runSALSA2D: Running SALSA for a spatial smooth with a CReSS basis

In lindesaysh/MRSea: Spatially adaptive regression splines using SALSA

Running SALSA for a spatial smooth with a CReSS basis

Description

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.

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.

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

Author(s)

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

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

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)

lindesaysh/MRSea documentation built on May 11, 2024, 11:30 p.m.