This function organizes input and output for conducting inference regarding cumulative distribution functions (CDFs) generated by a probability survey. Input can be either an object of class spsurvey.analysis (see the documentation for function spsurvey.analysis) or through use of the other arguments to this function.
cont.cdftest(sites=NULL, subpop=NULL, design=NULL, data.cont=NULL, popsize=NULL,
popcorrect=FALSE, pcfsize=NULL, N.cluster=NULL, stage1size=NULL,
sizeweight=FALSE, vartype="Local", testname="Wald_F", nclass=3,
spsurvey.obj=NULL)a data frame consisting of two variables: the first variable is site IDs, and the second variable is a logical vector indicating which sites to use in the analysis. If spsurvey.obj is not provided, then this argument is required. The default is NULL.
a data frame describing sets of populations and subpopulations for which estimates will be calculated. The first variable is site IDs. Each subsequent variable identifies a Type of population, where the variable name is used to identify Type. A Type variable identifies each site with one of the subpopulations of that Type. If spsurvey.obj is not provided, then this argument is required. The default is NULL.
a data frame consisting of design variables. If spsurvey.obj is not provided, then this argument is required. The default is NULL. Variables should be named as follows: siteID = site IDs wgt = final adjusted weights, which are either the weights for a single-stage sample or the stage two weights for a two-stage sample xcoord = x-coordinates for location, which are either the x-coordinates for a single-stage sample or the stage two x-coordinates for a two-stage sample ycoord = y-coordinates for location, which are either the y-coordinates for a single-stage sample or the stage two y-coordinates for a two-stage sample stratum = the stratum codes cluster = the stage one sampling unit (primary sampling unit or cluster) codes wgt1 = final adjusted stage one weights xcoord1 = the stage one x-coordinates for location ycoord1 = the stage one y-coordinates for location support = support values - the value one (1) for a site from a finite resource or the measure of the sampling unit associated with a site from an extensive resource, which is required for calculation of finite and continuous population correction factors swgt = size-weights, which is the stage two size-weight for a two- stage sample swgt1 = stage one size-weights
a data frame of continuous response variables. The first variable is site IDs. Subsequent variables are response variables. Missing data (NA) is allowed. If spsurvey.obj is not provided, then this argument is required. The default is NULL.
known size of the resource, which is used to perform ratio adjustment to estimators expressed using measurement units for the resource. For a finite resource, this argument is either the total number of sampling units or the known sum of size-weights. For an extensive resource, this argument is the measure of the resource, i.e., either known total length for a linear resource or known total area for an areal resource. The argument must be in the form of a list containing an element for each population Type in the subpop data frame, where NULL is a valid choice for a population Type. The list must be named using the column names for the population Types in subpop. If a population Type doesn't contain subpopulations, then each element of the list is either a single value for an unstratified sample or a vector containing a value for each stratum for a stratified sample, where elements of the vector are named using the stratum codes. If a population Type contains subpopulations, then each element of the list is a list containing an element for each subpopulation, where the list is named using the subpopulation names. The element for each subpopulation will be either a single value for an unstratified sample or a named vector of values for a stratified sample. The default is NULL. Example popsize for a stratified sample: popsize = list("Pop 1"=c("Stratum 1"=750, "Stratum 2"=500, "Stratum 3"=250), "Pop 2"=list("SubPop 1"=c("Stratum 1"=350, "Stratum 2"=250, "Stratum 3"=150), "SubPop 2"=c("Stratum 1"=250, "Stratum 2"=150, "Stratum 3"=100), "SubPop 3"=c("Stratum 1"=150, "Stratum 2"=150, "Stratum 3"=75)), "Pop 3"=NULL) Example popsize for an unstratified sample: popsize = list("Pop 1"=1500, "Pop 2"=list("SubPop 1"=750, "SubPop 2"=500, "SubPop 3"=375), "Pop 3"=NULL)
a logical value that indicates whether finite or continuous population correction factors should be employed during variance estimation, where TRUE = use the correction factor and FALSE = do not use the correction factor. The default is FALSE. To employ the correction factor for a single-stage sample, values must be supplied for argument pcfsize and for the support variable of the design argument. To employ the correction factor for a two-stage sample, values must be supplied for arguments N.cluster and stage1size, and for the support variable of the design argument.
size of the resource, which is required for calculation of finite and continuous population correction factors for a single-stage sample. For a stratified sample this argument must be a vector containing a value for each stratum and must have the names attribute set to identify the stratum codes. The default is NULL.
the number of stage one sampling units in the resource, which is required for calculation of finite and continuous population correction factors for a two-stage sample. For a stratified sample this variable must be a vector containing a value for each stratum and must have the names attribute set to identify the stratum codes. The default is NULL.
size of the stage one sampling units of a two-stage sample, which is required for calculation of finite and continuous population correction factors for a two-stage sample and must have the names attribute set to identify the stage one sampling unit codes. For a stratified sample, the names attribute must be set to identify both stratum codes and stage one sampling unit codes using a convention where the two codes are separated by the & symbol, e.g., "Stratum 1&Cluster 1". The default is NULL.
a logical value that indicates whether size-weights should be used in the analysis, where TRUE = use the size-weights and FALSE = do not use the size-weights. The default is FALSE.
the choice of variance estimator, where "Local" = local mean estimator and "SRS" = SRS estimator. The default is "Local".
name of the test statistic to be reported in the output data frame. Choices for the name are: "Wald", "Wald\_F", "Mean\_Eigenvalue", "Mean\_Eigenvalue\_F", "Satterthwaite", and "Satterthwaite\_F". The default is "Wald\_F".
number of classes into which the CDFs will be divided (binned), which must equal at least two. The default is 3.
A list of class spsurvey.analysis that was produced by the function spsurvey.analysis. Depending on input to that function, some elements of the list may be NULL. The default is NULL.
A data frame of CDF test results for all pairs of subpopulations within each population Type for every response variable. The data frame includes the test statistic specified by argument testname plus its degrees of freedom and p-value.
For every response variable and every population Type, differences between CDFs are tested for every pair of subpopulations within a Type. The inferential procedures divide the CDFs into a discrete set of intervals (classes) and then utilize procedures that have been developed for analysis of categorical data from probability surveys. Choices for inference are the Wald, Rao-Scott first order corrected (mean eigenvalue corrected), and Rao-Scott second order corrected (Satterthwaite corrected) test statistics. Both standard versions of the three statistics, which are distributed as Chi-squared random variables, and alternate version of the statistics, which are distributed as F random variables, are available. The default test statistic is the F distribution version of the Wald statistic.
Kincaid, T.M. (2000). Testing for differences between cumulative distribution functions from complex environmental sampling surveys. In 2000 Proceeding of the Section on Statistics and the Environment, American Statistical Association, Alexandria, VA.
# NOT RUN {
n <- 200
mysiteID <- paste("Site", 1:n, sep="")
mysites <- data.frame(siteID=mysiteID, Active=rep(TRUE, n))
mysubpop <- data.frame(siteID=mysiteID, Resource_Class=sample(c("Agr",
"Forest", "Urban"), n, replace=TRUE))
mydesign <- data.frame(siteID=mysiteID, wgt=runif(n, 10, 100),
xcoord=runif(n), ycoord=runif(n), stratum=rep(c("Stratum1",
"Stratum2"), n/2))
mypopsize <- list(Resource_Class=list(Agr=c(Stratum1=2500, Stratum2=1500),
Forest=c(Stratum1=1000, Stratum2=500), Urban=c(Stratum1=600, Stratum2=450)))
ContVar <- numeric(n)
tst <- mysubpop$Resource_Class == "Agr"
ContVar[tst] <- rnorm(sum(tst), 10, 1)
tst <- mysubpop$Resource_Class == "Forest"
ContVar[tst] <- rnorm(sum(tst), 10.1, 1)
tst <- mysubpop$Resource_Class == "Urban"
ContVar[tst] <- rnorm(sum(tst), 10.5, 1)
mydata.cont <- data.frame(siteID=mysiteID, ContVar=ContVar)
cont.cdftest(sites=mysites, subpop=mysubpop, design=mydesign,
data.cont=mydata.cont, popsize=mypopsize, testname="Mean_Eigenvalue")
# }
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