cont_cdftest {spsurvey}

Cumulative distribution function (CDF) inference for a probability survey

Description

This function organizes input and output for conducting inference regarding cumulative distribution functions (CDFs) generated by a probability survey. For every response variable and every subpopulation (domain) variable, differences between CDFs are tested for every pair of subpopulations within the domain. Data input to the function can be either a single survey or multiple surveys (two or more). If the data contain multiple surveys, then the domain variables will reference those surveys and (potentially) subpopulations within those surveys. 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, adjusted Wald, Rao-Scott first order corrected (mean eigenvalue corrected), and Rao-Scott second order corrected (Satterthwaite corrected) test statistics. The default test statistic is the adjusted Wald statistic. The input data argument can be either a data frame or a simple features (sf) object. If an sf object is used, coordinates are extracted from the geometry column in the object, arguments xcoord and ycoord are assigned values "xcoord" and "ycoord", respectively, and the geometry column is dropped from the object.

Usage

cont_cdftest(
  dframe,
  vars,
  subpops = NULL,
  surveyID = NULL,
  siteID = "siteID",
  weight = "weight",
  xcoord = NULL,
  ycoord = NULL,
  stratumID = NULL,
  clusterID = NULL,
  weight1 = NULL,
  xcoord1 = NULL,
  ycoord1 = NULL,
  sizeweight = FALSE,
  sweight = NULL,
  sweight1 = NULL,
  fpc = NULL,
  popsize = NULL,
  vartype = "Local",
  jointprob = "overton",
  testname = "adjWald",
  nclass = 3
)

Arguments

dframe

Data frame containing survey design variables, response variables, and subpopulation (domain) variables.

vars

Vector composed of character values that identify the names of response variables in the dframe data frame.

subpops

Vector composed of character values that identify the names of subpopulation (domain) variables in the dframe data frame. If a value is not provided, the value "All_Sites" is assigned to the subpops argument and a factor variable named "All_Sites" that takes the value "All Sites" is added to the dframe data frame. The default value is NULL.

surveyID

Character value providing name of the survey ID variable in the dframe data frame. If this argument equals NULL, then the dframe data frame contains data for a single survey. The default value is NULL.

siteID

Character value providing name of the site ID variable in the dframe data frame. For a two-stage sample, the site ID variable identifies stage two site IDs. The default value is "siteID".

weight

Character value providing name of the survey design weight variable in the dframe data frame. For a two-stage sample, the weight variable identifies stage two weights. The default value is "weight".

xcoord

Character value providing name of the x-coordinate variable in the dframe data frame. For a two-stage sample, the x-coordinate variable identifies stage two x-coordinates. Note that x-coordinates are required for calculation of the local mean variance estimator. The default value is NULL.

ycoord

Character value providing name of the y-coordinate variable in the dframe data frame. For a two-stage sample, the y-coordinate variable identifies stage two y-coordinates. Note that y-coordinates are required for calculation of the local mean variance estimator. The default value is NULL.

stratumID

Character value providing name of the stratum ID variable in the dframe data frame. The default value is NULL.

clusterID

Character value providing the name of the cluster (stage one) ID variable in the dframe data frame. Note that cluster IDs are required for a two-stage sample. The default value is NULL.

weight1

Character value providing name of the stage one weight variable in the dframe data frame. The default value is NULL.

xcoord1

Character value providing the name of the stage one x-coordinate variable in the dframe data frame. Note that x coordinates are required for calculation of the local mean variance estimator. The default value is NULL.

ycoord1

Character value providing the name of the stage one y-coordinate variable in the dframe data frame. Note that y-coordinates are required for calculation of the local mean variance estimator. The default value is NULL.

sizeweight

Logical value that indicates whether size weights should be used during estimation, where TRUE uses size weights and FALSE does not use size weights. To employ size weights for a single-stage sample, a value must be supplied for argument weight. To employ size weights for a two-stage sample, values must be supplied for arguments weight and weight1. The default value is FALSE.

sweight

Character value providing the name of the size weight variable in the dframe data frame. For a two-stage sample, the size weight variable identifies stage two size weights. The default value is NULL.

sweight1

Character value providing name of the stage one size weight variable in the dframe data frame. The default value is NULL.

fpc

Object that specifies values required for calculation of the finite population correction factor used during variance estimation. The object must match the survey design in terms of stratification and whether the design is single-stage or two-stage. For an unstratified design, the object is a vector. The vector is composed of a single numeric value for a single-stage design. For a two-stage unstratified design, the object is a named vector containing one more than the number of clusters in the sample, where the first item in the vector specifies the number of clusters in the population and each subsequent item specifies the number of stage two units for the cluster. The name for the first item in the vector is arbitrary. Subsequent names in the vector identify clusters and must match the cluster IDs. For a stratified design, the object is a named list of vectors, where names must match the strata IDs. For each stratum, the format of the vector is identical to the format described for unstratified single-stage and two-stage designs. Note that the finite population correction factor is not used with the local mean variance estimator.

Example fpc for a single-stage unstratified survey design:

⁠fpc <- 15000⁠

Example fpc for a single-stage stratified survey design:

⁠fpc <- list( Stratum_1 = 9000, Stratum_2 = 6000) ⁠

Example fpc for a two-stage unstratified survey design:

⁠fpc <- c( Ncluster = 150, Cluster_1 = 150, Cluster_2 = 75, Cluster_3 = 75, Cluster_4 = 125, Cluster_5 = 75) ⁠

Example fpc for a two-stage stratified survey design:

⁠fpc <- list( Stratum_1 = c( Ncluster_1 = 100, Cluster_1 = 125, Cluster_2 = 100, Cluster_3 = 100, Cluster_4 = 125, Cluster_5 = 50), Stratum_2 = c( Ncluster_2 = 50, Cluster_1 = 75, Cluster_2 = 150, Cluster_3 = 75, Cluster_4 = 75, Cluster_5 = 125)) ⁠

popsize

Object that provides values for the population argument of the calibrate or postStratify functions in the survey package. If a value is provided for popsize, then either the calibrate or postStratify function is used to modify the survey design object that is required by functions in the survey package. Whether to use the calibrate or postStratify function is dictated by the format of popsize, which is discussed below. Post-stratification adjusts the sampling and replicate weights so that the joint distribution of a set of post-stratifying variables matches the known population joint distribution. Calibration, generalized raking, or GREG estimators generalize post-stratification and raking by calibrating a sample to the marginal totals of variables in a linear regression model. For the calibrate function, the object is a named list, where the names identify factor variables in the dframe data frame. Each element of the list is a named vector containing the population total for each level of the associated factor variable. For the postStratify function, the object is either a data frame, table, or xtabs object that provides the population total for all combinations of selected factor variables in the dframe data frame. If a data frame is used for popsize, the variable containing population totals must be the last variable in the data frame. If a table is used for popsize, the table must have named dimnames where the names identify factor variables in the dframe data frame. If the popsize argument is equal to NULL, then neither calibration nor post-stratification is performed. The default value is NULL.

Example popsize for calibration:

⁠popsize <- list( Ecoregion = c( East = 750, Central = 500, West = 250), Type = c( Streams = 1150, Rivers = 350)) ⁠

Example popsize for post-stratification using a data frame:

⁠popsize <- data.frame( Ecoregion = rep(c("East", "Central", "West"), rep(2, 3)), Type = rep(c("Streams", "Rivers"), 3), Total = c(575, 175, 400, 100, 175, 75)) ⁠

Example popsize for post-stratification using a table:

⁠popsize <- with(MySurveyFrame, table(Ecoregion, Type))⁠

Example popsize for post-stratification using an xtabs object:

⁠popsize <- xtabs(~Ecoregion + Type, data = MySurveyFrame)⁠

vartype

Character value providing the choice of the variance estimator, where "Local" indicates the local mean estimator, "SRS" indicates the simple random sampling estimator, "HT" indicates the Horvitz-Thompson estimator, and "YG" indicates the Yates-Grundy estimator. The default value is "Local".

jointprob

Character value providing the choice of joint inclusion probability approximation for use with Horvitz-Thompson and Yates-Grundy variance estimators, where "overton" indicates the Overton approximation, "hr" indicates the Hartley-Rao approximation, and "brewer" equals the Brewer approximation. The default value is "overton".

testname

Name of the test statistic to be reported in the output data frame. Choices for the name are: "Wald", "adjWald", "RaoScott_First", and "RaoScott_Second", which correspond to the Wald statistic, adjusted Wald statistic, Rao-Scott first-order corrected statistic, and Rao-Scott second-order corrected statistic, respectively. The default is "adjWald".

nclass

Number of classes into which the CDFs will be divided (binned), which must equal at least 2. The default is 3.

Value

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.

Author(s)

Tom Kincaid [e-mail]

See Also

cdf_plot

for visualizing CDF plots

cont_cdfplot

for making CDF plots output to pdfs

Examples

n <- 200
mysiteID <- paste("Site", 1:n, sep = "")
dframe <- data.frame(
  siteID = mysiteID,
  wgt = runif(n, 10, 100),
  xcoord = runif(n),
  ycoord = runif(n),
  stratum = rep(c("Stratum1", "Stratum2"), n / 2),
  Resource_Class = sample(c("Agr", "Forest", "Urban"), n, replace = TRUE)
)
ContVar <- numeric(n)
tst <- dframe$Resource_Class == "Agr"
ContVar[tst] <- rnorm(sum(tst), 10, 1)
tst <- dframe$Resource_Class == "Forest"
ContVar[tst] <- rnorm(sum(tst), 10.1, 1)
tst <- dframe$Resource_Class == "Urban"
ContVar[tst] <- rnorm(sum(tst), 10.5, 1)
dframe$ContVar <- ContVar
myvars <- c("ContVar")
mysubpops <- c("Resource_Class")
mypopsize <- data.frame(
  Resource_Class = rep(c("Agr", "Forest", "Urban"), rep(2, 3)),
  stratum = rep(c("Stratum1", "Stratum2"), 3),
  Total = c(2500, 1500, 1000, 500, 600, 450)
)
cont_cdftest(dframe,
  vars = myvars, subpops = mysubpops, siteID = "siteID",
  weight = "wgt", xcoord = "xcoord", ycoord = "ycoord",
  stratumID = "stratum", popsize = mypopsize, testname = "RaoScott_First"
)