Package 'smwrStats'

Description

Useful tools for the analysis of hydrologic data, not inlcuding censored water-quality data.

Details

Regression applications:
allReg
binaryReg
hosmerLemeshow.test
leCessie.test
multReg
press
rmse
selBestWave
roc
vif
predictDuan
predictFerguson
predictMVUE
senSlope
seasonalPeak
seasonalWave

Record extension applications:
move.1
jackknifeMove.1
move.2
optimBoxCox

Trend applications:
curvi
kensen.test
regken
seaken
trends
serial.test
regken
trends

Summary statistics:
cor.all
printCor
percentile
quantile.numeric
qtiles.CI
skew
sumStats
timeWeightedMean
multicomp.test

Hypothesis tests:
grubbs.test
ppcc.test
serial.test

Author(s)

Dave Lorenz <[email protected]>

Maintainer: Dave Lorenz <[email protected]>

References

Helsel, D.R. and Hirsch, R.M., 2002, Statistical methods in water resources: U.S. Geological Survey Techniques of Water-Resources Investigations, book 4, chap. A3, 522 p.

Lorenz, D.L., in preparation. smwrStats—an R package for the analysis of hydrologic data, version 0.7.5.

Description

Creates a table of the best subsets of explanatory variables for a response variable.

Usage

allReg(x, y, wt = rep(1, nrow(x)), nmax = ncol(x), nbst = 3,
  na.rm.x = TRUE, lin.dep = 10)

Arguments

Value

A data frame containing these columns:

Note

This function is a wrapper for the regsubsets function in the leaps package.

References

Helsel, D.R. and Hirsch, R.M., 2002, Statistical methods in water resources: U.S. Geological Survey Techniques of Water-Resources Investigations, book 4, chap. A3, 522 p.

Mallow, C.L., 1973, Come comments of Cp: Technometrics, v. 15, p. 661–675.

Miller, A.J., 1990, Subset selection in regression in Monographs on Statistics and Applied Probability 40: London, Chapman and Hall.

See Also

regsubsets

Examples

# See the regression vignette for examples
.pager <- options("pager")
options(pager="console")
vignette(package="smwrStats")
options(.pager)

Description

Computes diagnostic statistics for an analysis of covariance (ANCOVA) with a single factor variable.

Usage

ancovaReg(object, find.best = TRUE, trace = FALSE)

Arguments

Details

The input model object (object) can be the complete ancova model including all interaction terms or it can be any form of an ANCOVA model. Most often, if it is not the complete ancova model, then find.best should be FALSE.
The find.best option uses the step function to select the "best" subset of terms in the model. In general, this can be used to retain or drop significant interaction terms. It will not look at individual factor levels in the model.

Value

A list of class "ancovaReg" containing these components:

If no factor variable is found in the final model, either because one was not specified or it was dropped from the model, then an object of class "multReg" is returned instead. See multReg for details.

Note

Objects of class "ancovaReg" have print and plot methods.

References

Draper, N.R. and Smith, H., 1998, Applied Regression Analysis, (3rd ed.): New York, Wiley, 724 p.

See Also

lm, plot.ancovaReg, multReg,

Description

Computes diagnostic statistics for logistic regression.

Usage

binaryReg(object, lc.max = 1000)

Arguments

Details

Because the le Cessie test is very slow to compute for many observations, the test is not performed if there are more than lc.max observations.

Value

A list of class "binaryreg" containing these components:

Note

Logistic regression can be very useful alternative method for heavily censored water-quality data.
The critical values for the test criteria are computed as: leverage, 3p/n; Cook's D, median quantile for the F distribution with p+1 and n-p degrees of freedonm; and dfits, the .01 quantile of the grubbs distribution for n observations, where p is the number of parameters estiamted in the regression and n is the number of observations.
Objects of class "binaryreg" have print and plot methods.

References

Harrell, F.E., Jr., 2001, Regression modeling strategies with applications to linear models, logistic regression and survival analysis: New York, N.Y., Springer, 568 p.

Helsel, D.R., and Hirsch, R.M., 2002, Statistical methods in water resources: U.S. Geological Survey Techniques of Water-Resources Investigations, book 4, chap. A3, 522 p.

McFadden, D., 1974, Conditional logit analysis of qualitative choice behavior: p. 105-142 in Zarembka, P. (ed.), Frontiers in Econometrics. London, Academic Press, 252 p.

See Also

roc, leCessie.test, hosmerLemeshow.test

Description

Reviews/accepts the results of an analysis: method for "default" data.

Usage

confirm(x, ...)

## Default S3 method:
confirm(x, ...)

Arguments

Value

The object returned depends on the specific method.

Note

The default method simply returns the object and issues a warning.

Description

Reviews/accepts the results of an analysis: method for "seasonalPeak" object.

Usage

## S3 method for class 'seasonalPeak'
confirm(x, all = FALSE, plot.only = FALSE, ...)

Arguments

Value

An object of class seasonalPeak. The confirmed object is a single value that represents the estimate of the timing of the peak and four or five aadditional ttributes.

NumPeaks: the number of seasonal peaks; either 1 or 2.
Models: candidate loading models. The number indicates the number of months of constituent loading.
hlife: candidate half-life values. The muner indicates the half-life in terms of months.
Confirmed: logical indicating that the object has not been confirmed.

If NumPeaks is 2, then an additional attirbute Second.peak that is a data frame of candidate parameters for the second peak is included. See seasonalWave for details.

References

Vecchia, A.V., Martin, J.D., and Gilliom, R.J., 2008, Modeling variability and trends in pesticide concentrations in streams: Journal of the American Water Resources Association, v. 44, no. 5, p. 1308-1324.

See Also

seasonalWave, seasonalPeak

Examples

## Not run: 
library(smwrData)
data(QW05078470)
# Simply click on the identified peak, and enter 1 for a single peak.
confirm(with(QW05078470, seasonalPeak(dectime(DATES), P00665)))

## End(Not run)

Description

Computes correlations among numeric data.

Usage

cor.all(data, method = "pearson", na.method = "pairwise",
  distribution = "normal")

Arguments

Details

The null hypothesis is that the data are not correlated with one another. The alternate hypothesis is that they are correlated with one another. This is a two-sided test. For other options, see cor.all.

If method is "pearson," then the correlation is based on Pearson's product moment correlation coefficient. If method is "kendall," then Kendall's tau is used to estimate a rank-based measure of association. If method is "spearman", then Spearman's rho is used to estimate the correlation of the ranks of the data. The last two methods may be used if the data do not necessarily come from a bivariate normal distribution.

If na.method is "fail," then cor.all stops if there are any missing numeric values. If it is "omit," then all rows with any missing values is removed before the correlations are computed. That option will always produce a correlation matrix that is positive definite. If na.method is "pairwise," then missing values are removed from each pairwise correlation.

If distribution is "normal," then the assumption for method = "pearson" is that the data are bivariate normal. If distribution is "lognormal," then the assumption for method = "pearson" is that the data are bivariate log-normal and all data are natural log-transformed. If distribution is "log1p," then the assumption for method = "pearson" is that the data are bivariate log-normal after adding 1 and all data are transformed using the log1p function. The data are transformed for any method, but only produce a different result for method = "pearson."

Value

An object of class "cor.all," which has these components:

Note

The print, plot, and summary methods are available for an object of class "cor.all."

References

Conover, W.J., 1980, Practical nonparametric statistics (2d ed.): New York, Wiley, 512 p.

Helsel, D.R. and Hirsch, R.M., 2002, Statistical methods in water resources: U.S. Geological Survey Techniques of Water-Resources Investigations, book 4, chap. A3, 522 p.

See Also

cor.test, plot.cor.all, summary.cor.all

Examples

## Not run: 
library(smwrData)
data(TNLoads)
cor.all(TNLoads[, 1:5])
cor.all(TNLoads, method="spearman")

## End(Not run)

Description

Generates a matrix for curvi-linear modeling of trends.

Usage

curvi(x, ..., style = c("mw", "se"))

Arguments

Details

Curvi-linear trends are described in Appendix 1 (equations 1–9 through 1–11) in Vecchia (2005). The original form of the trend was described in terms of the midpoint of the trend and the halfwidth. Specifying the start and end times of the trend are added as an easy-to-use option.

Value

A matrix with one column for each of the trends sprecified in ....

Note

Curvi-linear trends provide a pleasing visual trend with a gradual transition between trends in contrast to linear trends with sharp changes at the endpoints.
Each trend is 0 prior to the start, and then increases to a maximum of 1 and maintain that maximum value after the end. The overall change is described by the regresison coefficient, rather than as a rate described by trends, for example.

References

Vecchia, A.V., 2005, Water-quality trend analysis and sampling desgin for streams in the Red River fo the North basin, Minnesota, Norht Dakota, and South Dakota, 1970–2001: U.S. Geolgical Survey Scientific Investigations Report 2005–5224, 54 p. Available on line at http://pubs.usgs.gov/sir/2005/5224/.

See Also

trends,

Examples

# Model with a single curvi-linear trend from 2001 through 2003
# First using midpoint and half width (default) and then start and end.
curvi(2000 + seq(0,20)/5, c(2002, 1))
curvi(2000 + seq(0,20)/5, c(2001, 2003), style="se")

Description

Tests for a single outlier in a sample from a normal distribution.

Usage

grubbs.test(x, alternate = "two.sided")

Arguments

Value

An object of class "htest" having the following components:

References

Grubbs, F., 1969, Procedures for Detecting Outlying Observations in Samples, Technometrics, v. 11, no. 1, pp. 1-21.

See Also

pgrubbs, qgrubbs

Examples

# A random sample with a high value
set.seed(100)
grubbstest <- rnorm(32)
grubbs.test(grubbstest)
qqnorm(grubbstest)

Description

Performs the Hosmer-Lemeshow test for goodness-of-fit for a logistic regression model.

Usage

hosmerLemeshow.test(object, groups = 10)

Arguments

Value

An object of class "htest" having these components:

Note

The null hypothesis is "no lack of fit." Rejection of the null hypothesis indicates "some lack of fit."

References

Hosmer, D.W. and Lemeshow, S., 1980, Goodness-of-fit tests for the multiple logistic regression model: Communications in Statistics — Theory and Methods, v. 9, p. 1043–1069

See Also

binaryReg

Description

Computes the bias and variance of move.1 predictions using the jackknife estimator.

Usage

jackknifeMove.1(object, newdata, type = c("response", "link"))

Arguments

Details

If type is "response," then the predicted values are back-transformed. Otherwise, the predicted values are computed directly from the model equation.

Value

A vector of predictions matching newdata or the model data.

References

Lorenz, D.L., 2015, smwrStats-an R package for analyzing hydrologic data, version 0.7.0: U.S. Geological Survey Open-File Report 2015-XXXX, XX p.

See Also

move.1, predict.move.1

Examples

library(smwrData)
data(IonBalance)
# Build model for non missing Alkalinity
IB.move <- move.1(Anion_sum ~ Cation_sum, data=IonBalance, subset=abs(Pct_Diff) < 10)
print(IB.move)
# Predict Anion_sum for missing Alkalinity
predict(IB.move, IonBalance[1, ])

Description

Tests for a temporal trend using Kendall's tau and computes the Sen slope estimate of the trend.

Usage

kensen.test(y, t, n.min = 10)

Arguments

Value

An object of class "htest" containing the following components:

Note

A straight line of the form

 ytrend = sen.slope * (
t - median.time ) + median.data

may be used as a trend line for graphically portraying or detrending the data. It goes through the point

 (t,y) = ( median.time , median.data )

with slope sen.slope.

Many tied values can cause misleading results.

The p-values for uniformly spaced data (t values unit value like years) are adjusted for lag-1 autoregressive serial correlation according to the method described by Yue and Wang (2004) that adjusts for trend. In keeping with the logic of seaken, the p-value adjustment is never performed for fewer than 10 observations. The user can suppress the adjustment by setting the value of n.min to Inf.

References

Conover, W.J., 1980, Practical nonparametric statistics (2d ed.): New York, Wiley, 512 p.

Helsel, D.R., and Hirsch, R.M., 2002, Statistical methods in water resources: U.S. Geological Survey Techniques of Water-Resources Investigations, book 4, chap. A3, 522 p.

Hirsch, R.M., Alexander, R.B. , and Smith, R.A., 1991, Selection of methods for the detection and estimation of trends in water quality: Water Resources Research, v. 27 p. 803–813.

Kendall, M.G., 1938, A new measure of rank correlation: Biometrika v. 30, p. 81–89.

Kendall, M.G., 1976, Rank correlation methods (4th ed.): London, Griffin, 202 p.

Sen, P.K., 1968, Estimates of regression coefficient based on Kendall's tau: Journal of the American Statisical Association, v. 63, p. 1379–1389.

Yue, S. and Wang. C., 2004, The Mann-Kendall test modified by effective sample size to detect trend in serially correlated hydrological series: Water Resources Management v. 18, p. 201-218.

See Also

dectime, seaken

Examples

## Not run: 
library(smwrData)
data(SaddlePeaks)
with(SaddlePeaks, kensen.test(Flow, Year))

## End(Not run)

Description

Performs the le Cressie-van Houwelingen test for goodness-of-fit for a logistic regression model.

Usage

leCessie.test(object, bandwidth, newterms)

Arguments

Details

If bandwidth is missing, then the mean distance between observations is used.

Value

An object of class "lecessie" having these components:

Note

The null hypothesis is "no lack of fit." Rejection of the null hypothesis indicates "some lack of fit."

References

le Cessie, S. and van Houwelingen, H.C., 1995, Testing the fit of a regression model via score tests in random effects models: Biometrics, v. 51, p 600-614.

See Also

binaryReg

Description

Creates the right matrices for model.frame.default when predicting from models with trends terms. Used only internally.

Usage

## S3 method for class 'trends'
makepredictcall(var, call)

Arguments

Value

A replacement for call for the prediction variable.

Description

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

Usage

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

Arguments

Details

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" having these components:

Note

Objects of class "move.1" have print, predict, and plot methods.

References

Hirsch, R.M., 1982, A comparison of four streamflow record extension techniques: Water Resources Research, v. 18, p. 1081–1088.

See Also

predict.move.1, plot.move.1

Examples

library(smwrData)
data(IonBalance)
# Build model for non missing Alkalinity
IB.move <- move.1(Anion_sum ~ Cation_sum, data=IonBalance, subset=abs(Pct_Diff) < 10)
print(IB.move)

Description

Calculates the Maintenance Of Variance Extension, Type 2 (MOVE.2) for record extension by fitting a Line of Organic Correlation (LOC) regression model.

Usage

move.2(formula, data, subset, distribution = "normal", lag = 0)

Arguments

Details

MOVE.2 has a necessarily predefined method for missing values—the response variable is assumed to contain missing values and they are the values to be estimated by the model equation. For the function move.2, missing values in the explanatory variable are excluded from the computations.

If distribution is "normal," then the data in the explanatory variable and the response variable 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 the explanatory variable and the response variable before analysis. The natural logarithm is used if distribution is "lognormal" and the commmon logarithm is used if distribution is "commonlog." If either the response or the explanatory has zero values, then the "log1p" option can be used. That option adds 1 to each value and then computes the natural logarithm. Alternatively, the output from optimBoxCox that contains both the response and explanatory variables can be supplied to transform those variables by other than a logarithmic transform.

Value

An object of class "move.2" having these components:

Note

Objects of class "move.2" have print, predict, and plot methods.

References

Hirsch, R.M., 1982, A comparison of four streamflow record extension techniques: Water Resources Research, v. 18, p. 1081–1088.
Moog, D.B., Whiting, P.J., and Thomas, R.B., 1999, Streamflow record extension using power transformations and applicaitons to sediment transport: Water Resources Research, v. 35, p 243–254.

See Also

predict.move.2, plot.move.2, optimBoxCox

Examples

## Not run: 
# See the vignette:
vignette("RecordExtension", package="smwrStats")

## End(Not run)

Description

Performs multiple comparison tests among groups of data. The tests may be either parametric (Yandell, 1997), nonparametric (Higgins, 2004), or Dunn's nonparametric (Glantz, 2005).

Usage

multicomp.test(x, g, method = "parametric", critical.value = "",
  alpha = 0.05)

Arguments

Details

The choices for method are "parametric," "nonparametric," and "dunn." If the method is "parametric," then the comparisons are based on the means and variances of the raw data and the valid choices for critical.value are "tukey" (default), "bonferroni," or "lsd." Otherwise, the comparisons are based on the ranks of the data. Valid choices for critical.value are "tukey" (default), "bonferroni," or "lsd" when method is "nonparametric" and "sidak" (default) or "bonferroni" when method is "dunn." The basic diffference between the default nonparametric method and Dunn's nonparametric method is in the handling of ties.

Value

An object of class MCT containing the following components:

Note

All computations of the variance for unequal group sizes are based on the harmonic mean as described in Yandell (1997). That adjustment is only approximate when critical.value is "tukey" and method is "parametric" but useful when the design is slightly unbalanced.
The default nonparametric method method = "nonparametric" is only assymptotically unbiased when some data are tied. For smaller data sets with small numbers of ties, it may be preferable to use Dunn's nonparametric method method = "dunn."

References

Glantz, S.A., 2005, Primer of biostatistics: McGraw Hill, New York, 520 p.

Higgins, J.J., 2004, Introduction to modern nonparametric statistics: Pacific Grove, Calif., Brooks/Cole, 384 p.

Yandell, B.S., 1997, Practical data analysis for designed experiments: London, United Kingdom, Chapman & Hall, 437 p.

Description

Computes diagnostics for linear regression.

Usage

multReg(object)

Arguments

Value

A object of class "multReg" having the following components:

Note

The type II sum of squares are calculated according to the principle of marginality, testing each term after all others, except ignoring the term's higher-order relatives. This type sum of squares is useful for assessing the overall marginal effect of each term in the model.

The critical values for the test criteria are computed as: leverage, 3p/n; Cook's D, median quantile for the F distribution with p+1 and n-p degrees of freedom; and dfits, the .01 quantile of the grubbs distribution for n observations time the square root of (p/n), where p is the number of parameters estimated in the regression and n is the number of observations.

Objects of class "multReg" have print and plot methods.

References

Draper, N.R. and Smith, H., 1998, Applied Regression Analysis, (3rd ed.): New York, Wiley, 724 p.

See Also

lm, plot.multReg,

Description

Computes Box-Cox transformations that maximimize the log likelihood of the transformations.

Usage

optimBoxCox(X, start = NULL)

Arguments

Value

An object of class "optimBoxCox" having these components:

Note

The maximum likelihood estimate of the Box-Cox transformations corresponds to the minimum determinant of the variance-covariance matrix of the transformed X. The methodology is described in Andrews and others (1971).

References

Andrews, D.F., Gnanadesikan, R., and Warner, J.L., 1971, Transformations of multivariate data: Biometrics, v. 27, p. 825–840.

See Also

boxCox, optim

Description

Computes the empirical cumulative percent or percent exceedance of observed data for specific values.

Usage

percentile(x, q, test = ">=", na.rm = TRUE, percent = TRUE, ...)

## Default S3 method:
percentile(x, q, test = ">=", na.rm = TRUE,
  percent = 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(Xr, 1:5)

Description

Produce a series of diagnostic plots for statistical analyses.

Usage

## S3 method for class 'ancovaReg'
plot(x, which = "All", set.up = TRUE, span = 0.8, ...)

## S3 method for class 'binaryreg'
plot(x, which = 2:5, set.up = TRUE, bandw = 0.3, ...)

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

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

## S3 method for class 'move.1'
plot(x, which = "All", set.up = TRUE, span = 0.8, ...)

## S3 method for class 'move.2'
plot(x, which = "All", set.up = TRUE, span = 0.8, ...)

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

## S3 method for class 'senSlope'
plot(x, which = "All", set.up = TRUE, span = 0.8, ...)

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

Arguments

Details

For objects of class "ancovaReg" and "multReg," the argument which can be a character string, "All" or any of a sequence of numbers from 1 to 8. If it is "All," then all plots are produced. For class "multReg," can also be the name of an explanatory variable so that a residual dependence plot is created for a single variable.
Numeric values for which:

1. Fitted with separate factor levels 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 and Tukey boxplots for each factor level

6. Influence plot

7. Outliers plot

8. Residual dependence plots for each explanatory variable

For objects of class "binaryreg," the argument which can be a character string, "All" or any of a sequence of numbers from 1 to 5. If it is "All," then all plots are produced. By default, the le Cessie-van Houwelingen diagnotic plot is not shown as it can be difficult to interpret. Numeric values for which:

1. Le Cessie-van Houwelingen overall fit

2. Overall fit

3. Classification plot

4. ROC plot

5. Lin-Wei-Ying partial residual plots

For objects of class "cor.all," the argument which must be either "All," "Lower," or the name of one of the variables. If which is "All", then the full scatter plot matrix is shown if there are 4 or fewer variables, otherwise indivdual paired plots are shown. If which is "Lower", then the lower part of the scatter plot matrix is shown if there are 5 or fewer variables, otherwise indivdual paired plots are shown. If which is the name of a variable, then only the scatter plots of that variable and all others are shown.

For objects of class "lecessie," the argument which must be either "All," "First," the name of one or more of the variables, or a number indicating which variable to plot. If which is "All", then the fitted vs. Residual and all partial residual plots are created. If which is "First", then only the fitted vs. Residual plot is created. If which is one or more of the variable names, then those partial residual plots are created. If which is numeric, then the fitted vs. Residual (1) sequentially numbered partial residual plots are created.

For objects of class "move.1" or "move.2," the argument which can be a character string, "All" or any of a sequence of numbers from 1 to 3. If it is "All," then all plots are produced. Numeric values for which:

1. x on y and y on x

2. The LOC regression line with ellipse

3. Q-Q plot of x and y

For objects of class "roc," the argument which can be a character string, "All" or 1. The only graph is the receiver operating characteristics curve for a logistic regression.

For objects of class "senSlope," the argument which can be a character string, "All" or 1. The only graph avaialble is a scatter plot of the data with the regression line in green and a smoothed line in cyan.

Value

The object x is returned invisibly.

References

le Cessie, S. and van Houwelingen, H.C., 1995, Testing the fit of a regression model via score tests in random effects models: Biometrics, v. 51, p. 600–614.
Lin, D.Y., Wei, L.J., and Ying, Z., 2002, Model-checking techniques based on cumulative residuals: Biometrics, v. 58, p. 1–12.

See Also

ancovaReg, binaryReg, cor.all, leCessie.test, move.1, move.2, multReg, roc, senSlope, loess.smooth, setPage

Description

Creates diagnostic plots for selected hypothesis tests.

Usage

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

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

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

Arguments

Details

The kensen method for plot graphs the y and t data with the best fit line.

The ppcc method creates a single graph that shows the q-normal plot with a line showing the fit.

Value

The object x is returned invisibly.

Description

Computes the probability plot correlation coefficient test for departures from normality.

Usage

ppcc.test(x)

Arguments

Value

An object of class "htest" having the following 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 data. As such, it is related to the Shapiro-Wilk test (Shapiro and Wilk, 1965) for normality.

The distribution function of the test statistic is empirical. This application uses the "pocket calculator" approximation for computing the p-value of the observed statistic (Royston, 1992).

References

Filliben, 1975, The PPCC test for normality: Technometrics, v. 17, no. 1, p. 111–117.

Looney, S.W., and Gulledge, T.R., 1985, Use of the correlation coefficient with normal probability plots: The American Statistician, v. 39, p. 75–79.

Royston, J.P., 1992, A pocket-calculator algorithm for the Shapiro-Francia test of non-normality–an application to medicine: Statistics in Medicine, v. 12, p. 181–184.

Shapiro, S.S., and Wilk, M.B., 1965, An analysis of variance test for normality (complete samples): Biometrika, v. 52, p. 591–611.

See Also

shapiro.test

Examples

## These data should produce an attained p-value less than 0.001
set.seed(45)
ppcc.test.data <- rnorm(32)
qqnorm(ppcc.test.data)
abline(mean(ppcc.test.data), sd(ppcc.test.data))
ppcc.test(ppcc.test.data)

Description

Predicts new values from a maintenance of variance extension, type 1 (MOVE.1) model fit.

Usage

## S3 method for class 'move.1'
predict(object, newdata, type = c("response", "link"),
  var.fit = FALSE, ...)

Arguments

Details

If type is "response," then the predicted values are back-transformed. Otherwise, the predicted values are computed directly from the model equation.

Value

If var.fit is FALSE, then a vector of predictions matching newdata or the model data. If var.fit is TRUE, then a data frame containing the columns:

References

Lorenz, D.L., 2015, smwrStats-an R package for analyzing hydrologic data, version 0.7.0: U.S. Geological Survey Open-File Report 2015-XXXX, XX p.

See Also

move.1, jackknifeMove.1

Examples

library(smwrData)
data(IonBalance)
# Build model for non missing Alkalinity
IB.move <- move.1(Anion_sum ~ Cation_sum, data=IonBalance, subset=abs(Pct_Diff) < 10)
print(IB.move)
# Predict Anion_sum for missing Alkalinity
predict(IB.move, IonBalance[1, ])

Description

Predicts new values from a maintenance of variance extension, type 2 (MOVE.2) model fit.

Usage

## S3 method for class 'move.2'
predict(object, newdata, type = c("response", "link"), ...)

Arguments

Details

If type is "response," then the predicted values are back-transformed. Otherwise, the predicted values are computed directly from the model equation.

Value

A vector of predictions matching newdata or the model data.

Note

If lag was set to a non-zero value in the call to move.2, then the explanatory variable is lagged only when predictiong values from the calibration data (newdata is not supplied.) This facilitates prediction of selected statistics at the response site rather than the complete record.

See Also

move.2

Examples

## Not run: 
# See the vignette:
vignette("RecordExtension", package="smwrStats")

## End(Not run)

Description

Predicts new values from Sen slope (senSlope) model fit.

Usage

## S3 method for class 'senSlope'
predict(object, newdata, ...)

Arguments

Value

A vector of predictions matching newdata or the model data.

See Also

senSlope

Description

Predicts bias-corrected expected mean response values from a log-transformed regression model, using either the minimum variance unbiased estimate(MVUE), Duan's smoothing estimate, or Ferguson's maximum likelihood estimate.

Usage

predictDuan(object, newdata, back.trans = exp)

predictFerguson(object, newdata, Log10 = FALSE)

predictMVUE(object, newdata, Log10 = FALSE)

Arguments

Value

A vector of predictions matching newdata or the model data.

References

Bradu, D. and Mundlak, Y., 1970, Estimation in the lognormal linear models: Journal of the American Statistical Association, v. 65, no. 329, p. 198–211.

Duan, N., 1983, Smearing estimate: a nonparametric retransformation method: Journal of the American Statistical Association, v. 78, p. 159–178.

Ferguson, R.I. 1986, River loads underestimated by rating curves: Water Resources Research, v. 22, p 74–76.

Helsel, D.R. and Hirsch, R.M., 2002, Statistical methods in water resources: U.S. Geological Survey Techniques of Water-Resources Investigations, book 4, chap. A3, 522 p.

See Also

lm

Examples

## Generate random log-normal data and build the regression model
set.seed(111)
XX.df <- data.frame(x=sort(runif(32, 1, 5)), y=rlnorm(32, seq(1,2, length.out=32)))
XX.lm <- lm(log(y) ~ x, data=XX.df)
## Compare the results for x=1:5
## The simple back-transformed estimates
exp(predict(XX.lm, newdata=data.frame(x=1:5)))
## The bias corrected estimates of the mean response
predictFerguson(XX.lm, newdata=data.frame(x=1:5))
predictDuan(XX.lm, newdata=data.frame(x=1:5))
predictMVUE(XX.lm, newdata=data.frame(x=1:5))

Description

Computes the prediction error sum of squares statistic (PRESS) (Helsel and Hirsch, 2002) for a linear regression model.

Usage

press(model)

Arguments

Value

The prediction error sum of squares statistic.

References

Helsel, D.R. and Hirsch, R.M., 2002, Statistical methods in water resources: U.S. Geological Survey Techniques of Water-Resources Investigations, book 4, chap. A3, 522 p.

See Also

multReg, lm

Description

Prints the results of a analysis of covariance (ancovaReg).

Usage

## S3 method for class 'ancovaReg'
print(x, digits = 3, ...)

Arguments

Value

The object x is returned invisibly.

Note

The printed output contains the ANOVA table for the orignal models, the regression summary for the final model, variance inflation factors for each explanatory variable in the final model, and selected test criteria with observations that exceed one of more of the criteria.

Description

Prints the results of a logistic regression diagnotic analysis (binaryReg).

Usage

## S3 method for class 'binaryreg'
print(x, digits = 4, ...)

Arguments

Details

The original regression model should be the output from glm with binomial as the value for the family argument.

Value

The object x is returned invisibly.comp2 Description of 'comp2'

Note

The printed output contains the original call; a summary of the deviance residuals; the coefficients with their estimates, standard errors, z scores, and attained p-values; a summary of the deviance comparison between the model and null model (no explanatory varaibles), also known as the G-squared or -2 log-likelihood; the response profile, which matches the value of the response variable to 0 or 1 and the number of observations in each group; the le Cessie-van Houwelingen and Hosmer-Lemeshow goodness of fit tests; three assessments of the predictinve power: the MaFadden R-squared and the adjusted R-squared, the classification table, the concordance index, and the area under the reciever operating characteristics curve; and selected test criteria with observations that exceed one of more of the criteria.

Description

Prints the results of a correlation test (cor.all).

Usage

## S3 method for class 'cor.all'
print(x, digits = 4, lower = TRUE, ...)

Arguments

Value

The object x is returned invisibly.

Note

The printed output contains a description of the test; and 3 lines for each comparison that is printed: the correlation statistic, the attained p-value, and the number of pairs.

See Also

cor.all, printCor

Description

Prints the results of a le Cessie-van Houwelingen test (leCessie.test).

Usage

## S3 method for class 'lecessie'
print(x, digits = 4, ...)

Arguments

Value

The object x is returned invisibly.

Note

The printed ouput is very similar to the printed ouput for class "htest," the output from a hypothesis test, but includes the additional output summarizing the distance between observations, which can be useful for comparing the reults with different bamdwidth settings.

Description

Prints the results of a multiple comparison test (multicomp.test).

Usage

## S3 method for class 'MCT'
print(x, digits = 4, ...)

Arguments

Value

The object x is returned invisibly.

Note

The printed output contains a description of the test, critical values, the variables in the test, and two tables: the paired comparisons and associations among the groups. The table of the paried comparisons shows the groups in the comparison, the estimate of the difference between the group means, the standard error of the difference, lower and upper confidence intervals, and a flag that indicates if the confidence interval excludes 0, which indicates wheter the difference is significantly different from 0 at the user-specified value. The table of asociations shows the group, the mean value of the response, the number of observations in the group, and any number of columns names "A," "B," and so forth that represent possible associations of the groups whare an "X" is present in the group.

Description

Prints the results of a move.1 analysis (move.1).

Usage

## S3 method for class 'move.1'
print(x, digits = 4, ...)

Arguments

Value

The object x is returned invisibly.

Note

The printed output contains the call, the regression coefficients, and selected statistics of the variables.

Description

Prints the results of a MOVE.2 analysis (move.2).

Usage

## S3 method for class 'move.2'
print(x, digits = 4, ...)

Arguments

Value

The object x is returned invisibly.

Note

The printed output contains the call, the regression coefficients, and selected statistics of the variables.

Description

Prints the results of a multiple regression diagnostic analysis (multReg).

Usage

## S3 method for class 'multReg'
print(x, digits = 3, ...)

Arguments

Value

The object x is returned invisibly.

Note

The printed output contains the regression model call; a summary of the residuals; A table of the coefficients with their estiamtes, standard errors, t vlaues, and attained probability levels; the residual standard error; R-squared and F-statistical summaries; Model comparison statistics; if more than one explanatory variable a type II sum-of-squares analysis of variance table and variance inflation factors; and selected test criteria with observations that exceed one of more of the criteria.

Description

Prints the results of a multivariate unconditional Box-Cox transformation.

Usage

## S3 method for class 'optimBoxCox'
print(x, digits = 4, ...)

Arguments

Value

The object x is returned invisibly.

Note

The printed output contains a table showing the power transformation values and their standard errors.

See Also

boxCox

Description

Prints the results of a receiver operator characteristics (ROC) for a logistic regression model.

Usage

## S3 method for class 'roc'
print(x, digits = 3, ...)

Arguments

Value

The object x is returned invisibly.

Note

The printed output contains the area under to ROC curve.

Description

Prints the results of a seasonal peak analysis (seasonalPeak).

Usage

## S3 method for class 'seasonalPeak'
print(x, digits = 3, details = FALSE, ...)

Arguments

Value

The object x is returned invisibly.

Note

The printed output contains the default time-of-peak value and potential alternate values for unconfirmed peaks and the number of peaks, timing of the primary peak, and optionally the model information for confirmed peaks.

Description

Prints the results of a Sen slope analysis (senSlope).

Usage

## S3 method for class 'senSlope'
print(x, digits = 4, ...)

Arguments

Value

The object x is returned invisibly.

Note

The printed output contains the call, the smalles and largest residuals, the regression coefficients, and the confidence limits of the Sen slope.

Description

Prints the results of a correlation test (cor.all) or correlation matrix in a compact form indicating positive or negative correlation.

Usage

printCor(x, criterion = 0.75)

Arguments

Value

The object x is returned invisibly.

Note

The printed output is a compressed table showing "+" where the value in x is greater than criterion, "-" where the value in x is less than -criterion, "\" on the diagonal, if x is symmetric, and "." where x has a missing value, and " " otherwise.

See Also

cor.all

Examples

## Not run: 
library(smwrData)
data(TNLoads)
printCor(cor(TNLoads, method="spearman"), .5)

## End(Not run)

Description

Computes the cumulative probability and quantiles for the Grubbs distribution describing an outlier in a sample from Normal distribution.

Usage

qgrubbs(alpha, N)

pgrubbs(G, N)

Arguments

Value

The function pgrubbs returns the attained p-value, not the cumulative distribution, for the maximum scaled distance from the mean. the funciton qgrubbs returns the one-sided critical value for the maximum scaled difference from the mean.

References

Grubbs, F., 1969, Procedures for Detecting Outlying Observations in Samples, Technometrics, v. 11, no. 1, pp. 1-21.

See Also

grubbs.test

Examples

# The difference is due to rounding errors
pgrubbs(c(.9, .95, .99), 32)
qgrubbs(c(5.905348, 5.483234, 5.159097), 32)

Description

Computes sample quantiles and confidence limts for specified probabilities.

Usage

qtiles.CI(x, probs = 0.5, CI = 0.9, bound = c("two.sided", "upper",
  "lower"), na.rm = TRUE)

Arguments

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.

References

Helsel, D.R. and Hirsch, R.M., 2002, Statistical methods in water resources: U.S. Geological Survey Techniques of Water-Resources Investigations, book 4, chap. A3, 522 p.

See Also

quantile

Examples

## Generate a random sample
set.seed(222)
XX.rn <- rexp(32)
qtiles.CI(XX.rn, probs=c(.25, .5, .75))

Description

Computes sample quantiles corresponding to the given probabilities: method for "numeric" data. The smallest observation corresponds to a probability of 0 and the largest to a probability of 1. This method function is a simple wrapper for the default function that sets the default type to 2 for numeric data.

Usage

## S3 method for class 'numeric'
quantile(x, probs = seq(0, 1, 0.25), na.rm = FALSE,
  names = TRUE, type = 2, ...)

Arguments

Value

An optionally named vector corresponding to the quantiles of x for the selected probabilities.

Note

Helsel and Hirsh (2002) define the 75th percentile as "a value which exceeds no more than 75 percent of the data and is exceeded by no more than 25 percent of the data." This rule can be easily extended to other percentiles. The selection of type equal to 2 ensures that this rule is met for all data. The rule stated by Helsel and Hirsch is very useful for an emprical description of the data, but Hyndman and Fan (1996) describe the slection of type for other applications.

References

Helsel, D.R. and Hirsch, R.M., 2002, Statistical methods in water resources: U.S. Geological Survey Techniques of Water-Resources Investigations, book 4, chap. A3, 522 p.

Hyndman, R.J. and Fan, Y. 1996, Sample quantiles in statistical packages: American Statistician, v. 50, p. 361-365.

See Also

quantile.default

Examples

# The default value for type (7) will compute a value that is exceeded by 4 values
#  for a sample of size 14
quantile(seq(14), type=7)
# But 4/14 is greater than 25 percent. But setting type to 2 will result in
#  only 3 values that are larger than the computed 75th percentile.
quantile(seq(14))

Description

Computes the regional Kendall trend test with Sen slope estimator.

Usage

regken(series, correct = nrow(series) > 9)

Arguments

Value

An object of class "htest" also inhereting class "seaken" containing the following components:

Note

The value of p.value is p.value.raw if there are fewer than 10 years of data and is p.value.corrected otherwise.

The regional Kendall is described in Douglas and others (2000) and Helsel and others (2006). The adjustment for spatial correlation used in regken is based on equation 13 in Douglas and others (2000) and uses the Spearman correlation to account for monotonic correlations.

References

Douglas, E.M., Vogel, R.M., and Kroll, C.N., 2000, Trends in floods and low flows in the United States: impact of spatial correlation: Journal of Hydrology, v. 240, p. 90–105.

Helsel, D.R., Mueller, D.K., and Slack, J.R., 2006, Computer program for the Kendall family of trend tests: U.S. Geological Survey Scientific Investigations Report 2005–5275, 4 p.

See Also

seaken

Examples

# Need example?

Description

Computes the root-mean-squared error (RMSE) of the difference between observed values and the predicted values or the RMSE or relative percent differences (RPD) between samples and duplicates.

Usage

rmse(x, ...)

## Default S3 method:
rmse(x, y, ...)

## S3 method for class 'lm'
rmse(x, ...)

rpd(x, y, plotit = FALSE)

Arguments

Value

For the rmse functions, a single value representing the estimated RMSE. For rpd, the relative percent differences for each paired sample and duplicate.

Note

The definition for the RMSE of paired water-quality duplicates is

$RMSE = \sqrt{\frac{\sum{(x_i - y_i)^2}}{2n}}$

The definition for RPD for paired water-quality duplicates is

$RPD = abs(x - y)/(x + y)/2 * 100$

Other disciplines may use different equations.

References

Bland J.M. and Altman D.G., 1986 Statistical methods for assessing agreement between two methods of clinical measurement: Lancet, i, p. 307–310.

Clesceri, L.S., Greenberg, A.E., and Eaton, A.D., 1998, Standard methods for the examination of water and wastewater, 20th edition: Baltimore, Md, United Book Press, Inc., 1162 p.

Harvey, D., undated, Analytical chemistry 2.0: Analytical Sciences Digital Library: online at URL: http://www.asdlib.org/onlineArticles/ecourseware/Analytical

Helsel, D.R., and Hirsch, R.M., 2002, Statistical methods in water resources: U.S. Geological Survey Techniques of Water-Resources Investigations, book 4, chap. A3, 522 p.

Examples

# Example 15.2 from Harvey.
dupX1 <- c(160, 196, 207, 185, 172, 133)
dupX2 <- c(147, 202, 196, 193, 188, 119)
rmse(dupX1, dupX2)
rpd(dupX1, dupX2)

Description

Computes the receiver operator characteristics (ROC) for a logistic regression model.

Usage

roc(object)

Arguments

Value

An object of class "roc" haveing these components:

Note

Objects of class "roc" have print and plot methods.

References

Gonen, M., 2006, Receiver Operating Characteristics (ROC) Curves: SAS Users Group International Conference, Paper 210-31 18 p., available at http://www2.sas.com/proceedings/sugi31/210-31.pdf, last accessed Octocer 26, 2011.

Description

Computes the seasonal Kendall trend test with Sen slope estimator.

Usage

seaken(series, nseas = 12)

Arguments

Value

An object of class "htest" also inhereting class "seaken" containing the following components:

Note

The value of p.value is p.value.raw if there are fewer than 10 years of data and is p.value.corrected otherwise.

References

Hirsch, R.M., Alexander, R.B., and Smith, R.A., 1991, Selection of methods for the detection and estimation of trends in water quality: Water Resources Research, v. 27, p. 803–813.

Hirsch, R.M., Slack, J.R., and Smith, R.A., 1982, Techniques of trend analysis for monthly water quality data: Water Resources Research, v. 18, p. 107–121.

Hirsch, R.M., and Slack, J.R., 1984, A nonparametric trend test for seasonal data with serial dependence: Water Resources Research, v. 20, p. 727–732.

Kendall, M.G., 1938, A new measure of rank correlation: Biometrika v. 30, p. 81–89.

Kendall, M.G., 1976, Rank correlation methods (4th ed.): London, Griffin, 202 p.

Sen, P.K., 1968, Estimates of regression coefficient based on Kendall's tau: Journal of the American Statisical Association, v. 63, p. 1379–1389.

See Also

kensen.test, regularSeries

Examples

## Not run: 
library(smwrData)
library(smwrBase)
data(KlamathTP)
RegTP <- with(KlamathTP, regularSeries(TP_ss, sample_dt))
# The warning generated is expected and acceptable for these data
seaken(RegTP$Value, 12)
# Manaus river data is in package boot
library(boot)
data(manaus)
manaus.sk <- seaken(manaus, 12)
print(manaus.sk)
# Note for these data the large difference between the raw and corrected p-values.
#  p-value (raw) is << 0.001
manaus.sk$p.value.raw
#  p-value (with correlation correction) is = 0.10
manaus.sk$p.value.corrected
#  Hence, it may be concluded that these particular data show substantial serial correlation
#  as seen with see with acf(manaus).

## End(Not run)

Description

Computes the timing of the seasonal peak value. The timing of the seasonal peak is needed for the seasonalWave model (Vecchia and others, 2008).

Usage

seasonalPeak(x, y)

Arguments

Details

The timing of the peak of the data is computed by identifying the largest value produced by smoothing that data with supsmu. The remaining data in the attributes are used by using the seasonalPeak method of confirm.

Value

An object of class seasonalPeak. The unconfirmed object is a single value that represents the estimate of the timing of the peak and five additional attributes.

Data: a list of the x and y values where x is the fractional part of the original decimal time data. Missing values have been removed.
Smooth: a list of the x and y smoothed values.
Points: a list of 361 evenly spaced xout and yout values.
Extra: pointers to all the peaks in Points.
Confirmed: logical indicating that the object has not been confirmed.

Note

The generic functions print and confirm have methods for object of class seasonalPeak.

References

Vecchia, A.V., Martin, J.D., and Gilliom, R.J., 2008, Modeling variability and trends in pesticide concentrations in streams: Journal of the American Water Resources Association, v. 44, no. 5, p. 1308-1324

See Also

seasonalWave, confirm.seasonalPeak, supsmu, print.seasonalPeak

Examples

library(smwrData)
data(QW05078470)
with(QW05078470, seasonalPeak(dectime(DATES), P00665))
## Should be:
# Default value: 0.499
# Alternate values: 0.497

Description

Computes a seasonal wave model to describe the variation of a constituent over the course of a year. This model is particularly well suited to describe the concentration of pesticides.

Usage

seasonalWave(x, cmax, loading, hlife, second.peak = NULL)

Arguments

Details

The seasonal wave model $W(t)$ is expressed as a differential equation

$\frac{d}{dt} W(t) = \lambda(t) - \phi W(t) [0 \le t \le 1,$

$W(0)=W(1)]$

$\lambda(t) = \sum_{k=1}^12 \omega_k I(\frac{k-1}{12} \le t <$

$\frac{k}{12})$

where $\phi$ is a specified constant, which represents the rate of removal or chemical decay; $[\omega_k, k=1,2,...,12]$ are specified nonnegative constants, which represent monthly input amounts; $I(.)$ is the indicator function with $I(.)=1$ if $t$ lies in the given interval and $I(.)=0$ otherwise; and $\lambda(t)$ is the input amount at time $t$.

The value of hlife is used to define the decay rate $\phi$ in the differential equation. The value of $\phi$ is 12/hlife and $W(t)$ decays at a a rate of $exp(-\phi/12)$ per month.

The list for second.peak must contain these components:
la, the lag from the primary peak to the second peak, in months. This is always the time from the primary peak to the second peak, even if the second peak occurs earlier in the year.
lo, the loading duration in months, this value must be leas than la. w, the load scaling factor relative to the primary peak. Must be greater than 0 and less than or equal to 1. For practical pruposes, it should be greater than 0.5.

Value

A vector expressing the expected variation of concentration for each value in x; the values are scaled to a range of -0.5 to 0.5.

Author(s)

Dave Lorenz, original coding by Aldo Vecchia.

References

Vecchia, A.V., Martin, J.D., and Gilliom, R.J., 2008, Modeling variability and trends in pesticide concentrations in streams: Journal of the American Water Resources Association, v. 44, no. 5, p. 1308-1324.

See Also

seasonalPeak, confirm.seasonalPeak

Examples

## Not run: 
# Selected single peak models
# 1 month loading, 1 month half-life
curve(seasonalWave(x, 3/12, 1, 1), 0, 1, n=361, xlab='fraction of year', ylab="W")
# 1 month loading, 3 month half-life
curve(seasonalWave(x, 3/12, 1, 3), 0, 1, n=361, add=TRUE, col="blue")
# 3 month loading, 2 month half-life
curve(seasonalWave(x, 3/12, 3, 2), 0, 1, n=361, add=TRUE, col="green")
# Add a second peak model
curve(seasonalWave(x, 3/12, 3, 2, second.peak=list(la=6, lo=2, w=.75) ), 0, 1,
  n=361, add=TRUE, col="red")

## End(Not run)

Description

This is a support function for seasonalWave model (Vecchia and others, 2008).

Usage

seasonalWave.fit(cmax, wtx, pkt, phi)

Arguments

Value

A vector of 361 values describing the annual seasonal wave.

Note

This function is support for the seasonalWave function and is not intended to be called by the user.

Author(s)

Dave Lorenz, original coding by Aldo Vecchia.

References

Vecchia, A.V., Martin, J.D., and Gilliom, R.J., 2008, Modeling variability and trends in pesticide concentrations in streams: Journal of the American Water Resources Association, v. 44, no. 5, p. 1308-1324.

See Also

seasonalWave

Description

This is a support function for seasonalWave model (Vecchia and others, 2008).

Usage

seasonalWave.wt(loading, second.peak)

Arguments

Details

If second.peak is supplied, then it must be a list with these components:
la, the lag (number of months) between the primary and second peak;
lo, the loading duration (number of months) for the second peak (must be less than la;
w, the weigthing factor for the second peak loading, relative to the primary peak. Must be greater than 0 and less than or equal to 1.

Value

The weighting vector for the seasaon wave model. A vector of length 12 that represents the relative loading to the system.

Note

This function is support for the seasonalWave function and is not intended to be called by the user.

References

Vecchia, A.V., Martin, J.D., and Gilliom, R.J., 2008, Modeling variability and trends in pesticide concentrations in streams: Journal of the American Water Resources Association, v. 44, no. 5, p. 1308-1324.

See Also

seasonalWave

Description

Selects the "best" parameters for a seasonal wave fit.

Usage

selBestWave(formula, data, dec.time, wave.list, exhaustive = FALSE,
  Regression = lm, Test = AIC, ...)

Arguments

Details

For logistic regression, use Regression=glm, Test=deviance, family=binomial(link="logit").

Value

A 4- or 7-column matrix of the "best" models. The columns are the timing of the peak (Cmax), the primary peak loading (Loading), the half life (Hlife), and the test score (Test). If the model is a two-peak model, then additional columns (la, lo, and w) describeing the second peak are included.

References

Vecchia, A.V., Martin, J.D., and Gilliom, R.J., 2008, Modeling variability and trends in pesticide concentrations in streams: Journal of the American Water Resources Association, v. 44, no. 5, p.1308–1324.

Examples

## See the SeasonalWave demo

Description

Computes the Sen slope with confidence interval and an intercept for paired data.

Usage

senSlope(formula, data, subset, na.action, intercept = "Ac", CI = 0.95)

Arguments

Details

The argument intercept may be either "Ac" or "A1m." If it is "Ac," then the intercept is computed from the median of y and x, also known as the Conover method. If it is "A1m," then the intercept is chosen so that the median of the residuals is zero.

Value

An object of class "senSlope" with these components:

References

Dietz, E.J., 1989, Teaching regression in a nonparametric statistics course: The American Statstician, v. 43, p. 35–40

Helsel, D.R., and Hirsch, R.M., 2002, Statistical methods in water resources: U.S. Geological Survey Techniques of Water-Resources Investigations, book 4, chap. A3, 522 p.

Sen, P.K., 1968, Estimates of the regression coefficient based on Kendall's tau: Journal of the American Statistical Association, v. 63 p. 1379–1389

See Also

kensen.test, serial.test

Examples

## Not run: 
library(smwrData)
data(SaddlePeaks)
senSlope(Flow ~ Year, data=SaddlePeaks)

## End(Not run)

Description

Performs either of two nonparametric tests (Wilcoxon Rank-Sum test or runs test) for serial correlation. Both tests compute Z, which is the product of sequential values of x after removing any trend and normalizing so that the median of Z values is 0.

Usage

serial.test(x, method = "wilcoxon")

Arguments

Details

If the method is "wilcoxon," then the Wilcoxon Rank-Sum test (Wilcoxon, 1945) is performed to compare the distribution of positive Z values to the distribution of negative Z values. Excessive numbers of positive Z values suggests positive serial correlation and excessive negative Z values suggests negative serial correlation.

If the method is "runs," then the runs test (Wald and Wolfowitz, 1940) is performed on sequences of positive and negative values of Z. If there is a larger than expected number of runs, then that suggest negative serial correlation and if fewer than the expected number of runs, then positive serial correlation.

Value

An object of class htest containing the following components:

Note

The null hypothesis is that the data are uncorrelated.

References

Dufour, J.M., 1981, Rank test for serial dependence: Journal of the Time Series Analysis, v. 2, no. 3, p. 117–128.

Wald, A., and Wolfowitz, J., 1940, On a test whether two samples are from the same population: Annals of Mathematical Statistics, v. 11, p. 147–162.

Wilcoxon, F., 1945, Individual comparisons by ranking methods: Biometrics, v. 1, p. 80–83.

Description

Produces a plot of time-series data by season that shows seasonal and overall trends: method for "seaken" object.

Usage

## S3 method for class 'seaken'
seriesPlot(x, SeasonLine = list(name = "", what = "vertical",
  color = "black"), SeasonPoint = list(name = "", what = "points", symbol =
  "circle", filled = TRUE, size = 0.09, color = "black"), yaxis.log = FALSE,
  yaxis.range = c(NA, NA), ylabels = 7, xlabels = x$seasonames,
  xtitle = "", ytitle = deparse(substitute(x)), caption = "",
  margin = c(NA, NA, NA, NA), SeasonTrend = list(name = "", what = "lines",
  color = "brown"), TrendLine = list(name = "", what = "lines", color =
  "blue"), ...)

Arguments

Details

The argument what for SeasonLine must be either "lines" or "vertical." See monthplot for more information.
The argument what for either SeasonPoint, SeasonTrend, or trendLine may be set to "none" to suppress drawing of that feature.

Value

Information about the graph.

See Also

monthplot, seasonPlot, seaken

Description

Computes the skewness statistic.

Usage

skew(x, na.rm = TRUE, method = "fisher")

Arguments

Value

a single value representing the skewness of the data in x.

References

Helsel, D.R. and Hirsch, R.M., 2002, Statistical methods in water resources: U.S. Geological Survey Techniques of Water-Resources Investigations, book 4, chap. A3, 522 p.

Examples

skew(c(1.0, 1.2, 1.5, 1.9, 2.5))

Description

Summarizes the correlations: method for "cor.all" object.

Usage

## S3 method for class 'cor.all'
summary(object, p.adjust = "holm", variable = NULL, ...)

Arguments

Value

A data frame containing columns of the paired variables, the correlation, the adjusted p-value, and the number of observations in the correlation.

See Also

cor.all

Examples

library(smwrData)
data(TNLoads)
# Extract only the correlations with the log of total nitrogen
summary(cor.all(TNLoads[, 1:5]), variable="LOGTN")

Description

Creates a dataset of specified summary statistics from a collection of data.

Usage

sumStats(..., group = NULL, Num = "Num", Stats = list(Mean = mean, StdDev
  = sd), Probs = (0:4)/4, na.rm = TRUE)

Arguments

Value

A data frame containing columns identifying each variable in ..., any grouping variables, and the requested statistics as named in the call.

Note

Commonly used functions referenced in the Stats arguments include mean, sd, skew and var.

The statistics requested by the Probs argument are computed by the quantile function using type=2.

References

Helsel, D.R. and Hirsch, R.M., 2002, Statistical methods in water resources: U.S. Geological Survey Techniques of Water-Resources Investigations, book 4, chap. A3, 522 p.

See Also

mean, sd, skew, var, quantile,

Examples

## Generate a random sample
set.seed(222)
XX.rn <- rexp(32)
sumStats(XX.rn)

Description

Computes the mean weighted by the duration between values.

Usage

timeWeightedMean(x, time, na.rm = TRUE, fill = TRUE, by.period = FALSE,
  excessive = 2.5)

Arguments

Details

The values of time are expected to be in decimal format, where the integer part indicates the period and the fractional part linearly distributed through the period. For example, the year 2000 begins at 2,000.0 and July 2, 2000 is 2,000.5. The function dectime can be used to convert Date or POSIX to decimal format. If time is of class "Date," or any "POSIX" classs, it is converted using dectime.
If na.rm is FALSE and byeriod is TRUE, then missing values are returned only for periods that contain a missing value (NA).

Value

If by.period is TRUE, then a vector with one entry per period, otherwise the mean for the entire data set.

References

Crawford,C.G., 2004, Sampling strategies for estimating acute and chronic exposures of pesticides in streams: Journal of the American Water Resources Association, v. 40, n. 2, p 485-502.

See Also

weighted.mean, dectime

Examples

## Not run: 
library(smwrData)
data(QW05078470)
with(QW05078470, timeWeightedMean(P00665, dectime(DATES)))

## End(Not run)

Description

Generates a basis matrix for piecewise linear modeling of trends.

Usage

trends(x, breaks, boundary.breaks = c(FALSE, FALSE), steps)

Arguments

Value

A matrix of dimension length of x by number of linear trend and step trends. The breaks are included as an attribute.

Note

Each trend is 0 prior to the break, and then increases at the rate of 1 per unit and maintain that maximum value after the break. The regression coefficient then reprents the trend as a rate. A step trend is 0 before the step and 1 after it.

See Also

floor, ceiling, curvi

Examples

# model two piecewise linear trends from 2000 to 2004, with a break at 2001 and 2003
trends(2000 + seq(0,20)/5, breaks=c(2001, 2003))

Description

Computes the variance inflation factor (Helsel and Hirsch, 2002) for each variable in a linear regression fit.

Usage

vif(model, ...)

## S3 method for class 'lm'
vif(model, ...)

Arguments

Value

A named numeric vector containing the variance inflation factors for each variable.

References

Helsel, D.R. and Hirsch, R.M., 2002, Statistical methods in water resources: U.S. Geological Survey Techniques of Water-Resources Investigations, book 4, chap. A3, 522 p.