Generalized Random-Tessellation Stratified (GRTS) Survey Design

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Description

Selects a sample using a generalized random-tessellation stratified (GRTS) survey design. The GRTS survey design may include stratification, unequal probability using categories, unequal selection proportional to an auxiliary variable, survey over time structures, and provision for an oversample.

Usage

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grts(design, DesignID="Site", SiteBegin=1, type.frame="finite",
   src.frame="shapefile", in.shape=NULL, sp.object=NULL, att.frame=NULL,
   id=NULL, xcoord=NULL, ycoord=NULL, stratum=NULL, mdcaty=NULL, startlev=NULL,
   maxlev=11, maxtry=1000, shift.grid=TRUE, do.sample=rep(TRUE, length(design)),
   shapefile=TRUE, prjfilename=NULL, out.shape="sample")

Arguments

design

named list of stratum design specifications, where each element of design is a list containing the design specifications for a stratum. For an unstratified sample, design contains a single list. If the sample is stratified, the names in design must occur among the strata names in the stratum column of the attributes data frame (att.frame). If the sample is unstratified, the name of the single list in design is arbitrary. Each list in design has four components:
panel = named vector of sample sizes for each panel in stratum
seltype = the type of random selection, which must be one of following: "Equal" - equal probability selection, "Unequal" - unequal probability selection by the categories specified in caty.n and mdcaty, or "Continuous" - unequal probability selection proportional to auxiliary variable mdcaty
caty.n = if seltype equals "Unequal", a named vector of sample sizes for each category specified by mdcaty, where sum of the sample sizes must equal sum of the panel sample sizes, and names must be a subset of values in mdcaty
over = number of replacement sites ("oversample" sites) for the entire design, which is set equal to 0 if none are required

Example design for a stratified sample:
design <- list("Stratum 1"=list(panel=c(Panel=50), seltype="Equal", over=10),
"Stratum 2"=list(panel=c("Panel One"=50, "Panel Two"=50), seltype="Unequal",
caty.n=c(CatyOne=25, CatyTwo=25, CatyThree=25, CatyFour=25), over=75))

Example design for an unstratified sample:
design <- list(None=list(panel=c(Panel1=50, Panel2=100, Panel3=50), seltype="Unequal",
caty.n=c("Caty 1"=50, "Caty 2"=25, "Caty 3"=25, "Caty 4"=25, "Caty 5"=75), over=100))

DesignID

name for the design, which is used to create a site ID for each site. The default is "Site".

SiteBegin

number to use for first site in the design. The default is 1.

type.frame

the type of frame, which must be one of following: "finite", "linear", or "area". The default is "finite".

src.frame

source of the frame, which equals "shapefile" if the frame is to be read from a shapefile, "sp.object" if the frame is obtained from an sp package object, or "att.frame" if type.frame equals "finite" and the frame is included in att.frame. The default is "shapefile".

in.shape

name (without any extension) of the input shapefile. If src.frame equal "shapefile" and in.shape equals NULL, then the shapefile or shapefiles in the working directory are used. The default is NULL.

sp.object

name of the sp package object when src.frame equals "sp.object". The default is NULL.

att.frame

a data frame composed of attributes associated with elements in the frame, which must contain the columns used for stratum and mdcaty (if required). If src.frame equals "shapefile" and att.frame equals NULL, then att.frame is created from the dbf file(s) in the working directory. If src.frame equals "sp.object" and att.frame equals NULL, then att.frame is created from the sp object. If src.frame equals "att.frame", then att.frame must include columns that contain x-coordinates and y-coordinates for each element in the frame. The default is NULL.

id

a character string containing the name of the column from att.frame that identifies the ID value for each element in the frame. If id equals NULL, a column named "id" that contains values from one through the number of rows in att.frame is added to att.frame. The default is NULL.

xcoord

a character string containing the name of the column from att.frame that identifies x-coordinates when src.frame equals "att.frame". If xcoord equals NULL, then xcoord is given the value "x". The default is NULL.

ycoord

a character string containing the name of the column from att.frame that identifies y-coordinates when src.frame equals "att.frame". If ycoord equals NULL, then ycoord is given the value "y". The default is NULL.

stratum

a character string containing the name of the column from att.frame that identifies stratum membership for each element in the frame. If stratum equals NULL, the design is unstratified, and a column named "stratum" (with all its elements equal to the stratum name specified in design) is added to att.frame. The default is NULL.

mdcaty

a character string containing the name of the column from att.frame that identifies the unequal probability category for each element in the frame. The default is NULL.

startlev

initial number of hierarchical levels to use for the GRTS grid, which must be less than or equal to maxlev (if maxlev is specified) and cannot be greater than 11. The default is NULL.

maxlev

maximum number of hierarchical levels to use for the GRTS grid, which cannot be greater than 11. The default is 11.

maxtry

maximum number of iterations for randomly generating a point within a grid cell to select a site when type.frame equals "area". The default is 1000.

shift.grid

option to randomly shift the hierarchical grid, where TRUE means shift the grid and FALSE means do not shift the grid, which is useful if one desires strict spatial stratification by hierarchical grid cells. The default is TRUE.

do.sample

named vector that provides the option controlling sample selection for each stratum, where TRUE means select a sample from a stratum and FALSE means return the sample frame for a stratum in reverse hierarchical order. Note that FALSE can only be used when type.frame equals "points" and seltype equals "Equal". Names for the vector must match the names in design. If the vector is not named, then the names in design are used. The default is TRUE for each stratum.

shapefile

option to create a shapefile containing the survey design information, where TRUE equals create a shapefile and FALSE equals do not create a shapefile. The default is TRUE.

prjfilename

name (without any extension) of the projection file for the input shapefile, which is use to name the projection file for the output shapefile. The default is NULL.

out.shape

name (without any extension) of the output shapefile containing the survey design information. The default is "sample".

Details

The GRTS survey design process selects a spatially balanced sample based on the survey design specification.

Function dsgnsum(), can be used to summarize the sites selected for a survey design.

Value

An sp package object containing the survey design information and any additional attribute variables that were provided. The object is assigned class "SpatialPointsDataFrame". For further information regarding the output object, see documentation for the sp package. Optionally, a shapefile can be created that contains the survey design information.

Author(s)

Tony Olsen Olsen.Tony@epa.gov
Tom Kincaid Kincaid.Tom@epa.gov

References

Stevens, D.L., Jr., and A.R. Olsen. (2004). Spatially-balanced sampling of natural resources. Journal of the American Statistical Association 99, 262-278.

See Also

grtspts grtslin grtsarea albersgeod dsgnsum

Examples

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## Not run: 
The following example will select a sample from an area resource.  The design
includes two strata.  For Stratum 1, an equal probability sample of size 50
will be selected for a single panel.  For Stratum 2, an unequal probability
sample of size 50 will be selected for each of two panels.  The sample for
Stratum 2 will be approportioned into samples of size 25 for each of four
unequal probability categories.  In addition both strata will include
oversamples (size 10 for Stratum 1 and size 75 for Stratum 2).  It is assumed
that a shapefile defining the polygons for the area resource is located in the
folder from which R is started.  Attribute data for the design will be read
from the dbf file of the shapefile, which is assumed to have variables named
"test.stratum" and "test.mdcaty" that specify stratum membership value and
unequal probability category, respectively, for each record in the shapefile.
A shapefile named "test.sample" containing the survey design information will
be created.
test.design <- list("Stratum 1"=list(panel=c(Panel=50), seltype="Equal",
   over=10), "Stratum 2"=list(panel=c("Panel One"=50, "Panel Two"=50),
   seltype="Unequal", caty.n=c(CatyOne=25, CatyTwo=25, CatyThree=25,
   CatyFour=25), over=75))
test.attframe <- read.dbf("test.shapefile")
test.sample <- grts(design=test.design, DesignID="Test.Site", type.frame="area",
   src.frame="shapefile", in.shape="test.shapefile", att.frame=test.attframe,
   stratum="test.stratum", mdcaty="test.mdcaty", shapefile=TRUE,
   out.shape="test.sample")

## End(Not run)

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