optimCORR: 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 bivariate association/correlation between the covariates (CORR).

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

objCORR(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.

Association/Correlation between covariates

The correlation between two numeric covariates is measured using the Pearson's r, a descriptive statistic that ranges from -1 to +1. This statistic is also known as the linear correlation coefficient.

When the set of covariates includes factor covariates, all numeric covariates are transformed into factor covariates. The factor levels are defined using the marginal sampling strata created from one of the two methods available (equal-area or equal-range strata).

The association between two factor covariates is measured using the Cramér's V, a descriptive statistic that ranges from 0 to +1. The closer to +1 the Cramér's V is, the stronger the association between two factor covariates.

The main weakness of using the Cramér's V is that, while the Pearson's r shows the degree and direction of the association between two covariates (negative or positive), the Cramér's V only measures the degree of association (weak or strong). The effect of replacing the Pearson's r with the Cramér's V on the spatial modelling outcome still is poorly understood.

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

objCORR 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

Cramér, H. Mathematical methods of statistics. Princeton: Princeton University Press, p. 575, 1946.

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

cramer, optimACDC

data(meuse.grid, package = "sp")
candi <- meuse.grid[1:1000, 1:2]
covars <- meuse.grid[1:1000, 5]
schedule <- scheduleSPSANN(
  initial.temperature = 5, chains = 1, x.max = 1540, y.max = 2060, 
  x.min = 0, y.min = 0, cellsize = 40)
set.seed(2001)
res <- optimCORR(
  points = 10, candi = candi, covars = covars, use.coords = TRUE, 
  schedule = schedule)
objSPSANN(res) - objCORR(
  points = res, candi = candi, covars = covars, use.coords = TRUE)