "Simplifying model..."
#> [1] "******************************************************************************"
#> [1] "e"
#> [1] "And we're done..."
#> [1] "******************************************************************************"
#> [1] "Initialising..."
#> [1] "******************************************************************************"
#> [1] "Initialising model..."
#> [1] "Initial model fitted..."
#> [1] "Fitting Initial Radii"
#> [1] "initialising complete"