optimDIST: Optimization of sample configurations for spatial trend...
In spsann: Optimization of Sample Configurations using Spatial Simulated Annealing

Description Usage Arguments Details Value Note Author(s) References See Also Examples

Optimize a sample configuration for spatial trend identification and estimation. A criterion is defined so that the sample reproduces the marginal distribution of the covariates (DIST).

optimDIST(points, candi, covars, strata.type = "area",
  use.coords = FALSE, schedule = scheduleSPSANN(), plotit = FALSE,
  track = FALSE, boundary, progress = "txt", verbose = FALSE)

objDIST(points, candi, covars, strata.type = "area",
  use.coords = FALSE)

`points`	Integer value, integer vector, data frame or matrix, or list. Integer value. The number of points. These points will be randomly sampled from `candi` to form the starting sample configuration. Integer vector. The row indexes of `candi` that correspond to the points that form the starting sample configuration. The length of the vector defines the number of points. Data frame or matrix. An object with three columns in the following order: `[, "id"]`, the row indexes of `candi` that correspond to each point, `[, "x"]`, the projected x-coordinates, and `[, "y"]`, the projected y-coordinates. List. An object with two named sub-arguments: `fixed`, a data frame or matrix with the projected x- and y-coordinates of the existing sample configuration – kept fixed during the optimization –, and `free`, an integer value defining the number of points that should be added to the existing sample configuration – free to move during the optimization.
`candi`	Data frame or matrix with the candidate locations for the jittered points. `candi` must have two columns in the following order: `[, "x"]`, the projected x-coordinates, and `[, "y"]`, the projected y-coordinates.
`covars`	Data frame or matrix with the covariates in the columns.
`strata.type`	(Optional) Character value setting the type of stratification that should be used to create the marginal sampling strata (or factor levels) for the numeric covariates. Available options are `"area"`, for equal-area, and `"range"`, for equal-range. Defaults to `strata.type = "area"`.
`use.coords`	(Optional) Logical value. Should the spatial x- and y-coordinates be used as covariates? Defaults to `use.coords = FALSE`.
`schedule`	List with 11 named sub-arguments defining the control parameters of the cooling schedule. See `scheduleSPSANN`.
`plotit`	(Optional) Logical for plotting the optimization results, including a) the progress of the objective function, and b) the starting (gray circles) and current sample configuration (black dots), and the maximum jitter in the x- and y-coordinates. The plots are updated at each 10 jitters. When adding points to an existing sample configuration, fixed points are indicated using black crosses. Defaults to `plotit = FALSE`.
`track`	(Optional) Logical value. Should the evolution of the energy state be recorded and returned along with the result? If `track = FALSE` (the default), only the starting and ending energy states are returned along with the results.
`boundary`	(Optional) SpatialPolygon defining the boundary of the spatial domain. If missing and `plotit = TRUE`, `boundary` is estimated from `candi`.
`progress`	(Optional) Type of progress bar that should be used, with options `"txt"`, for a text progress bar in the R console, `"tk"`, to put up a Tk progress bar widget, and `NULL` to omit the progress bar. A Tk progress bar widget is useful when using parallel processors. Defaults to `progress = "txt"`.
`verbose`	(Optional) Logical for printing messages about the progress of the optimization. Defaults to `verbose = FALSE`.

Details about the mechanism used to generate a new sample configuration out of the current sample configuration by randomly perturbing the coordinates of a sample point are available in the help page of spJitter.

Marginal distribution of covariates

Reproducing the marginal distribution of the numeric covariates depends upon the definition of marginal sampling strata. These marginal sampling strata are also used to define the factor levels of all numeric covariates that are passed together with factor covariates. Two types of marginal sampling strata can be used: equal-area and equal-range.

Equal-area marginal sampling strata are defined using the sample quantiles estimated with quantile using a discontinuous function (type = 3). Using a discontinuous function avoids creating breakpoints that do not occur in the population of existing covariate values.

Depending on the level of discretization of the covariate values, quantile produces repeated breakpoints. A breakpoint will be repeated if that value has a relatively high frequency in the population of covariate values. The number of repeated breakpoints increases with the number of marginal sampling strata. Repeated breakpoints result in empty marginal sampling strata. To avoid this, only the unique breakpoints are used.

Equal-range marginal sampling strata are defined by breaking the range of covariate values into pieces of equal size. Depending on the level of discretization of the covariate values, this method creates breakpoints that do not occur in the population of existing covariate values. Such breakpoints are replaced with the nearest existing covariate value identified using Euclidean distances.

Like the equal-area method, the equal-range method can produce empty marginal sampling strata. The solution used here is to merge any empty marginal sampling strata with the closest non-empty marginal sampling strata. This is identified using Euclidean distances as well.

The approaches used to define the marginal sampling strata result in each numeric covariate having a different number of marginal sampling strata, some of them with different area/size. Because the goal is to have a sample that reproduces the marginal distribution of the covariate, each marginal sampling strata will have a different number of sample points. The wanted distribution of the number of sample points per marginal strata is estimated empirically as the proportion of points in the population of existing covariate values that fall in each marginal sampling strata.

optimDIST returns an object of class OptimizedSampleConfiguration: the optimized sample configuration with details about the optimization.

objDIST returns a numeric value: the energy state of the sample configuration – the objective function value.

The distance between two points is computed as the Euclidean distance between them. This computation assumes that the optimization is operating in the two-dimensional Euclidean space, i.e. the coordinates of the sample points and candidate locations should not be provided as latitude/longitude. spsann has no mechanism to check if the coordinates are projected: the user is responsible for making sure that this requirement is attained.

Alessandro Samuel-Rosa alessandrosamuelrosa@gmail.com

Hyndman, R. J.; Fan, Y. Sample quantiles in statistical packages. The American Statistician, v. 50, p. 361-365, 1996.

Everitt, B. S. The Cambridge dictionary of statistics. Cambridge: Cambridge University Press, p. 432, 2006.

optimACDC

require(sp)
data(meuse.grid)
candi <- meuse.grid[, 1:2]
covars <- meuse.grid[, 5]
schedule <- scheduleSPSANN(initial.temperature = 1, chains = 1,
                           x.max = 1540, y.max = 2060, x.min = 0, 
                           y.min = 0, cellsize = 40)
set.seed(2001)
res <- optimDIST(points = 10, candi = candi, covars = covars,
                 use.coords = TRUE, schedule = schedule)
objSPSANN(res) -
  objDIST(points = res, candi = candi, covars = covars, use.coords = TRUE)