Package 'smwrQW'

Description

A collection of tools for the analysis of left- and multiply-censored data that focuses on the analysis of water-quality data.

Details

Modern water-quality information requires much more that a value and remark code to characterize the data. The tools in this library focus on the "qw" class, which store the value and the remark code, but also information about the reporting level, the units, the methods of analysis analysis, and the analyte itself.
Some specialized analytical tools for left-only censored data, requiring objects of class "lcens" have been developed and are included in this library. Other analytical tools for multiply- or any censored data are alos included. The tools include automatic conversion of "qw" data into the "best" (left-only or multiply censored) format.
Need a general description of the tools by group–a brief synopsis of the OFR.

References

Lorenz, D.L., in preparation.

Description

Extracts or subsets a vector: methods for "lcens," "mcens," and "qw" data.

Usage

## S3 method for class 'lcens'
x[i, ...]

## S3 method for class 'mcens'
x[i, ...]

## S3 method for class 'qw'
x[i, ...]

## S3 method for class 'qw'
subset(x, subset, ...)

Arguments

Details

The values for i can be either numeric indexes or logical.
Valid slot names are "remark.codes," "reporting.level," "reporting.method," "reporting.units," "analyte.method," "analyte.name," and "unique.code."

Value

A subset of the object x.

Note

In general, assignment of specific values should not be done using the "[" extraction operator because it does not modify the meta data assiciated with a value. But any value can be set to NA by treating the value as a matrix and setting the equivalent of the row to NA. See the example below.

See Also

[.qw

Examples

Xcens <- as.lcens(c(1, 2, 3, 4), 2)
# Extract the 3rd value
Xcens[3]
# Change the 3rd value to NA and print the data
Xcens[3,] <- NA
Xcens

Description

Checks for the possibility that two values are equal. If there is any overlap in range, they are considered possibly equal and TRUE is returned, otherwise FALSE is returned.

Usage

e1 %~=% e2

Arguments

Details

Missing values are permitted in either e1 or e2. wherever either are missing the returned element is set to NA.

Value

A logical vector that matches the length of the longer of e1 or e2, set to TRUE is there is overlap in the values, and FALSE otherwise.

See Also

Compare,qw,numeric-method

Examples

as.mcens(1, 2) %~=% 0.5
as.mcens(1, 2) %~=% 1.5
as.mcens(1, 2) %~=% 2.5

Description

Adds or subtracts water-quality data while trying to maintain the integrity of the data.

Usage

add(..., analyte, pcode = "", gt0 = TRUE)

Arguments

Details

The ... arguments must not be named in the call. Only objects of class "qw" or "numeric" are allowed. To perform a subtraction, simply preceed the argument with the unary - sign in the call. The first argument must be a positive valued object of class "qw."

Value

An object of class "qw" that is the result of the requested operations.

Description

Some limited arithmetic methods are possible and well-defined for censored data. Water-quality data require specialized functions to maintain data integrity.

Usage

## S4 method for signature 'lcens,numeric'
Arith(e1, e2)

## S4 method for signature 'numeric,lcens'
Arith(e1, e2)

## S4 method for signature 'lcens,lcens'
Arith(e1, e2)

## S4 method for signature 'mcens,numeric'
Arith(e1, e2)

## S4 method for signature 'numeric,mcens'
Arith(e1, e2)

## S4 method for signature 'mcens,mcens'
Arith(e1, e2)

## S4 method for signature 'qw,numeric'
Arith(e1, e2)

## S4 method for signature 'numeric,qw'
Arith(e1, e2)

## S4 method for signature 'qw,qw'
Arith(e1, e2)

Arguments

Value

An object of the appropriate class for the data.

See Also

add, ratio

Examples

as.lcens(c(1, 3), 2) + 1
as.lcens(c(1, 3), 2) * 2

Description

Creates character representations of censored and water-quality data: methods for "lcens," "mcens," and "qw" data.

Usage

## S3 method for class 'lcens'
as.character(x, ...)

## S3 method for class 'mcens'
as.character(x, ...)

## S3 method for class 'qw'
as.character(x, ...)

Arguments

Value

Creates a character representation of x.

Description

Creates data frames from censored and water-quality data: methods for "lcens," "mcens," and "qw" data.

Usage

## S3 method for class 'lcens'
as.data.frame(x, row.names = NULL, optional = FALSE, ...,
  nm = deparse(substitute(x)))

## S3 method for class 'mcens'
as.data.frame(x, row.names = NULL, optional = FALSE, ...,
  nm = deparse(substitute(x)))

## S3 method for class 'qw'
as.data.frame(x, row.names = NULL, optional = FALSE, ...,
  nm = deparse(substitute(x)), expand = FALSE)

Arguments

Value

A data frame constructred from x.

See Also

data.frame

Description

Converts data to numeric values: method for "qw" data.

Usage

## S3 method for class 'qw'
as.double(x, ...)

Arguments

Value

A numeric representation of x, using a method commonly refered to as simple substitution.

Note

The process of simple substitution proceeds in 4 steps for each kind of censoring: none, interval, left and right. First uncensored data are retained as is. Interval-censored data are converted by computing the mid rnge. Left-censored data are converted sequentially from the lowest censoring level, which is set to 1/2 the reporting level, any subsequent levels are replaced by the mean of all values less than the current reporting level. Conversion of right-censored data are not implemented in the current version and result in an error.

The function as.double is executed for as.numeric.

See Also

fillIn

Examples

## Create a simple qw object 
Test.qw <- as.qw(c(1,2,3,2,4,4), c("<", "<", "<", " ", " ", " "), "", NA_real_,
"Miss", "None", "Mine", "TEST", "")
as.double(Test.qw)
as.numeric(Test.qw)

Description

Converts data to a left-censored data (lcens) object: various methods.

Usage

as.lcens(values, detlim, censor.codes)

## S4 method for signature 'lcens,missing,missing'
as.lcens(values, detlim, censor.codes)

## S4 method for signature 'numeric,missing,missing'
as.lcens(values, detlim, censor.codes)

## S4 method for signature 'numeric,numeric,missing'
as.lcens(values, detlim, censor.codes)

## S4 method for signature 'numeric,numeric,logical'
as.lcens(values, detlim, censor.codes)

## S4 method for signature 'numeric,numeric,character'
as.lcens(values, detlim, censor.codes)

## S4 method for signature 'numeric,missing,logical'
as.lcens(values, detlim, censor.codes)

## S4 method for signature 'numeric,missing,character'
as.lcens(values, detlim, censor.codes)

## S4 method for signature 'qw,missing,missing'
as.lcens(values, detlim, censor.codes)

## S4 method for signature 'qw,numeric,missing'
as.lcens(values, detlim, censor.codes)

## S4 method for signature 'character,missing,missing'
as.lcens(values, detlim, censor.codes)

Arguments

Value

An S4 object of class "lcens." These objects are the basis for the analysis of left-censored data.

Note

All methods force values to be no less than the corresponding detlim. All values that are less than detlim are treated as left-censored values at detlim. This ensures unbiased analytical results.

References

Lorenz, D.L., in preparation

See Also

as.mcens

Examples

## The first value is censored at 2
as.lcens(c(1,3), 2)
## Set the first value to censored at that level and the detection limit is
# carried forward
as.lcens(c(1,3), censor.codes=c("<", ""))
# For combined remark and values:
as.lcens(c("<1", "1", "<1", "1", "2"))

Description

Converts data to a multiply-censored data (mcens) object: various methods.

Usage

as.mcens(lower.val, upper.val, censor.codes)

## S4 method for signature 'mcens,missing,missing'
as.mcens(lower.val, upper.val, censor.codes)

## S4 method for signature 'lcens,missing,missing'
as.mcens(lower.val, upper.val, censor.codes)

## S4 method for signature 'numeric,missing,missing'
as.mcens(lower.val, upper.val, censor.codes)

## S4 method for signature 'numeric,numeric,missing'
as.mcens(lower.val, upper.val, censor.codes)

## S4 method for signature 'numeric,missing,numeric'
as.mcens(lower.val, upper.val, censor.codes)

## S4 method for signature 'numeric,missing,integer'
as.mcens(lower.val, upper.val, censor.codes)

## S4 method for signature 'numeric,missing,character'
as.mcens(lower.val, upper.val,
  censor.codes)

## S4 method for signature 'qw,missing,missing'
as.mcens(lower.val, upper.val, censor.codes)

## S4 method for signature 'character,missing,missing'
as.mcens(lower.val, upper.val,
  censor.codes)

Arguments

Details

In keeping with the logic of Surv, NA is permitted to indicate left- or right-censored data. If both are NA, then the observation is treated as missing.

Value

An S4 object of class "mcens." These objects are the basis for the analysis of censored data that are not strictly left censored.

References

Lorenz, D.L., in preparation

See Also

Surv

Examples

## Create one of each type of censoring, including uncensored
# the last value is missing
as.mcens(c(-Inf, 2, 2, 5, NA), c(1, 2, 3, Inf, NA))
# For combined remark and values:
as.mcens(c("<1", "1", ">3", "1", "2"))

Description

Converts data and meta data to a water-quality data (qw) object: various methods.

Usage

as.qw(values, remark.codes, value.codes, reporting.level, reporting.method,
  reporting.units, analyte.method, analyte.name, unique.code, value2)


  ## S4 method for signature 
## 'numeric,
##   character,
##   character,
##   numeric,
##   character,
##   character,
##   character,
##   character,
##   character,
##   missing'
as.qw(values,
  remark.codes, value.codes, reporting.level, reporting.method, reporting.units,
  analyte.method, analyte.name, unique.code, value2)


  ## S4 method for signature 
## 'numeric,
##   character,
##   character,
##   numeric,
##   character,
##   character,
##   character,
##   character,
##   character,
##   numeric'
as.qw(values,
  remark.codes, value.codes, reporting.level, reporting.method, reporting.units,
  analyte.method, analyte.name, unique.code, value2)

Arguments

Details

Two methods for constructing water-quality data are defined in the current version. The first method works well for un-, left-, and right-censored data where the remark code and value can completely define the numeric values. The second method works for any censored data, including interval-censored data, where an upper and lower range of values are required. For the second method, values is the lower limit of the range and for left-censored data, may be either -Inf, NA, or 0. If -Inf, then the value is treated as strictly left-censored, otherwise, the lower limit is set to 0, which corresponds to the traditional interpretation of left-censored water-quality data. For the second method, value2 is the upper limit and for right-censored data will always be set to Inf.

Value

An object of class "qw" that contains the numeric data in a two-column matrix and the meta data as additional slot information.

Note

The class "qw" is intended to be a flexible and user-friendly way to store and manage water-quality data. The meta data that are stored with the numeric and remark data are essential for unbiased statistical analysis and for reducing other errors in interpretation or computation.

Objects of class "qw" also have a slot named "rounding" that controls how the data are roudend when printed. That slot is an integer vector of length 2, the first element is the maximum number of significant figures and the second is the maximum number of decimal places to show. The default value used by as.qw is c(2L,3L). It can be changed by specifically modifying the slot value.

References

Lorenz, D.L., in preparation

See Also

importNWISqw

Description

Atrazine Data A dataset of atrazine samples, replicates, and blanks collected by the U.S. Geological Survey from October 1, 2001 through September 30, 2012.

Usage

atrazine.df

Format

Data frame with 13106 rows and 12 columns

Details

The sample medium codes are regular water-quality sample, WS; replicate water-quality sample, WSQ; and field blank, OAQ. The sample type codes are regular sample with no QAQC sample, 9; regular sample with QAQC or the replicate sample, 7; and field blank , 2.

Source

Data retreived from the national water information system and processed by Jeffery Martin and Laura Medalie of the U.S. Geological Survey.

Examples

data(atrazine.df)
# How many different kinds of samples?
with(atrazine.df, table(MEDIUM_CD))
# Now many stations?
with(atrazine.df, table(staid))

Description

Atrazine Reporting Data A dataset of the reporting and detection levels for atrazine from the U.S. Geological Survey National Water Quality Lab.

Usage

atrazine.dl

Format

Data frame with 23 rows and 9 columns

Source

Data retrieved from the U.S. Geological Survey National Water Quality Lab reporting level database on January 4, 2016.

Examples

data(atrazine.dl)
# What methods; 39632 is the parameter code for atrazine
with(atrazine.dl, unique(TestID))

Description

Atrazine Spike Data A dataset of atrazine environmental and spike samples collected by the U.S. Geological Survey from October 1, 2001 through September 30, 2012.

Usage

atrazine.spk

Format

Data frame with 596 rows and 22 columns

Details

A map of the study units can be found at https://water.usgs.gov/nawqa/nawqamap.html. Some of the study unit codes represent combined study units from that map.

Source

Data retreived from the national water information system and processed by Jeffery Martin of the U.S. Geological Survey.

Examples

data(atrazine.spk)
# The mean spike recovery
mean(atrazine.spk$Recovery)

Description

Produces an estimated or censored style box plot for truncated, Tukey, simple, or extended type box plot: methods for "lcens" and "qw" data. The Tukey type box plot requires an estimated style box plot.

Usage

## S3 method for class 'lcens'
boxPlot(..., group = NULL, Box = list(type = "truncated",
  show.counts = TRUE, censorbox = NA, censorstyle = "censored", nobox = 5, width
  = "Auto", fill = "none", truncated = c(10, 90)), yaxis.log = TRUE,
  yaxis.range = c(NA, NA), ylabels = "Auto", xlabels = "Auto",
  xlabels.rotate = FALSE, xtitle = "", ytitle = "", caption = "",
  margin = c(NA, NA, NA, NA))

## S3 method for class 'qw'
boxPlot(..., group = NULL, Box = list(type = "truncated",
  show.counts = TRUE, censorbox = NA, censorstyle = "censored", nobox = 5, width
  = "Auto", fill = "none", truncated = c(10, 90)), yaxis.log = TRUE,
  yaxis.range = c(NA, NA), ylabels = "Auto", xlabels = "Auto",
  xlabels.rotate = FALSE, xtitle = "", ytitle = "", caption = "",
  margin = c(NA, NA, NA, NA))

## S3 method for class 'data.frame'
boxPlot(..., group = NULL, Box = list(type =
  "truncated", show.counts = TRUE, censorbox = NA, censorstyle = "censored",
  nobox = 5, width = "Auto", fill = "none", truncated = c(10, 90)),
  yaxis.log = FALSE, yaxis.range = c(NA, NA), ylabels = "Auto",
  xlabels = "Auto", xlabels.rotate = FALSE, xtitle = "", ytitle = "",
  caption = "", margin = c(NA, NA, NA, NA))

Arguments

Details

If group is numeric, then the boxes will be plotted along a continuous numeric axis. Otherwise the x-axis will be discrete groups.

Value

Information about the graph.

Note

The censored style box plot truncates the boxplot at the largest value of the reporting level. The estimated style box plot estimates values for left-censored data and uses those estimates to construct the full boxplot; the range of estimated values is shown in gray. The maximum reporting level, except for some simple heuristics for identifying elevated reporting levels, is used for the censoring level when there are multiple reporting levels.

The fillIn function is used to estimate values that are censored. If yaxis.log is TRUE, then the "log ROS" method is used to estimate those values, otherwise, the "ROS" method is used. Occasionally, estimated values by fillIn will estimate values for censored data that are greater than the censoring level. In those cases, a red bar is drawn on the box plot at the largest estimated value.

The default method for data frames in smwrGraphs is replaced with a method that supports data frames that contain columns of class "qw" or "lcens."

See Also

fillIn

Examples

## Not run: 
set.seed(1932)
Xu <- rlnorm(32)
setPage("sq") # required page set up
boxPlot(as.lcens(Xu, 1.0))

## End(Not run)

Description

Computes the statistics for a left-censored data boxplot.

Usage

boxPlotCensStats(x, Box, yaxis.log)

Arguments

Value

Info to actually plot the boxplot.

Description

Combines arguments to form a vector for censored or water-quality data: methods for "cens," "mcens," and "qw" data. All arguments are coerced to a common type which is the type of the first argument, except for the qw method,

Usage

## S3 method for class 'lcens'
c(..., recursive = FALSE)

## S3 method for class 'mcens'
c(..., recursive = FALSE)

## S3 method for class 'qw'
c(..., recursive = FALSE)

Arguments

Value

A vector of an appropriate class.

Examples

c(as.lcens(c(1,3), 2), 2)

Description

Computes the maximum likelihood estimate of the correlation between two possibly left-censored vectors. It is equivalent the the Pearson product-moment correlation for uncensored data.

Usage

censCor(x, y, Full = TRUE, na.rm = TRUE)

Arguments

Details

Full may be either logical or a numeric vector. If Full is TRUE, then estimate the means and standard deviations for x and y. If Full is FALSE, use the initial maximum likelihood estimate for those statistics. Otherwise Full can be a named vector containing mnx, the mean for x; sdx, the standard deviation for x; mny, the mean for y; sdy, the standard deviation for y. Full can be set to FALSE if the optimization fails at large censoring levels or to improve processing speed for large sample sizes.

Value

A vector with these names:

References

Lyles, R.H., Williams, J.K., and Chuachoowong R., 2001, Correlating two viral load assays with known detection limits: Biometrics, v. 57 no. 4, p. 1238–1244.

Examples

# Simple no censoring
set.seed(450)
tmp.X <- rnorm(25)
tmp.Y <- tmp.X/2 + rnorm(25)
cor(tmp.X, tmp.Y)
censCor(tmp.X, tmp.Y)
# Some censoring
censCor(as.lcens(tmp.X, -1), as.lcens(tmp.Y, -1))

Description

Performs a test for differences in left-censored samples from 2 or more groups.

Usage

censKSample.test(x, groups, type = "Peto", data.names)

Arguments

Value

An object of class "htest."

Null Hypothesis

The null hypothesis is that the distributions in each group are not different from one another.

Note

The censKSample.test function use the survdiff function to test for differences. Helsel (2012) describes flipping the left-censored data so that small values become large and left-censored values become right-censored values and adapt nonparametric techniques from survival analysis.

Tableman and others (2004) state, "the Peto test emphasizes the beginning of the survival curve in that earlier failures receive larger weights. The log-rank test emphasizes the tail of the survival curve in that it gives equal weight to each failure." For flipped data, earlier failures translates to larger uncensored values. In general, the Peto test gives results that are more similar to the Wilcoxon test if all data are uncensored.

References

Helsel, D.R. 2012, Statistics for censored environmental data using Minitab and R: New York, Wiley, 324 p.

Peto, R., and Peto, J., 1972, Asymptotically efficient rank invariant test procedures (with discussion): Journal of the Royal Statistical Society, Series A v. 135, p. 185-206.

Prentice, R.L. 1978, Linear rank tests with right-censored data: Biometika, v 65, p 167-179.

Prentice, R.L., and Marke, P., 1979, A qualitative discrepancy between censored data rank tests: Biometrika, v. 35, p. 861-867.

Tableman, M., and Kim, J.S., 2004, Survival analysis using S—analysis of time-to-event data: Boca Raton, Fla., Chapman and Hall, 280 p.

See Also

survdiff, lcens-class

Examples

# Compare uncensored results
set.seed(69)
Xu <- rlnorm(22, 0, 1)
Yu <- rlnorm(22, .4, 1)
Zu <- rlnorm(22, 1, 1)
Gu <- factor(rep(c("X", "Y", "Z"), each=22))
censKSample.test(c(Xu, Yu, Zu), Gu)
kruskal.test(c(Xu, Yu, Zu), Gu)
# Censor the data at 1
censKSample.test(as.lcens(c(Xu, Yu, Zu), 1), Gu)

Description

Computes the mean and confidence limits of left-censored data.

Usage

censMean.CI(x, method = "log AMLE", CI = 0.9, bound = c("two.sided",
  "upper", "lower"), alpha = 0.4)

Arguments

Details

The methods available in the current version are "log MLE," "MLE," "log ROS," "ROS," "log AMLE," and "AMLE." The methods "log ROS," "log MLE," and "log AMLE" are described by Helsel (2012) and Helsel and Cohn (1988). The methods "ROS," "MLE," and "AMLE" are similar to the previous except that no log- and back-transforms are made on the data. For "log" methods, if any value in x is negative, then a warning is generated and the returned value contains missing values.

Value

A matrix of the mean, the lower confidence limit, the upper confidence limit, and the probability represented by the confidence interval.

Note

Helsel (2012) describes computing the confidence interval for the mean of normally dsitributed data in Sections 7.4.1 and 7.4.2; those approaches are used for method "MLE" and "AMLE." Helsel (2012) describes computing the confidence interval for the mean of lognormally dsitributed data in Sections 7.5.1 and 7.5.2; those approaches are used for method "log MLE" and "log AMLE." Helsel (2012) describes bootstrapping the confidence interval for the mean when method is "ROS" or "log ROS" in Section 7.6. For this function, the number of replicates is set to a value to guarantee at least 50 replicate values lie outside of the requested confidence interval. The percentage type confidence interval is reported.

References

Helsel, D.R. 2012, Statistics for censored environmental data using Minitab and R: New York, Wiley, 324 p.

See Also

censStats

Examples

## Generate a random lognormal sample
set.seed(221)
XX.rn <- rlnorm(30)
# Compare log AMLE and log ROS
censMean.CI(XX.rn, method="log AMLE", CI=.80)
censMean.CI(XX.rn, method="log ROS", CI=.80)
# check upper bound for AMLE
censMean.CI(XX.rn, method="log AMLE", CI=.90, bound="upper")

Description

Calculates the Maintenance Of Variance Extension, Type 1 (MOVE.1) for record extension by fitting a Line of Organic Correlation (LOC) regression model to left-censored data.

Usage

censMove.1(formula, data, subset, na.action, distribution = "normal")

Arguments

Details

The left- or right-hand side of the formula may be any numeric variable, just as with move.1 or a variable of class "lcens." The response variable must be the name of a column and not converted using as.lcens in the call.

If distribution is "normal," then the data in x and y are assumed to have a bivariate normal distribution. Otherwise, they are assumed to have a bivariate log-normal distribution and a logarithmic transform is applied to both x and y before analysis. The natural logarithm is used if distribution is "lognormal" and the commmon logarithm is used if distribution is "commonlog."

Value

An object of class "move.1" as decribed in the documentation for move.1. Except, there are no fitted.values or residuals components, the values of x and y include estimated values (See Note), and components cx and cy, which indicate left-censoring are included.

Note

Because predictions are made using the predict method for class "move.1," and do not expect censored values, the explanatory variable in formula must refer to a column in data and not converted using the as.lcens function; the user must convert the explanatory variable column to class "lcens" before using censMove.1.

The components x and y are the actual values if the data are uncensored. If y is censored and x is not censored, then y is the expected value of y, given its censored value and the value of x and likewise for x censored and y not censored. If both are cesnored, then the values are computed from their expected values given the censored value without respect to any condition of the other.

References

will need some.

See Also

move.1

Examples

## Not run: 
library(smwrData)
data(IonBalance)
# Build model for non missing Alkalinity
move.1(Anion_sum ~ Cation_sum, data=IonBalance, 
 subset=abs(Pct_Diff) < 10) 
# Compare to censored
censMove.1(Anion_sum ~ Cation_sum, data=IonBalance, 
 subset=abs(Pct_Diff) < 10) 
# The difference in standard deviations is due to using sd/MLE 

## End(Not run)

Description

Performs a multiple nonparametric comparison test among groups of left-censored data.

Usage

censMulticomp.test(x, groups, method = "holm", alpha = 0.05)

Arguments

Value

An object of class "censMCT."

Note

need some kind of general description.

References

Helsel, D.R. 2012, Statistics for censored environmental data using Minitab and R: New York, Wiley, 324 p.

See Also

censKSample.test

Examples

set.seed(69)
Xu <- rlnorm(22, 0, 1)
Yu <- rlnorm(22, .4, 1)
Zu <- rlnorm(22, 1, 1)
Gu <- factor(rep(c("X", "Y", "Z"), each=22))
# Censor the data at 1
censKSample.test(as.lcens(c(Xu, Yu, Zu), 1), Gu)
censMulticomp.test(as.lcens(c(Xu, Yu, Zu), 1), Gu)

Description

Censors a vector at user-set limits for left- or right-censoring.

Usage

censor(x, left = -Inf, right = Inf)

Arguments

Value

An S4 object of class "lcens" if right is Inf, otherwise an S4 object of class "mcens."

Note

Missing velues are generated wherever right is less than or equal to left.
The censor function is provided as a simple function to create either left- or multiply-censored data from numeric values, primarily for simulation pruposes. The functions as.lcens or as.mcens offer greater flexibility and should be used for real data.

References

Lorenz, D.L., in preparation

See Also

as.lcens, as.mcens

Examples

## Create a random vector
set.seed(651)
x.tmp <- rnorm(5)
censor(x.tmp, 0, .75)

Description

Returns the type of censoring ("none," "left," "multiple") for an object.

Usage

censoring(x)

## Default S3 method:
censoring(x)

## S3 method for class 'lcens'
censoring(x)

## S3 method for class 'mcens'
censoring(x)

## S3 method for class 'qw'
censoring(x)

Arguments

Value

A character string "none," "left," or "multiple" describing the type of censoring present in the object.

Note

This function is mostly used within other functions to determine the 'best' technique to use for analysis.

See Also

censorLevels

Examples

censoring(2.3) # a simple number
censoring(as.lcens(1, 2)) # left-censored

Description

Returns all censoring levels for an object.

Usage

censorLevels(x, type = "left")

## Default S3 method:
censorLevels(x, type = "left")

## S3 method for class 'lcens'
censorLevels(x, type = "left")

## S3 method for class 'mcens'
censorLevels(x, type = "left")

## S3 method for class 'qw'
censorLevels(x, type = "left")

Arguments

Value

A numeric vector of the sorted censoring levels. If all data are uncensored, then -Inf is returned for type = "left" and Inf is returned for type = "right."

Note

Interval censoring is not characterized by a single value, so it is not an option for type.

See Also

censoring

Examples

censorLevels(2.3) # a simple number
censorLevels(as.lcens(1, 2)) # left-censored

Description

Generates the sequence of probability points for uncensored and censored values

Usage

censpp(x, a = 0.44)

## Default S3 method:
censpp(x, a = 0.44)

## S3 method for class 'lcens'
censpp(x, a = 0.44)

## S3 method for class 'mcens'
censpp(x, a = 0.44)

Arguments

Value

A list with these components:

Note that xrcn and pprcn are provided only if there are right-censored values.

Note

The left-censored plotting positions are adjusted by the method of Helsel and Cohn (1988), which produces a mean of 0.5 for all data.

References

Helsel, D.R. and Cohn, T.A., 1988, Estimation of descriptive statistics for multiply censored water quality data: Water Resources Research v. 24, n. 12, pp.1997-2004

See Also

ppoints

Examples

# This example demonstrates the probability adjustments made for censoring
# The raw, uncensored data:
ppoints(7, .44)
# censor ar 0.5 (the lowest 3 values)
censpp(as.lcens(ppoints(7, .44), 0.5))

Description

Computes the probability plot correlation coefficient test for departures from normality for left-censored data.

Usage

censPPCC.test(x)

Arguments

Value

An object of class "htest" having these components:

Note

The PPCC test is attractive because it has a simple, graphical interpretation: it is a measure of the correlation in a Q-normal plot of the uncensored data and is related to the Shapiro-Francia test for normality described by Royston (1993). The extension to multiple detection limit data is described in the help files in Millard (2001). The attained p-value for multiple detection limit data is only approximate.

References

Millard, S.P., 2001, EnvironmentalStats for Spotfire S+ Help, Version 2.0. Probability, Statistics & Information, Seattle, WA.
Royston, P., 1993, A toolkit for testing for non-normality in complete and censored samples: The Statistician, v. 42, p. 37–43.

See Also

ppcc.test, censpp

Description

Computes sample quantiles and confidence limits of left-censored data for specified probabilities.

Usage

censQtiles.CI(x, probs = 0.5, CI = 0.9, bound = c("two.sided", "upper",
  "lower"))

Arguments

Details

The survfit function in the survival package is used to compute the flipped Kaplan-Meier statistics. The type of confidence interval is "plain," which produces symmetric confidence intervals that maintain consistency when back flipping the estimates and is consisten with the B-C method described by Helsel (2012).

Value

A matrix of sample quantiles, the lower confidence limit, the upper confidence limit, and the probability represented by the confidence interval corresponding to the probs levels in the sorted x data. Missing values denote values less than the minimum (either censored or uncensored) value. The minimum value is included as the "minimum" attribute of the matrix. The maximum value is included as the "maximum" attribute of the matrix.

References

Helsel, D.R. 2012, Statistics for censored environmental data using Minitab and R: New York, Wiley, 324 p.

See Also

censQuantile

Examples

## Generate a random sample
set.seed(222)
XX.rn <- rexp(32)
# Compare uncensored to the binomial method
censQtiles.CI(XX.rn, probs=c(.25, .5, .75))
qtiles.CI(XX.rn, probs=c(.25, .5, .75))

Description

Computes sample or estimated quantiles corresponding to the given probabilities. The smallest observation (censored or uncensored) corresponds to a probability of 0 and the largest to a probability of 1.

Usage

censQuantile(x, probs = seq(0, 1, 0.25), na.rm = FALSE, method = "ROS",
  type = 2, alpha = 0.4)

## Default S3 method:
censQuantile(x, probs = seq(0, 1, 0.25), na.rm = FALSE,
  method = "", type = 2, alpha = 0.4)

## S3 method for class 'lcens'
censQuantile(x, probs = seq(0, 1, 0.25), na.rm = FALSE,
  method = "ROS", type = 2, alpha = 0.4)

## S3 method for class 'mcens'
censQuantile(x, probs = seq(0, 1, 0.25), na.rm = FALSE,
  method = "flipped K-M", type = 2, alpha = 0.4)

## S3 method for class 'qw'
censQuantile(x, probs = seq(0, 1, 0.25), na.rm = FALSE,
  method = "log MLE", type = 2, alpha = 0.4)

Arguments

Details

The methods available in the current version are "flipped K-M," "log ROS," "ROS," "log MLE," and "MLE." The method "flipped K-M" produces quantiles using the Kaplan-Meier method on fliiped data described by Helsel (2012). The methods "log ROS" and "log MLE" are described by Helsel, 2012 and Helsel and Cohn (1988). The methods "ROS" and "MLE" are similar to "log ROS" and "log MLE" except that no log- and back-transforms are made on the data.

Value

An object of class "censQuantile" with one named component for each level requested in probs. The values returned for method="flipped K-M" can be of class "lcens."

References

Helsel, D.R. 2012, Statistics for censored environmental data using Minitab and R: New York, Wiley, 324 p.
Helsel, D.R. and Cohn, T.A., 1988, Estimation of descriptive statistics for multiply censored water quality data: Water Resources Research v. 24, n. 12, pp. 1997-2004

See Also

quantile, quantile.lcens

Examples

set.seed(28)
Xu <- rnorm(23)
censQuantile(Xu) # Uncensored (true) quartiles
censQuantile(as.lcens(Xu, 0)) # How'd ROS do?
censQuantile(as.lcens(Xu, 0), method="MLE") # How'd ROS do?

Description

Builds a linear regression model for censored response data.

Usage

censReg(formula, data, subset, weights, na.action, dist = "normal")

Arguments

Details

The left-hand side of the formula may be any numeric variable, just as with lm or a variable of class "lcens," "mcens," or "qw."
For un- or left-censored data, AMLE is used unless weights are specified in the model, then MLE is used, through a call to survreg. For any other censored data, MLE is used.
If dist is "normal," then the regression analysis assumes that the residuals are normally distributed. If dist is "lognormal," then the regression analysis assumes that the residuals are lognormally distributed. In this case, predicted values are back transformed and optionally bias corrected to represent the expected mean. If dist is "commonlog," then the response data are transformed using log10 and those residuals are assumed to be normally distributed. No back transformation is made for predicted values.

Value

An object of class "censReg."

Note

A special feature of censReg is the ability to expand the formula passed as a variable rather than as an expressly entered formula. This feature is intended to facilitate certain kinds of scripts that construct a formula from combinations of variables in a dataset.

Objects of class "censReg" have these methods:

coef

extract the regression coefficents

extractAIC

compute another information criterion (AIC) value

fitted

extract the fitted values

logLik

compute the log-likelihood of the fitted model

nobs

extract the number of observations used to fit the model

plot

create some basic diagnostic plots

predict

predict new values from the model

print

print the model

residuals

extract the residuals from the model

rmse

compute the root mean squared error (residual standard error)

summary

compute summary information about the model

vcov

extract the variance-covariance matrix from the model

vif

compute the variance inflation factors for the explanatory variables in the model

The AMLE method has arbitrary limitations on the size of the data: 24 explanatory variables and 5000 observations. Exceeding these will generate a warning message with the error code in the output object.

References

Lorenz, 2015, smwrQW.
Breen, R., 1996, Regression models: censored, sample selected, or truncated data: Sage University Paper series on Quantitative Applications in the Social Sciences, 07-111, Thousand Oaks, CA,
Cohn, T.A., 1988, Adjusted maximum likelihood estimation of moments of lognormal populations from type I censored samples: U.S. Geological Survey Open-File Report 88-350, 34 p.

See Also

lm, survreg

Examples

set.seed(345)
X <- runif(24, 1, 5)
Y <- X/2 + rnorm(24)
lm(Y ~ X) # the uncensored regression
censReg(as.lcens(Y, 1) ~ X) # censored at 1

Description

These are support functions for fitting censored regression. They perform either AMLE or MLE regression.

Usage

censReg_AMLE.fit(Y, X, dist = "normal")

censReg_MLE.fit(Y, X, Wt, dist = "normal")

Arguments

Value

a list containing the output from the FORTRAN code,or converted from survreg.

See Also

censReg, survreg

Description

Support function for censored regression to predict values from a censored regression model.

Usage

censReg_AMLE.pred(fit, XPRED)

Arguments

Value

A list containing the output from the FORTRAN code.

See Also

censReg,

Description

Computes the mean and standard deviation of censored data.

Usage

censStats(x, method = "MLE", na.rm = FALSE, alpha = 0.4)

## Default S3 method:
censStats(x, method = "MLE", na.rm = FALSE, alpha = 0.4)

## S3 method for class 'lcens'
censStats(x, method = "MLE", na.rm = FALSE, alpha = 0.4)

## S3 method for class 'mcens'
censStats(x, method = "MLE", na.rm = FALSE, alpha = 0.4)

## S3 method for class 'qw'
censStats(x, method = "log MLE", na.rm = FALSE, alpha = 0.4)

Arguments

Details

The methods available in the current version are "log MLE," "MLE," "log ROS," "ROS," "log AMLE," "AMLE," and "flipped K-M." The method "flipped K-M" produces statistics using the Kaplan-Meier method on flipped data described by Helsel (2012). The methods "log ROS," "log MLE," and "log AMLE" are described by Helsel (2012) and Helsel and Cohn (1988). The methods "ROS," "MLE," and "AMLE" are similar to the previous except that no log- and back-transforms are made on the data. For "log" methods, if any value in x is negative, then a warning is generated and the returned list contains missing values.

Value

A list with one component for mean and sd. If "log" methods are specified, then the meanlog amd meansd components are also included. The values returned for method="flipped K-M" can be of class "mcens."

References

Helsel, D.R. 2012, Statistics for censored environmental data using Minitab and R: New York, Wiley, 324 p.

Helsel, D.R. and Cohn, T.A., 1988, Estimation of descriptive statistics for multiply censored water quality data: Water Resources Research v. 24, n. 12, pp.1997–2004

See Also

mdlAMLE, mdlKM, mdlKMstats, mdlMLE, mdlROS

Examples

set.seed(936)
Y <- rlnorm(32)
# Uncensored statistics
censStats(Y, method="log MLE")
# Censored statistics, at 1 (37.5 percent)
censStats(as.lcens(Y, 1), method="log MLE")

Description

Computes selected summary statistics for censored data.

Usage

censSumStats(..., group = NULL, Nums = TRUE, Stats = TRUE,
  Probs = (0:4)/4, na.rm = TRUE, method = "log MLE")

Arguments

Value

A data.frame with the selected statistcs for each variable in ... grouped by each unique value in group.

Description

Recodes censored data to a binary coding system with 0 indicating less than some critical value and 1 indicating greater than or equal to that critical value.

Usage

code01(..., criteria)

## Default S3 method:
code01(..., criteria)

## S3 method for class 'data.frame'
code01(..., criteria)

Arguments

Value

A data frame containing the binary coded values. Each column has an attribute called "critical.value" that reports the critical value used to recode the values in that column. The column names are taken from ...; the rownames are derived from the sequential numbers of the original data.

Description

Recodes censored data to u-scores, which is the sum of the sign of the differences beween each value and all other values. It is equivalent to the rank but scaled so the the mean is 0.

Usage

codeU(...)

## Default S3 method:
codeU(...)

## S3 method for class 'data.frame'
codeU(...)

Arguments

Value

A data frame containing the u-coded values. The column names are taken from ...; the rownames are derived from the sequential numbers of the original data.

Description

Extracts the model coefficients from a censored regression object: method for "censReg" object.

Usage

## S3 method for class 'censReg'
coef(object, summary = FALSE, ...)

Arguments

Value

Either a names vector of the coefficients, if summary is FALSE or a matrix of the coefficients, their standard errors, z-scores, and attained p-values, if summary is TRUE.

Note

The attained p-values are computed from the log-likelihood test for AMLE regression and from a Wald chi-square test for MLE regression.

See Also

censReg,

Description

Comprisons are possible and well-defined between numeric and censored or water-quality data. Comparisons between censored data types are not supported in this version.

Usage

## S4 method for signature 'lcens,numeric'
Compare(e1, e2)

## S4 method for signature 'mcens,numeric'
Compare(e1, e2)

## S4 method for signature 'qw,numeric'
Compare(e1, e2)

## S4 method for signature 'numeric,lcens'
Compare(e1, e2)

## S4 method for signature 'numeric,mcens'
Compare(e1, e2)

## S4 method for signature 'numeric,qw'
Compare(e1, e2)

Arguments

Details

For all comparisons, the censored data are converted to multiply censored data, class "mcens." The conversion from class "qw" preserves the strict interpretation of less-than values as greater than or equal to 0 and less than the reporting level. The distinction of being strictly less than is lost for the conversion of left-censored data, class "lcens."

Value

A logical vector the represents the result of the comparison between each element in e1 and e2.

Examples

as.lcens(c(1, 3), 2) > 1
as.lcens(c(1, 3), 2) < 4

Description

Converts information from discrete water-quality samples to data of class "qw." Attempts to construct the best-fit estimates for data of class "qw" from more limited data sources like just remark codes and values. But will also convert data created by as.data.frame(object of class qw, expand=TRUE).

Usage

convert2qw(data, scheme = "booker")

Arguments

Details

The options for scheme are "booker," "qw," and "partial." The "booker" naming scheme assumes that remark columns begin with "R" or "r" and the value columns begin with "P" or "p." That scheme is the most limited form because it forces missing values or blanks for almost all other of the meta data. The "qw" scheme assumes that the columns are named according to as.data.frame(object of class qw, expand=TRUE). The "partial" scheme assumes that the basic scheme from as.data.frame(object of class qw, expand=TRUE) is retained, but not all columns are required. Variations include no suffix for the value and .dl in lieu of .rlv for the detection limit. When .dl is used, the method detection limit is assumed to be "MDL" if not supplied. If the scheme is "partial," then at least the value and remark or detetion limit or reporting limit must be supplied.

Value

A data frame of the water-quality data of class "qw" organized by sample. Column names for the water-quality constituents are generated automatically. Other columns are retained unchanged.

References

Lorenz, D.L., 2014, smwrQW OFR.
See information about discrete samples at https://nwis.waterdata.usgs.gov/usa/nwis/qw.

See Also

readNWISqw, makeColNames

Examples

# Make a dummy partial dataset
tmp.dum <- data.frame(sta=c("A", "B"),
 Val=c(1, 1.2),
 Val.rmk=c("<", ""),
 Val.dl=c(1, 1), stringsAsFactors=FALSE)
convert2qw(tmp.dum, scheme="partial")

Description

Converts information from data of class "qw" to separate columns representing the data in the "qw" columns. This can facilitate transfer to other systems or editing the meta data in a "qw" column. Uses as.data.frame(object of class qw, expand=TRUE) to convert each "qw" column.

Usage

convertFqw(data, columns = "")

Arguments

Value

A data frame of the converted water-quality data and all other columns in the original dataset.

Note

This function can be used in conjunction with convert2qw to update or modify reporting levels or inspect the details of the meta data.

References

Lorenz, D.L., 2014, USGSwsQW OFR.
See information about discrete samples at https://nwis.waterdata.usgs.gov/usa/nwis/qw.

See Also

readNWISqw, convert2qw

Examples

# Make a dummy partial dataset
tmp.dum <- data.frame(sta=c("A", "B"),
 Val=c(1, 1.2),
 Val.rmk=c("<", ""),
 Val.dl=c(1, 1), stringsAsFactors=FALSE)
tmp.qw <- convert2qw(tmp.dum, scheme="partial")
# Expand the result
convertFqw(tmp.qw)

Description

Imputes values for missing detection limits for left-censored data.

Usage

dlimit(values, censor.codes, default = 1e-25)

Arguments

Value

A vector of detection limits matched with each of the input values.

Warning

Tim Cohn, written communication, 5 Nov 2002 states that there are several problems with this approach:

1) for large data sets, it may be difficult for the user to group the observations into subsets as in the example above. If the observations are not grouped into subsets or the subsets do not have the censored observations as the first records, incorrect detection limits may be applied to the uncensored data.

2) for the case of multiple constituents, it may be impossible to place the censored observation within each subset at the top of the subset. Consider constituents Y and Z, each analyzed at Lab B, and each with one censored observation. The censored observations occur on different dates. In this case its not possible to have both observations as the first line in the subset from Lab B. (Note: the user could work around this problem by doing seperate runs for each constituent.)

3) When a subset of observations is completely uncensored, the detection limit from another subset will be applied. Consider the example above, but with the 10 observations from Lab B being completely uncensored. In this case, the detection limit from Lab A will be used for all 20 observations.

4) When all of the observations are uncensored (no '<' signs for a given constituent), there is no way for the user to specify the detection limit(s). In this case, a default value of 1.E-25 is used for all observations (consistent with ESTIMATOR).

Despite these problems, the approach is satisfactory for most applications: "the estimates are not very sensitive to the precise value of the censoring threshold for the above-threshold values."

Note

This function is based on the DLIMIT function in LOADEST (Runkel and others, 2004). The general assumption for imputing detection limits is that the data are sorted by time and the detection limits changes in a consistent pattern over time.

References

Runkel, R.L., Crawford, C.G., and Cohn, T.A., 2004, Load estimator (LOADEST) a FORTRAN program for estiamting constituent laods in streams and rivers: U.S. Gelogical Survey Techniques and Methods 4-A5, 69. Available online as https://pubs.er.usgs.gov/publication/tm4A5.

See Also

readNWQLdl

Examples

## The actual detection limits are 2,2,2,1,1,1.
dlimit(c(2,2,3,1,1,2), c(" ", "<", " ", " ", "<", " "))

Description

Produces a dot plot: methods for "mcens" and "qw" data.

Usage

## S4 method for signature 'mcens'
dotPlot(x, y, Plot = list(name = "", what = "points", type =
  "solid", width = "standard", symbol = "circle", filled = TRUE, size = 0.09,
  color = "black"), yaxis.orient = "table", yaxis.order = "none",
  yaxis.grid = TRUE, xaxis.log = FALSE, xaxis.range = c(NA, NA),
  ylabels = "full", xlabels = 7, xtitle = deparse(substitute(x)),
  ytitle = "", caption = "", margin = c(NA, NA, NA, NA),
  jitter.y = TRUE, Censored = list(name = "", what = "points", symbol =
  "circle", filled = FALSE, size = 0.09, color = "black", bar = TRUE), ...)

## S4 method for signature 'qw'
dotPlot(x, y, Plot = list(name = "", what = "points", type =
  "solid", width = "standard", symbol = "circle", filled = TRUE, size = 0.09,
  color = "black"), yaxis.orient = "table", yaxis.order = "none",
  yaxis.grid = TRUE, xaxis.log = FALSE, xaxis.range = c(NA, NA),
  ylabels = "full", xlabels = 7, xtitle = deparse(substitute(x)),
  ytitle = "", caption = "", margin = c(NA, NA, NA, NA),
  jitter.y = TRUE, Censored = list(name = "", what = "points", symbol =
  "circle", filled = FALSE, size = 0.09, color = "black", bar = TRUE), ...)

Arguments

Details

The what component of the Plot argument must be either "points" or "none."

Value

Information about the graph.

Note

A call should be made to setPage to set up the graphics environment before calling dotPlot.

See Also

setPage

Description

Produces a graph of the empirical distribution function: methods for "lcens" and "qw" data.

Usage

## S3 method for class 'lcens'
ecdfPlot(x, group = NULL, Plot = list(name = "Auto", what =
  "stairstep", type = "solid", width = "standard", symbol = "circle", filled =
  TRUE, size = 0.09, color = "Auto"), xaxis.log = TRUE, xaxis.range = c(NA,
  NA), xlabels = 11, ylabels = 5, ytitle = "Cumulative Probability",
  xtitle = deparse(substitute(x)), caption = "", margin = c(NA, NA, NA,
  NA), ...)

## S3 method for class 'qw'
ecdfPlot(x, group = NULL, Plot = list(name = "Auto", what =
  "stairstep", type = "solid", width = "standard", symbol = "circle", filled =
  TRUE, size = 0.09, color = "Auto"), xaxis.log = TRUE, xaxis.range = c(NA,
  NA), xlabels = 11, ylabels = 5, ytitle = "Cumulative Probability",
  xtitle = deparse(substitute(x)), caption = "", margin = c(NA, NA, NA,
  NA), ...)

Arguments

Value

Information about the graph.

See Also

probPlot.lcens

Examples

## Not run: 
set.seed(1932)
Xu <- rlnorm(32)
setPage("sq") # required page set up
ecdfPlot(as.lcens(Xu, 1.0))

## End(Not run)

Description

Computes the Akaike (1974) An Information Criterion for a censored regression object: method for "censReg" object.

Usage

## S3 method for class 'censReg'
extractAIC(fit, scale = 0, k = 2, correct = FALSE, ...)

Arguments

Value

A vector of length 2, giving the equivalent degrees of freedom and the AIC for fit.

References

Akaike, H., 1974, A new look at the statistical model identification: IEE transactions on Automatic Control, v. 19, no. 6, p. 716–723.

See Also

censReg, extractAIC

Description

Estimates values for censored data.

Usage

fillIn(x, method, alpha)

## S3 method for class 'numeric'
fillIn(x, method, alpha)

## S3 method for class 'lcens'
fillIn(x, method = "ROS", alpha = 0.4)

## S3 method for class 'mcens'
fillIn(x, method = "ROS", alpha = 0.4)

Arguments

Details

The methods of Regression on Order Statistics (ROS) and MLE is explained in Helsel (2012). The "log ROS" first log-transforms the data and back-transforms the estimated values. The triangular method distributes the censored value assuming a triangular distribution between 0 and the single detection limit. Quinn and Keogh (2003) describe alternatives to simple substituion of a single value that sample from an alternate distribution. The triangular distribution is a reasonable distribution when the percentage of censored data is relatively small, say less than 30 percent. The "fill" and "log fill" methods implement the method described by Gleit (1985).

Value

A vector of sorted estimates and actual values with an attribute of the censoring levels.

References

Helsel, D.R. 2012, Statistics for censored environmental data using Minitab and R: New York, Wiley, 324 p.
Quinn, G.P. and Keogh, M.J., 2003, Experimental design and data analysis for biologists, Cambridge University Press, Cambridge, UK, 539 p.

See Also

as.double.qw

Examples

set.seed(5420)
XR <- sort(rnorm(10))
XF <- fillIn(as.lcens(XR, -1)) # censors lowest 3 values
#How'd we do?
rbind(XR, XF)
#Note that this is unusual because all 10 random values were less than the mean!

Description

Extracts the fitted values from a censored regression object: method for "censReg" object.

Usage

## S3 method for class 'censReg'
fitted(object, suppress.na.action = FALSE,
  type = c("response", "link", "mean"), ...)

Arguments

Value

The fitted values from the regression.

See Also

censReg

Description

Formats data for pretty printing: methods for "lcens," "mcens," and "qw" data.

Usage

## S3 method for class 'lcens'
format(x, digits = NULL, ...)

## S3 method for class 'mcens'
format(x, digits = NULL, ...)

## S3 method for class 'qw'
format(x, round = TRUE, units = FALSE, style = "asis", ...)

Arguments

Details

The argument style must be one of "asis," which tries to format the data to best show the values; "simple," which is like "asis" except that interval censored data are the midrange values preceded by "I"; or "interpreted," which shows the values as they would be used in analysis and round is ignored. Only the first letter is required.

Value

A character representations of the elements of x.

Note

For style set to "asis," it is often useful to set round to a single value so that the interval data are not rounded to the same value.

Examples

format(as.lcens(1:3, 1))
format(as.mcens(1:3, 1:3))

Description

Computes Gehan scores that compare the values in one group to the values in another group.

Usage

gehanScores(x, y, na.rm = FALSE)

Arguments

Details

If y is missing, then x is compared to itself (with NAs removed) and the output is the u-score described in Helsel (2012).

Value

A numeric vector that is the result of the comparison of each value in x to all values in y. It is the equivalent of the "h" score in described by Helsel, but the signs are reversed so that larger values in x have larger values in the output.

Note

If the output is the u-score, y is missing, then the values can be converted to ranks by dividing by 2 and adding the mean rank, (length(x) + 1)/2.

References

Gehan, E.A., 1965, A generalized Wilcoxon test for comparing arbitraritly singly censored samples: Biometrika, v. 52, p. 203-223.

Helsel, D.R. 2012, Statistics for Censored Environmental Data Using Minitab and R: New York, Wiley, 324 p.

See Also

survdiff, survfit, lcens-class

Description

This function tests for differences in censored samples from 2 groups. Two methods are available—the Peto-Prentice test is appropriate only for left-censored data. The Gehan test has been extended to multiply censored data as suggested in Gehan (1965) but uses a permutation test to compute the variance.

Usage

genWilcox.test(x, y, alternative = "two.sided", method = "best", data.names,
  gehan.seed = 0)

Arguments

Details

If y is either type character or factor, then it is assumed to be a group identifier. Anything else is treated as another set of sample and forced to the appropriate class of censored data.

The argument method must be one of "peto" or "gehan." It may also be "best," which selects "peto" for uncensored or left-censored data and "gehan" otherwise.

Value

An object of class "htest" that inherits "genWilcox."

Null Hypothesis

The null hypothesis is that the distributions are not different from one another.

Note

The genWilcox.test function uses the survfit function. Helsel (2012) describes flipping the left-censored data so that small values become large and left-censored values become right-censored values and adapt nonparametric techniques from survival analysis. The results from survfit are printed as the sample estimates when printing the output, the important columns are records, the number in each group; events, the number of uncensored values; and median, the group median.
A plot method is supported for the returned object.

References

Gehan, E.A., 1965, A generalized Wilcoxon test for comparing arbitraritly singly censored samples: Biometrika, v. 52, p. 203-223.

Harrington, D.P., and Fleming, T.R., 1982, A class of rank test procedures for censored survival data: Biometrika, v. 69, p. 553-566.

Helsel, D.R. 2012, Statistics for Censored Environmental Data Using Minitab and R: New York, Wiley, 324 p.

Peto, R., and Peto, J., 1972, Asymptotically efficient rank invariant test procedures (with discussion): Journal of the Royal Statistical Society, Series A v. 135, p. 185-206.

Prentice, R.L. 1978, Linear rank tests with right-censored data: Biometika, v 65, p 167-179.

Prentice, R.L., and Marke, P., 1979, A qualitative discrepancy between censored data rank tests: Biometrika, v. 35, p. 861-867.

See Also

survdiff, survfit, lcens-class

Examples

# Compare uncensored results
# First for grouped data
set.seed(69)
Xu <- rlnorm(22, 0, 1)
Yu <- rlnorm(22, .6, 1)
genWilcox.test(Xu, Yu)
wilcox.test(Xu, Yu)
# Compare effect of censoring
genWilcox.test(as.lcens(Xu, 1), Yu)
genWilcox.test(as.lcens(Xu, 1), as.lcens(Yu, 1))

Description

Imports discrete water-quality sample data from NWISweb.

Usage

importNWISqw(sites, params = "All", begin.date = "", end.date = "",
  keep = NULL, use.pnames = FALSE)

Arguments

Details

Valid parameter code groups are "All," or group codes:

Value

A data frame of the water-quality data of class "qw" organized by sample. Column names for the water-quality constituents are generated automatically, but can be set by the user, see makeColNames.

Note

The sample information columns that are automatically retained are the USGS station identifier, sample date, sample time, time zone code, and medium code. If composite samples are found in the data, then sample end date and sample end time are also included. Use the keep argument to retain more if needed.

NWIS has several remark codes that have special meaning in addition to "<," which indicates a left-censored value and ">," which indicates a right censored value. Most other codes are ignored in processing, but passed through and retained as the remark code in the data; a warning is printed when special remark codes are retained. NWIS also uses the remark code "M" to indicate whan a result value is rounded to 0. In that case, importNWISqw tries to recode the data as less than the reportiong level, but is the reporting level is the missing value NA, the remark code "M" is retained. Warnings are generated for both conversion and retention of the "M" remark codes.

References

Lorenz, D.L., 2014, smwrQW OFR.
See information about discrete samples at https://nwis.waterdata.usgs.gov/usa/nwis/qw.

See Also

readNWISqw

Examples

## Not run: 
importNWISqw("05330000", "00608") # Ammonia samples from the Minnesota River at Jordan.
Empty <- importNWISqw('05330000',c('00400','00403'),begin.date='2008-01-01')

## End(Not run)

Description

Converts a dataset containing stacked discrete water-quality sample data to a dataset representing those data as class "qw."

Usage

importQW(data, keep = c("STAID", "DATES", "TIMES", "MEDIM"),
  values = "VALUE", remark.codes = "REMRK", value.codes = "NWIS",
  reporting.level = "RPLEV", reporting.method = "RLTYP",
  reporting.units = "UNITS", analyte.method = "METHD",
  analyte.name = "PSNAM", unique.code = "PCODE", ColNames = "Auto")

Arguments

Details

Only values and remark.codes are required. All others can be interpreted as constant values if the column name is not in data. For automatic generation of column names, see makeColNames.
For reporting.level, it is better to use NA than to use an arbitrary small value because the functions to convert to objects for analysis will create reasonable reporting level values if they are not known.
For other columns when the actual value is not known, the actual value is less important for analysis and more important for the user, so arbitrary values can be used.

Value

A data frame containing the columns in keep and those generated by converting the other columns into class "qw."

Note

Need some notes

References

Lorenz, D.L., 2014, USGSqw OFR.
See information about discrete samples at https://nwis.waterdata.usgs.gov/usa/nwis/qw.

See Also

readNWISqw, importNWISqw, makeColNames

Examples

## Not run: 
# Convert the stacked qw data supplied in smwrData
library(smwrData)
data(QWstacked)
QWstacked$result_va <- as.numeric(QWstacked$result_va) # raw data are character
# The units are both mg/l, no analyte name, generate column names from parameter codes
head(importQW(QWstacked, c("site_no", "sample_dt", "sample_tm", "medium_cd"),
 "result_va", "remark_cd", "val_qual_tx", "rpt_lev_va", "rpt_lev_cd", 
 "mg/l", "meth_cd", "", "parm_cd", "parm_cd"))
# A simple example having the minimum information
data(QW05078470)
importQW(QW05078470, c("DATES", "TIMES"), "P00665", "R00665", "", 0.005, "User", 
"mg/l", "Unk", "Dissolved Phosporus", "00665", "DissP")

## End(Not run)

Description

Imputes substitute values for left-censored values using the expectation maximization method.

Usage

imputeLessThans(..., type = c("MLE", "robust"), initial = c("complete.obs",
  "multRepl"))

## Default S3 method:
imputeLessThans(..., type = c("MLE", "robust"),
  initial = c("complete.obs", "multRepl"))

## S3 method for class 'data.frame'
imputeLessThans(..., group = NULL, type = c("MLE",
  "robust"), initial = c("complete.obs", "multRepl"))

Arguments

Details

Imputation of left-censored data requires the assumption of multivariate log-normality for a single population. If the data represent samples from multiple populations, then they should be identified by the group argument. The minimum size for any group is 3.

Value

A data frame containing the original data with imputed censored values.

See Also

lrEM, mImputeLessThans

Description

Indicates which elements are missing: methods for "lcens," "mcens," and "qw" data.

Usage

## S3 method for class 'lcens'
is.na(x)

## S3 method for class 'mcens'
is.na(x)

## S3 method for class 'qw'
is.na(x)

Arguments

Value

A logical vector of the same length as its argument x, containing TRUE for those elements marked NA and FALSE otherwise.

Examples

is.na(as.lcens(c(1,3, NA), 2))

Description

Computes Kendall's tau for left-censored data and the Akritas and others (1995) Theil-Sen slope estimator.

Usage

kendallATS.test(x, y, na.rm = TRUE)

Arguments

Value

an object of class "htest" having these components:

Note

The intercept is computed as slope * -median.x + median.y. The coef vector is designed to graphically represent the relation between x and y. It is not intended for prediction proposes.

References

Akritas, M.G., Murphy, S.A., and LaValley, M.P., 1995, The Theil-Sen estimator with doubly-censored data and applications to astronomy: Journal of the American Statistical Association, v. 90, p. 170–177.
Helsel, D.R. 2005, Nondetects and data analysis: New York, Wiley, 266 p.

Examples

# Simple no censoring
set.seed(450)
tmp.X <- rnorm(25)
tmp.Y <- tmp.X/2 + rnorm(25)
cor.test(tmp.X, tmp.Y, method="k", exact=FALSE, continuity=TRUE)
kendallATS.test(tmp.X, tmp.Y)
# Some censoring
kendallATS.test(as.lcens(tmp.X, -1), as.lcens(tmp.Y, -1))

Description

Class "lcens" describes left-censored data.

Slots

.Data

a 2-column matrix that contains the value and the detection limit of the left-censored data. Missing values are permitted.

censor.codes

a logcial value, TRUE indicates a censored value, FALSE indates an uncensored value. Missing values are permitted only for missing values in .Data.

names

a character vector of unique names for each element in .Data.

Objects from the Class

Objects can be created by calls to as.lcens.

References

Lorenz, D.L., in preparation

Examples

showClass("lcens")

Description

Gets the length of a vector: methods for "lcens," "mcens," and "qw" data.

Usage

## S3 method for class 'lcens'
length(x)

## S3 method for class 'mcens'
length(x)

## S3 method for class 'qw'
length(x)

## S3 method for class 'mcens'
length(x)

## S3 method for class 'qw'
length(x)

Arguments

Value

An integer of length 1 indicating the number of elements in x.

Examples

length(as.lcens(c(1,3, NA), 2))

Description

Extracts the log-likelihood statistic from a censored regression object: method for "censReg" object.

Usage

## S3 method for class 'censReg'
logLik(object, ...)

Arguments

Value

An object of class "logLik" containing the log-likelihood and the attributes "df" (degrees of freedom) and "nobs" (number of observations).

See Also

censReg,

Description

Creates valid, unique column names for water-quality constituents.

Usage

makeColNames(params, name, short)

Arguments

Details

The arguments name and short are expected to be columns retreived by those arguments in the function pcodeNWISqw.

Value

A data frame containing the columns parm_cd and col_name.

Note

This function is a support function designed to be called within other functions.

See Also

pcodeNWISqw, pcodeColData

Description

Some limited mathematical methods are possible and well-defined for censored or water-quality data.

Usage

## S4 method for signature 'lcens'
Math(x)

## S4 method for signature 'mcens'
Math(x)

## S4 method for signature 'qw'
Math(x)

Arguments

Examples

log(as.lcens(c(1, 3), 2))

Description

Support function for computing statistics for multiply-censored data.

Usage

mcenKM(x, group)

Arguments

Value

An object of class "survfit."

Description

Support function for computing statistics for multiply-censored data extended from the maximum likelihood method (Helsel and Cohn, 1988).

Usage

mcenMLE(x, method = "MLE", alpha = 0.4)

Arguments

Value

A list containing the mean and standard deviation, filled in values for the censored values, and the censored levels. If method is "log MLE," then the list also contains the mean and standard deviation of the natural log-transformed values computed by maximum likelihood.

References

Helsel, D.R. and Cohn, T.A., 1988, Estimation of descriptive statistics for multiply censored water quality data: Water Resources Research v. 24, n. 12, pp.1997-2004

Description

Support function for computing statistics for multiply-censored data extended from the "fill-in" probability plotting procedure method (Helsel and Cohn, 1988), now known as regression on order statistics.

Usage

mcenROS(x, method = "ROS", alpha = 0.4)

Arguments

Value

A list containing the mean and standard deviation, filled in values for the censored values, and the censored levels. If method is "log ROS," then the list also contains the mean and standard deviation of the natural log-transformed values computed by regression on order statistics.

References

Helsel, D.R. and Cohn, T.A., 1988, Estimation of descriptive statistics for multiply censored water quality data: Water Resources Research v. 24, n. 12, pp.1997-2004

Description

Class "mcens" describes right- or multiply-censored data.

Slots

.Data

a 2-column matrix that contains the lower and upper value for the data. Missing values are permitted.

censor.codes

an integer vector that indicates censoring; -1 indicates left-censored, 0 indicates uncensored, and 1 indicates rigth-censored. Missing values are permitted only for elements of .Data that are missing.

interval

a logical value; TRUE indicates that the value is interval censored and FALSE indicates otherwise. Missing values are permitted only for elements of .Data that are missing.

names

a character vector of unique names for each element in .Data.

Objects from the Class

Objects can be created by calls to as.mcens.

Note

Note that censor.codes and interval are not necessary, but included to make some manipulations easier.

References

Lorenz, D.L., in preparation

Examples

showClass("mcens")

Description

Support function for computing statistics for left-censored data using the adjusted maximum-likelihood method (Cohn, 1988)

Usage

mdlAMLE(x, method = "AMLE", alpha = 0.4)

Arguments

Value

A list containing the mean and standard deviation, filled in values for the censored values, and the maximum censor level. If method is "log AMLE," then the list also contains the mean and standard deviation of the natural log-transformed values computed by maximum likelihood.

References

Cohn, T.A., 1988, Adjusted maximum likelihood estimation of the moments of lognormal populations from type 1 censored samples: U.S. Geological Survey Open-File Report 88-350, 34 p.

Description

Support function for computing statistics for left-censored data.

Usage

mdlKM(x, group, conf.int = 0.95)

Arguments

Value

An object of class "survfit."

Description

Support function for computing statistics for left- and multiply censored data.

Usage

mdlKMstats(x, probs = c(0.25, 0.5, 0.75))

Arguments

Value

A list containing summary statistics.

Description

Support function for computing statistics for left-censored data using the maximum likelihood method (Helsel and Cohn, 1988).

Usage

mdlMLE(x, method = "MLE", alpha = 0.4)

Arguments

Value

A list containing the mean and standard deviation, filled in values for the censored values, and the censored levels. If method is "log MLE," then the list also contains the mean and standard deviation of the natural log-transformed values computed by maximum likelihood.

References

Helsel, D.R. and Cohn, T.A., 1988, Estimation of descriptive statistics for multiply censored water quality data: Water Resources Research v. 24, n. 12, p.1997–2004

Description

Support function for computing statistics for left-censored data using the "fill-in" probability plotting procedure method (Helsel and Cohn, 1988), now known as regression on order statistics. This method is also known as the "robust" approach (Helsel, 2012).

Usage

mdlROS(x, method = "ROS", alpha = 0.4)

Arguments

Value

A list containing the mean and standard deviation, filled in values for the censored values, and the censored levels. If method is "log ROS," then the list also contains the mean and standard deviation of the natural log-transformed values computed by regression on order statistics.

References

Helsel, D.R. and Cohn, T.A., 1988, Estimation of descriptive statistics for multiply censored water quality data: Water Resources Research v. 24, n. 12, pp.1997–2004

Helsel, D.R. 2012, Statistics for censored environmental data using Minitab and R: New York, Wiley, 324 p.

Description

Computes the arithemtic mean. These functions return NA and are designed to stop the user from accidentally using the function mean on censored data.

Usage

## S3 method for class 'lcens'
mean(x, ...)

## S3 method for class 'mcens'
mean(x, ...)

Arguments

Value

An error message.

Note

The mean and standard deviation of censored data should be computed using censStats.

See Also

censStats

Description

Computes the arithmetic mean of water-quality data. This function is intended primarily to compute a useful mean of a small set of data, for example to compute the mean of daily samples. See Note.

Usage

## S3 method for class 'qw'
mean(x, lt.tol = 0.5, ...)

Arguments

Details

The lt.tol argument can be used to collapse interval censored data, creating an uncensored value, when the range of interval censored data is less than lt.tol time the detection limit. This generally results in reasonable estimates of values for the intended purpose.

Value

The mean of thw water-quality data as class "qw."

Note

The mean and standard deviation of censored water-quality data should be computed using censStats.

See Also

censStats

Description

Computes the sample median: methods for "lcens," "mcens," and "qw" data.

Usage

## S3 method for class 'lcens'
median(x, na.rm = FALSE, ...)

## S3 method for class 'mcens'
median(x, na.rm = FALSE, ...)

## S3 method for class 'qw'
median(x, na.rm = FALSE, ...)

Arguments

Value

A vector of length one representing the sample median.

Note

The median is computed using the flipped Kaplan-Meier method described in Helsel (2012).

References

Helsel, D.R. 2012, Statistics for censored environmental data using Minitab and R: New York, Wiley, 324 p.

See Also

censQuantile

Examples

median(as.lcens(1:4, 2))

Description

Imputes substitute values left-censored values multiple times using the data augmentation method.

Usage

mImputeLessThans(..., m = 10, initial = c("lrEM", "complete.obs",
  "multRepl"))

## Default S3 method:
mImputeLessThans(..., m = 10, initial = c("lrEM",
  "complete.obs", "multRepl"))

## S3 method for class 'data.frame'
mImputeLessThans(..., group = NULL, m = 10,
  initial = c("lrEM", "complete.obs", "multRepl"))

Arguments

Details

Imputation of left-censored data requires the assumption of multivariate log-normality for a single population. If the data represent samples from multiple populations, then they should be identified by the group argument. The minimum size for any group is 3.

Value

A list of length m containing data frames with imputed censored values. If group is used, then the returned object is a tagged list with names corresponding to the values in the grouping column. Each group contains the m repititions of imputed values.

See Also

lrDA, imputeLessThans

Description

Multiplies water-quality data by a number while maintaining the integrity of the data.

Usage

multiply(x, factor, units, analyte, analyte.method = "ALGOR", pcode = "")

Arguments

Details

Multiplication is not defined for objects of class "qw" because it can change some of the metadata, in particular the units, the analytical method, or the unique identifier (pcode).

Value

An object of class "qw" that is the result of the requested operation.

Description

Extracts the number of observations from a censored regression object: method for "censReg" object.

Usage

## S3 method for class 'censReg'
nobs(object, ...)

Arguments

Value

The number of observations used to construct the model.

See Also

censReg

Description

Tests for differences in paired left-censored samples from two groups using Pratt's (1959) adjustment for ties.

Usage

pairedPratt.test(x, y, alternative = "two.sided", mu = 0, data.names)

Arguments

Value

An object of class "htest" that inherits "ppw."

Null Hypothesis

The null hypothesis is that the distributions are not different from one another.

Note

The Pratt (1959) adjustment to the Wilcoxon signed-rank test was used by Lindsey and Rupert (2012) to evaluate decadal changes in groundwater quality. Lindsey and Rupert (2012) used a fixed reporting level (0.06, the largest among all of the data) and used a simple substitute value 0.0599 for the censored values. The approach in pairedPratt.test is to recensor values at the largest reporting limit, use one-half that value as the simple substitute and round differences greater than the simple substitute value to multiples of the largest reporting limit; nonzero differences less than or equal to the simple substitute value are rounded to that value. That rounding scheme eliminates the ambiguity of comparing interval values created by the difference between a censored value and an uncensored value.

A plot method is supported for the returned object.

References

Lindsey, B.D., and Rupert, M.G., 2012, Methods for evaluating temporal groundwater quality data and results of decadal-scale changes in chloride, dissolved solids, and nitrate concentrations in groundwater in the United States, 1988–2010: U.S. Geological Survey Scientific Investigations Report 2012–5049, 46 p.

Pratt, J.W., 1959, Remarks on zeros and ties in the Wilcoxon signed rank procedures: Journal of the American Statistical Association, v. 54, no. 287 p. 655–667.

See Also

ppw.test, lcens-class

Examples

# Compare uncensored results
set.seed(699)
Xu <- sort(rlnorm(22, 0, 1))
Yu <- sort(rlnorm(22, .425, 1))
# Treat as paired samples
pairedPratt.test(Xu, Yu)
wilcox.test(Xu, Yu, paired=TRUE)
# The differences in the p-values are due to use of approximate p-value for
# the Pratt test

Description

Selected U.S. Gelogical Survey (USGS) parameter codes to create column names and data type conversion when importing data from NWISweb

Usage

pcodeColData

Format

Data frame with 1178 rows and 3 columns

Note

This data set can be copied and modifed by the user to add or change column names. The data_type must be either "qw" or "numeric" any other value will be ignored.

References

Lorenz, D.L., 2016, smwrQW—An R Package for Managing and Analyzing Water-Quality Data, Version 0.7.3

Examples

data(pcodeColData)
# just print some rows
head(pcodeColData)
tail(pcodeColData)

Description

Returns information about parameter codes. Support function for importNWISqw.

Usage

pcodeNWISqw(params = "all", group = TRUE, name = TRUE, CASRN = FALSE,
  short = TRUE, units = TRUE, col.name = FALSE)

Arguments

Details

Valid groups for param are "All," "INF," "PHY," "INM," "INN," "NUT," "MBI," "BIO," "IMN," "IMM," "TOX," "OPE," "OPC," "OOT," "RAD," "SED," or "POP."

Value

A data frame with the parameter codes and the selected columns.

References

Lorenz, D.L., 2014, smwrQW OFR.
See information about discrete samples at https://nwis.waterdata.usgs.gov/usa/nwis/qw.

See Also

readNWISpCode

Examples

## Not run: 
pcodeNWISqw("00925")

## End(Not run)

Description

Computes the percentage of censoring ("left," "right," or "multiple") for an object.

Usage

pctCens(x, type = "multiple")

Arguments

Value

The percentage of the kind of censoring specified by type is returned. Zero is returned if all data are missing!

Note

This function will work for any type of data that has a method for censoring and as.mcens.

See Also

censoring

Examples

pctCens(as.lcens(c(1:5, NA), 2)) # left-censored

Description

Computes the empirical cumulative percent or percent exceedance of observed data for specific values: methods for "lcens" and "qw" data.

Usage

## S3 method for class 'lcens'
percentile(x, q, test = ">=", na.rm = TRUE,
  percent = TRUE, exact = TRUE, ...)

## S3 method for class 'qw'
percentile(x, q, test = ">=", na.rm = TRUE, percent = TRUE,
  exact = TRUE, ...)

Arguments

Value

A named vector as long as q corresponding to the requested value.

Note

The stats package contains the ecdf function that performs a similar function when test is "<=."

See Also

ecdf

Examples

set.seed(2342)
Xr <- rlnorm(24)
# The percentage of the observarions greater than or equal to 2
percentile(as.lcens(Xr, 2), 1:5)
# Compare to the raw data:
percentile(Xr, 1:5)

Description

Plot simple AMLE/MLE model diagnostics.

Usage

## S3 method for class 'censReg'
plot(x, which = "All", set.up = TRUE, ...)

Arguments

Details

Two graphs can be produced by this function. Number 1 is a plot of fitted versus actual and number 2 is a Q–normal plot. More complete diagnostic plots are available from the summary.censReg output.

Value

The object x is returned invisibly.

See Also

censReg

Description

Create diagnostic plots for selected hypothesis tests.

Usage

## S3 method for class 'ppw'
plot(x, which = "All", set.up = TRUE, labels, ...)

## S3 method for class 'genWilcox'
plot(x, which = "All", set.up = TRUE,
  xaxis.log = TRUE, ...)

Arguments

Details

The ppw method for plot creates 2 graphs on a single page. The first graph is the scaled differences from the PPW test with the mean difference shown by a blue line. The second graph is the actual differences in the paired values, assuming that the true minimum for left-censored data is 0. The median difference is shown by a blue line.

The genWilcox method creates a single graph that shows the emprical cumulative distributions for each group.

Value

The object x is returned invisibly.

Description

Create a diagnostics plot of the reporting levels and observations

Usage

## S3 method for class 'qw'
plot(x, which = "All", set.up = TRUE, ...)

Arguments

Value

A plot is created and the data are invisibly returned.

See Also

timePlot-censored

Examples

## see vignettes

Description

Plot summary AMLE/MLE model diagnostics.

Usage

## S3 method for class 'summary.censReg'
plot(x, which = "All", set.up = TRUE, span = 1,
  ...)

Arguments

Details

Seven graphs can be produced by this function. If which is "All," then all plots are produced. The argument which can also be the name of an explanatory variable so that a partial residual plot is created for a single variable. Or which can be any of a sequence of numbers from 1 thorugh 7. Numeric values for which:

1. Fitted vs. Observed

2. Fitted vs. Residual

3. S-L plot

4. A correlogram if dates are available in the model or in the data set

5. Q-normal plot

6. Influence plot

7. Partial residual plots for each explanatory variable

Value

The object x is returned invisibly.

Note

The q-normal plot (number 5) plots the working residuals and portrays fits for relatively small percentages of censoring very well. For larger percentages of censoring, the q-normal plot in plot.censReg (number 2) can portray the normality of the residuals more accurately.

See Also

censReg, plot.censReg

Description

Raises censored data to a positive power.

Usage

pow(x, lambda, out = "Auto")

Arguments

Value

An object of class "mcens" that is the result of the requested operations. Each of the range of the lower and upper values are raised to the power of lambda and the result divided by lambda to approximately maintain scale. But the reciprocal value of lambda cannot be used to restore the original values.

Examples

pow(as.mcens(c(0,2), c(1,2)), 2)
pow(as.mcens(c(0,2), c(1,2)), .5)
# Numeric values
pow(c(1,3), 2)