Package {ppwdeming}

Weighted Deming – Rocke-Lorenzato - known sigma, kappa

Description

This code fits the weighted Deming regression on predicate readings (X) and test readings (Y), with user-supplied Rocke-Lorenzato ("RL") parameters sigma (\sigma) and kappa (\kappa).

Usage

PWD_RL(X, Y, sigma, kappa, lambda=1, alpha=NA, beta=NA, mu=NA, epsilon=1e-8)

Arguments

Details

The Rocke-Lorenzato precision profile model assumes the following forms for the variances, with proportionality constant \lambda:

• predicate precision profile model: g_i = var(X_i) = \lambda\left(\sigma^2 + \left[\kappa\cdot \mu_i\right]^2\right) and

• test precision profile model: h_i = var(Y_i) = \sigma^2 + \left[\kappa\cdot (\alpha + \beta\mu_i)\right]^2.

The algorithm uses maximum likelihood estimation. Proportionality constant \lambda is assumed to be known or estimated externally.

Value

A list containing the following components:

Author(s)

Douglas M. Hawkins, Jessica J. Kraker krakerjj@uwec.edu

References

Hawkins DM and Kraker JJ (2026). Precision Profile Weighted Deming Regression for Methods Comparison. The Journal of Applied Laboratory Medicine, 11(2), 379-392. https://doi.org/10.1093/jalm/jfaf183

Hawkins DM (2014). A Model for Assay Precision. Statistics in Biopharmaceutical Research, 6, 263-269. https://doi.org/10.1080/19466315.2014.899511

Examples

# library
library(ppwdeming)

# parameter specifications
n <- 100

sigma <- 1
kappa <- 0.08
alpha <- 1
beta  <- 1.1
true  <- 8*10^((0:(n-1))/(n-1))
truey <- alpha+beta*true
# simulate single sample - set seed for reproducibility
set.seed(1039)
# specifications for predicate method
X     <- sigma*rnorm(100)+true *(1+kappa*rnorm(n))
# specifications for test method
Y     <- sigma*rnorm(100)+truey*(1+kappa*rnorm(n))

# fit RL with given sigma and kappa
RL_results <- PWD_RL(X,Y,sigma,kappa)
cat("\nWith given sigma and kappa, the estimated intercept is",
    signif(RL_results$alpha,4), "and the estimated slope is",
    signif(RL_results$beta,4), "\n")

Estimate of Variance Profile Functions (proportional)

Description

This code estimates the variance profiles, assumed proportional, of the Rocke-Lorenzato form; also provides the resulting weighted Deming fit and residuals.

Usage

PWD_get_gh(X, Y, lambda = 1,
           rho=lifecycle::deprecated(),
           alpha=lifecycle::deprecated(), beta=lifecycle::deprecated(),
           mu=lifecycle::deprecated(),
           quad=FALSE, epsilon = 1e-8,
           printem=lifecycle::deprecated())

Arguments

Details

This workhorse routine optimizes the likelihood in the unknown g, h setting over its n+4 or n+5 parameters: the two Rocke-Lorenzato precision profile parameters \sigma and \kappa, the intercept \alpha and slope \beta (and coefficien of the squared term \gamma, if quadratic), and the n latent true concentrations \mu_i.

That is, the assumed forms are:

• predicate precision profile model: g_i = var(X_i) = \lambda\left(\sigma^2 + \left[\kappa\cdot \mu_i\right]^2\right) and

• test precision profile model: h_i = var(Y_i) = \sigma^2 + \left[\kappa\cdot (\alpha + \beta\mu_i)\right]^2.

The search algorithm implements an efficient approach via reparameterization to the ratio \rho = \frac{\sigma}{\kappa}.

Value

A list containing the following components:

Author(s)

Douglas M. Hawkins, Jessica J. Kraker krakerjj@uwec.edu

References

Hawkins DM and Kraker JJ (2026). Precision Profile Weighted Deming Regression for Methods Comparison. The Journal of Applied Laboratory Medicine, 11(2), 379-392. https://doi.org/10.1093/jalm/jfaf183

Rocke DM, Lorenzato S (2012). A Two-Component Model for Measurement Error in Analytical Chemistry. Technometrics, 37:2:176-184.

Examples

# library
library(ppwdeming)

# parameter specifications
n <- 100

quad  <- FALSE   # for a linear fit
quad  <- TRUE    # for a quadratic fit
sigma <- 1
kappa <- 0.08
alpha <- 1
beta  <- 1.1
gamma <- 0
if (quad) gamma <- -0.005
true  <- 8*10^((0:(n-1))/(n-1))
truey <- alpha+beta*true+gamma*true^2
# simulate single sample - set seed for reproducibility
set.seed(1039)
# specifications for predicate method
X     <- sigma*rnorm(100)+true *(1+kappa*rnorm(n))
# specifications for test method
Y     <- sigma*rnorm(100)+truey*(1+kappa*rnorm(n))

# fit with RL precision profile to estimate parameters
RL_gh_fit  <- PWD_get_gh(X,Y, quad=quad)

# results
summary(RL_gh_fit)

Precision-Profile Weighted Deming Regression – Inference

Description

This routine fits the regression and uses the jackknife to get its precision. Implements Rocke-Lorenzato as the variance profile model.

Usage

PWD_inference(X, Y, lambda=1,
              rho=lifecycle::deprecated(),
              alpha=lifecycle::deprecated(), beta=lifecycle::deprecated(),
              mu=lifecycle::deprecated(),
              MDL=NA,
              quad=FALSE, epsilon=1e-8,
              printem=lifecycle::deprecated())

Arguments

Details

For the linear model relating the predicate and test readings, the standard errors of the estimators \hat{\alpha}, \hat{\beta}, (and \hat{\gamma}, if quadratic) and their covariance are estimated by the jackknife. The point estimates of the intercept and slope are output, along with their standard errors and covariance.

These estimates are further used to estimate the predictions at the input MDL, if appropriate.

Value

A list containing the following components:

Author(s)

Douglas M. Hawkins, Jessica J. Kraker krakerjj@uwec.edu

References

Hawkins DM and Kraker JJ (2026). Precision Profile Weighted Deming Regression for Methods Comparison. The Journal of Applied Laboratory Medicine, 11(2), 379-392. https://doi.org/10.1093/jalm/jfaf183

Efron, B (1982). The jackknife, the bootstrap and other resampling plans. Society for Industrial and Applied Mathematics.

Examples

# library
library(ppwdeming)

# parameter specifications
n <- 100

sigma <- 1
kappa <- 0.08
alpha <- 1
beta  <- 1.1
quad  <- FALSE # or
#quad  <- TRUE
gamma <- 0
if (quad) gamma <- -0.005
true  <- 8*10^((0:(n-1))/(n-1))
truey <- alpha+beta*true+gamma*true^2
# simulate single sample - set seed for reproducibility
set.seed(1039)
# specifications for predicate method
X     <- sigma*rnorm(100)+true *(1+kappa*rnorm(n))
# specifications for test method
Y     <- sigma*rnorm(100)+truey*(1+kappa*rnorm(n))

# fit with RL precision profile to estimate parameters and variability
RL_inf <- PWD_inference(X,Y,MDL=12, quad=quad)

# summary of results
summary(RL_inf)

Weighted Deming Regression – general weights

Description

This code is used for the setting of known precision profiles implemented in user-provided R functions called gfun and hfun.

Usage

PWD_known(X, Y, gfun, hfun, gparms, hparms, epsilon=1e-8,
          MDL=NA, getCI=TRUE,
          printem=lifecycle::deprecated())

Arguments

Details

The functions gfun and hfun are allowed as inputs, to support flexibility in specification of the forms of these variance functions. The known precision profiles specified by the functions gfun and hfun, when provided with estimated vectors of \mu and \alpha + \beta\mu respectively and with any required parameters, will produce the vectors g and h. These vectors are then integrated into the iterative estimation of the slope and intercept of the linear relationship between predicate and test readings.

Value

A list containing the following components:

Author(s)

Douglas M. Hawkins, Jessica J. Kraker krakerjj@uwec.edu

Examples

# library
library(ppwdeming)

# parameter specifications
n <- 100

alpha <- 1
beta  <- 1.1
true  <- 8*10^((0:(n-1))/(n-1))
truey <- alpha+beta*true
# forms of precision profiles
gfun    <- function(true, gparms) {
  gvals = gparms[1]+gparms[2]*true^gparms[3]
  gvals
}
hfun    <- function(true, hparms) {
  hvals = hparms[1]+hparms[2]*true^hparms[3]
  hvals
}

# Loosely motivated by Vitamin D data set
g     <- 4e-16+0.07*true^1.27
h     <- 6e-2+7e-5*truey^2.2
# simulate single sample - set seed for reproducibility
set.seed(1039)
# specifications for predicate method
X     <- true +sqrt(g)*rnorm(n)
# specifications for test method
Y     <- truey+sqrt(h)*rnorm(n)

# fit with to estimate linear parameters
pwd_known_fit <- PWD_known(X, Y, gfun, hfun,
                           gparms=c(4e-16, 0.07, 1.27),
                           hparms=c(6e-2, 7e-5, 2.2), MDL=12)
# display results
summary(pwd_known_fit)

Weighted Deming Regression – Outlier scanning

Description

This function tests for outliers from the fitted regression, and refits on a sanitized data set (with outliers removed).

Usage

PWD_outlier(X, Y, K, lambda=1, Pcut=0.01,
            rho=lifecycle::deprecated(),
            alpha=lifecycle::deprecated(), beta=lifecycle::deprecated(),
            mu=lifecycle::deprecated(),
            quad=FALSE)

Arguments

Details

The method is modeled on the Rosner sequential ESD outlier procedure and assumes the sample is large enough to ignore the effect of random variability in the parameter estimates on the distribution of the residuals.

Value

A list containing the following components:

Author(s)

Douglas M. Hawkins, Jessica J. Kraker krakerjj@uwec.edu

References

Hawkins DM and Kraker JJ (2026). Precision Profile Weighted Deming Regression for Methods Comparison. The Journal of Applied Laboratory Medicine, 11(2), 379-392. https://doi.org/10.1093/jalm/jfaf183

Hawkins DM (2008). Outliers in Wiley Encyclopedia of Clinical Trials, eds R. D’Agostino, L. Sullivan, and J. Massaro. Wiley, New York.

Examples

# library
library(ppwdeming)

# parameter specifications
n <- 100

sigma <- 1
kappa <- 0.08
alpha <- 1
beta  <- 1.1
true  <- 8*10^((0:(n-1))/(n-1))
truey <- alpha+beta*true
# simulate single sample - set seed for reproducibility
set.seed(1069)
# specifications for predicate method
X     <- sigma*rnorm(100)+true *(1+kappa*rnorm(n))
# specifications for test method
Y     <- sigma*rnorm(100)+truey*(1+kappa*rnorm(n))
# add some outliers
Y[c(1,2,100)] <- Y[c(1,2,100)] + c(-10,9,-50)

# check for outliers and store output
outliers_assess <- PWD_outlier(X, Y, K=5)

# summary of process
summary(outliers_assess)

Fit Rocke-Lorenzato profile model to residuals

Description

This routine fits the Rocke-Lorenzato precision profile model to the residuals from the fit.

Usage

PWD_resi(true, resi, epsilon=1e-8,
         printem=lifecycle::deprecated())

Arguments

Details

The Rocke-Lorenzato precision profile model is

SD^2 = \sigma_r^2 + (\kappa_r\cdot true)^2

for the residuals from a precision-profile model fit.

Under this model, the approach for reviewing residuals is to fit a variance profile model to the residuals r_i themselves. The output of this function includes a maximum-likelihood estimate of the remaining parameter in the special cases of:

• constant variance (\kappa_r = 0); and

• constant coefficient of variation (\sigma_r = 0).

Value

A list containing the following components:

Author(s)

Douglas M. Hawkins, Jessica J. Kraker krakerjj@uwec.edu

References

Hawkins DM and Kraker JJ (2026). Precision Profile Weighted Deming Regression for Methods Comparison. The Journal of Applied Laboratory Medicine, 11(2), 379-392. https://doi.org/10.1093/jalm/jfaf183

Hawkins DM (2014). A Model for Assay Precision. Statistics in Biopharmaceutical Research, 6, 263-269. http://dx.doi.org/10.1080/19466315.2014.899511

Examples

# library
library(ppwdeming)

# parameter specifications
n <- 100

sigma <- 1
kappa <- 0.08
alpha <- 1
beta  <- 1.1
true  <- 8*10^((0:(n-1))/(n-1))
truey <- alpha+beta*true
# simulate single sample - set seed for reproducibility
set.seed(1039)
# specifications for predicate method
X     <- sigma*rnorm(100)+true *(1+kappa*rnorm(n))
# specifications for test method
Y     <- sigma*rnorm(100)+truey*(1+kappa*rnorm(n))

# fit the model and store output
RL_gh_fit  <- PWD_get_gh(X,Y)
# run the residual analysis from the model output
post  <- PWD_resi(X, RL_gh_fit$resi)
summary(post)

Weighted Deming Regression

Description

This code fits the weighted Deming regression on predicate readings (X) and test readings (Y).

Usage

WD_General(X, Y, g, h, epsilon=1e-8)

Arguments

Details

This function is used when the variances of X and Y are already known, as can be the case from an adequate number of replicate X and Y readings of each sample. For input vectors g and h containing the variances of predicate readings X and test readings Y, respectively, iteratively fits weighted Deming regression.

Value

A list containing the following components:

Author(s)

Douglas M. Hawkins, Jessica J. Kraker krakerjj@uwec.edu

References

Ripley BD and Thompson M (1987). Regression techniques for the detection of analytical bias. Analyst, 112, 377-383.

Examples

# library
library(ppwdeming)

# parameter specifications
n <- 100

alpha <- 1
beta  <- 1.1
true  <- 8*10^((0:(n-1))/(n-1))
truey <- alpha+beta*true
# Loosely motivated by Vitamin D data set
g     <- 4e-16+0.07*true^1.27
h     <- 6e-2+7e-5*truey^2.2

# simulate single sample - set seed for reproducibility
set.seed(1039)
# specifications for predicate method
X     <- true +sqrt(g)*rnorm(n)
# specifications for test method
Y     <- truey+sqrt(h)*rnorm(n)

# fit with to estimate linear parameters
wd_fit <- WD_General(X,Y,g,h)
cat("\nWith given g and h, the estimated intercept is",
    signif(wd_fit$alpha,4), "and the estimated slope is",
    signif(wd_fit$beta,4), "\n")

Linnet proportional CV weighted Deming

Description

This routine, provided for convenience, makes Linnet’s constant CV fit.

Usage

WD_Linnet(X, Y, lambda=1, MDL=NA, getCI=TRUE, epsilon=1e-10, printem=FALSE)

Arguments

Details

Note that in cases where sigma happens to come out zero, Linnet’s constant CV fit differs from the precision-profile fit since the underlying precision profile models are not the same.

Value

A list containing the following components:

Author(s)

Douglas M. Hawkins, Jessica J. Kraker krakerjj@uwec.edu

References

Linnet K (1993). Evaluation of regression procedures for methods comparison studies. Clinical Chemistry, 39: 424-432.

Examples

# library
library(ppwdeming)

# parameter specifications
n <- 100
alpha <- 1
beta  <- 1.1
true  <- 8*10^((0:(n-1))/(n-1))
truey <- alpha+beta*true
kappa <- 0.1

# simulate single sample - set seed for reproducibility
set.seed(1039)
# specifications for predicate method
X     <- true *(1+kappa*rnorm(n))
# specifications for test method
Y     <- truey *(1+kappa*rnorm(n))

# fit with to estimate linear parameters
wd_fit <- WD_Linnet(X, Y, MDL=12, printem=TRUE)
cat("\nThe Linnet constant-CV estimated intercept is",
    signif(wd_fit$alpha,4), "and the estimated slope is",
    signif(wd_fit$beta,4), "\n")

Multiple Instrument Weighted Deming Regression

Description

This code estimates the Rocke-Lorenzato precision profile parameters and the regression of each instrument’s values on the underlying latent true concentration.

Usage

multi_PWD(X, names, refine=1)

Arguments

Details

The function optimizes the likelihood over the parameter rho, the ratio of the Rocke-Lorenzato parameters sigma to kappa: \rho = \frac{\sigma}{\kappa}. Calls multi_PWD_inner to provide the estimates of the other parameters.

Value

A list containing the following components:

Author(s)

Douglas M. Hawkins, Jessica J. Kraker krakerjj@uwec.edu

References

Hawkins DM and Kraker JJ. Multiple Instrument Methods Comparison by Precision weighted Deming Regression, on Arxiv (2026) https://doi.org/10.48550/arXiv.2607.11776

.

Examples

# library
library(ppwdeming)

# parameter specifications
n  <- 100
I  <- 4
alpha  <- c(0  , 0  , 2  , -2 )
beta   <- c(0.9, 1.1, 1.2, 0.8)
names   <- c("Inst_1", "Inst_2", "Inst_3", "Inst_4")
lambda <- c(1.8, 0.45, 0.9, 0.9)
rutlam <- sqrt(lambda)
sigma  <- 2
kappa  <- 0.08
true   <- 8*10^((0:(n-1))/(n-1))

# simulated data
set.seed(1039)
X     <- NULL
for (i in 1:I)  {
  truey <- alpha[i] + beta[i]*true
  X <- cbind(X, truey+rutlam[i]*(sigma*rnorm(n) + truey*kappa*rnorm(n)))
}

# fit with RL precision profile to estimate parameters
fit <- multi_PWD(X, names=names)

# results
summary(fit)

Jack-knife inference on the parameters of the Multiple Instrument fit

Description

This code uses jackknifing of the Multiple-Instrument fit to get standard errors of the regression parameters and lambda values.

Usage

multi_PWD_inf(X, names=NA, refine=1)

Arguments

Details

Uses jackknifing to get standard errors for the slopes beta, intercepts alpha, and lambda values of the I instruments.

Value

A list containing the following components:

Author(s)

Douglas M. Hawkins, Jessica J. Kraker krakerjj@uwec.edu

References

Hawkins DM and Kraker JJ. Multiple Instrument Methods Comparison by Precision weighted Deming Regression, on Arxiv (2026) https://doi.org/10.48550/arXiv.2607.11776

Examples

# library
library(ppwdeming)

# parameter specifications
n  <- 100
I  <- 4
alpha  <- c(0  , 0  , 2  , -2 )
beta   <- c(0.9, 1.1, 1.2, 0.8)
names   <- c("Inst_1", "Inst_2", "Inst_3", "Inst_4")
lambda <- c(1.8, 0.45, 0.9, 0.9)
rutlam <- sqrt(lambda)
sigma  <- 2
kappa  <- 0.08
true   <- 8*10^((0:(n-1))/(n-1))

# simulated data
set.seed(1039)
X     <- NULL
for (i in 1:I)  {
  truey <- alpha[i] + beta[i]*true
  X <- cbind(X, truey+rutlam[i]*(sigma*rnorm(n) + truey*kappa*rnorm(n)))
}

# application
inf <- multi_PWD_inf(X, names=names)
inf$alpha; inf$beta

# summary
summary(inf)

Multiple Instrument Parameter Estimation from rho

Description

This is primarily a workhorse routine that multi_PWD calls and, given a value of rho, estimates the other model parameters.

Usage

multi_PWD_inner(X, rho, refine=1, eps=1e-9)

Arguments

Details

Using the specified \rho, the routine calculates the estimates of the regression parameters and \lambda.

Value

A list containing the following components:

Author(s)

Douglas M. Hawkins, Jessica J. Kraker krakerjj@uwec.edu

References

Hawkins DM and Kraker JJ. Multiple Instrument Methods Comparison by Precision weighted Deming Regression, on Arxiv (2026) https://doi.org/10.48550/arXiv.2607.11776

.

Examples

# library
library(ppwdeming)

# parameter specifications
n  <- 100
I  <- 4
alpha  <- c(0  , 0  , 2  , -2 )
beta   <- c(0.9, 1.1, 1.2, 0.8)
names   <- c("Inst_1", "Inst_2", "Inst_3", "Inst_4")
lambda <- c(1.8, 0.45, 0.9, 0.9)
rutlam <- sqrt(lambda)
sigma  <- 2
kappa  <- 0.08
true   <- 8*10^((0:(n-1))/(n-1))

# simulated data
set.seed(1039)
X     <- NULL
for (i in 1:I)  {
  truey <- alpha[i] + beta[i]*true
  X <- cbind(X, truey+rutlam[i]*(sigma*rnorm(n) + truey*kappa*rnorm(n)))
}

Locate and test for outliers of the fit

Description

The routine uses a conventional multivariate outlier test statistic set, in the framework of Rosner’s multiple outlier search methodology, for the Multiple-Instrument fit. The vectors tested as multivariate outliers are the vectors of scaled residuals of each case.

Usage

multi_PWD_out(X, K=NA, names=NA, refine=1, Pcut=0.01)

Arguments

Details

A forward selection step identifies the K sequentially most extreme cases using scaled residuals from a sequence of fits. This is done by finding the Mahalanobis distance of each case’s vector of scaled residuals from the mean vector of all cases currently thought to be "clean". The case with the largest such distance is moved from the "clean" list to the "suspect" list and the model refitted using the new "clean" list. This is repeated until K cases are on the suspect list.

Backward re-inclusion follows. The model is fitted to the clean cases, and the Hotelling T^2 statistic between each suspect and the set of clean cases is computed. The case with the minimum T^2 is found and its Bonferroni P value computed. If it is not significant, the case is moved from the suspect back to the clean list. The process is repeated until either all suspects have been exonerated or a set of statistically significant outliers remains.

Value

A list containing the following components:

Author(s)

Douglas M. Hawkins, Jessica J. Kraker krakerjj@uwec.edu

References

Hawkins DM and Kraker JJ. Multiple Instrument Methods Comparison by Precision weighted Deming Regression, on Arxiv (2026) https://doi.org/10.48550/arXiv.2607.11776

Examples

# library
library(ppwdeming)

# parameter specifications
n  <- 100
I  <- 4
alpha  <- c(0  , 0  , 2  , -2 )
beta   <- c(0.9, 1.1, 1.2, 0.8)
names   <- c("Inst_1", "Inst_2", "Inst_3", "Inst_4")
lambda <- c(1.8, 0.45, 0.9, 0.9)
rutlam <- sqrt(lambda)
sigma  <- 2
kappa  <- 0.08
true   <- 8*10^((0:(n-1))/(n-1))

# simulated data
set.seed(1039)
X     <- NULL
for (i in 1:I)  {
  truey <- alpha[i] + beta[i]*true
  X <- cbind(X, truey+rutlam[i]*(sigma*rnorm(n) + truey*kappa*rnorm(n)))
}

# add outliers
X[1,4] <- X[1,4] + 15
X[n,2] <- X[n,2] / 1.5

# application
out <- multi_PWD_out(X, K=4, names=names)

# full summary of process
summary(out)

Summary information of output from PWD_get_gh or multi_PWD

Description

The function, invisible to the user, is called by summary() to display the formatted results of a model fitted by PWD_inference or by multi_PWD.

Usage

## S3 method for class 'pwdgetgh'
summary(object, digits = 6, ...)

Arguments

Value

object is returned invisibly per generic summary method conventions.

Examples

# library
library(ppwdeming)

# parameter specifications
quad  <- FALSE   # for a linear fit
quad  <- TRUE    # for a quadratic fit
sigma <- 1
kappa <- 0.08
alpha <- 1
beta  <- 1.1
gamma <- 0
if (quad) gamma <- -0.005
true  <- 8*10^((0:99)/99)
truey <- alpha+beta*true+gamma*true^2
# simulate single sample - set seed for reproducibility
set.seed(1039)
# specifications for predicate method
X     <- sigma*rnorm(100)+true *(1+kappa*rnorm(100))
# specifications for test method
Y     <- sigma*rnorm(100)+truey*(1+kappa*rnorm(100))

# fit with RL precision profile to estimate parameters
RL_gh_fit  <- PWD_get_gh(X,Y, quad=quad)

# results
summary(RL_gh_fit)

Summary information of output from PWD_inference or multiPWD_inf

Description

The function, invisible to the user, is called by summary() to display the formatted results of a model fitted by PWD_inference or by multiPWD_inf.

Usage

## S3 method for class 'pwdinf'
summary(object, conflevel = 0.95, digits = 4, ...)

Arguments

Value

object is returned invisibly per generic summary method conventions.

Examples

# library
library(ppwdeming)

# parameter specifications
sigma <- 1
kappa <- 0.08
alpha <- 1
beta  <- 1.1
true  <- 8*10^((0:99)/99)
truey <- alpha+beta*true
# simulate single sample - set seed for reproducibility
set.seed(1039)
# specifications for predicate method
X     <- sigma*rnorm(100)+true *(1+kappa*rnorm(100))
# specifications for test method
Y     <- sigma*rnorm(100)+truey*(1+kappa*rnorm(100))

# fit with RL precision profile to estimate parameters and variability
RL_inf <- PWD_inference(X,Y,MDL=12)
summary(RL_inf)

Summary information of output from PWD_known

Description

The function, invisible to the user, is called by summary() to display the formatted results of a model fitted by PWD_known.

Usage

## S3 method for class 'pwdknown'
summary(object, digits = 4, ...)

Arguments

Value

object is returned invisibly per generic summary method conventions.

Examples

# library
library(ppwdeming)

# parameter specifications
alpha <- 1
beta  <- 1.1
true  <- 8*10^((0:99)/99)
truey <- alpha+beta*true
# forms of precision profiles
gfun    <- function(true, gparms) {
  gvals = gparms[1]+gparms[2]*true^gparms[3]
  gvals
}
hfun    <- function(true, hparms) {
  hvals = hparms[1]+hparms[2]*true^hparms[3]
  hvals
}

# Loosely motivated by Vitamin D data set
g     <- 4e-16+0.07*true^1.27
h     <- 6e-2+7e-5*truey^2.2
# simulate single sample - set seed for reproducibility
set.seed(1039)
# specifications for predicate method
X     <- true +sqrt(g)*rnorm(100)
# specifications for test method
Y     <- truey+sqrt(h)*rnorm(100)

# fit with to estimate linear parameters
pwd_known_fit <- PWD_known(X, Y, gfun, hfun,
                           gparms=c(4e-16, 0.07, 1.27),
                           hparms=c(6e-2, 7e-5, 2.2), MDL=12)
summary(pwd_known_fit)

Summary information of output from PWD_outlier or multi_PWD_out

Description

The function, invisible to the user, is called by summary() to display the formatted results of a model fitted by PWD_outlier or by multi_PWD_out.

Usage

## S3 method for class 'pwdout'
summary(object, ...)

Arguments

Value

object is returned invisibly per generic summary method conventions.

Examples

# library
library(ppwdeming)

# parameter specifications
sigma <- 1
kappa <- 0.08
alpha <- 1
beta  <- 1.1
true  <- 8*10^((0:99)/99)
truey <- alpha+beta*true
# simulate single sample - set seed for reproducibility
set.seed(1069)
# specifications for predicate method
X     <- sigma*rnorm(100)+true *(1+kappa*rnorm(100))
# specifications for test method
Y     <- sigma*rnorm(100)+truey*(1+kappa*rnorm(100))
# add some outliers
Y[c(1,2,100)] <- Y[c(1,2,100)] + c(-10,9,-50)

# check for outliers, re-fit, and store output
outliers_assess <- PWD_outlier(X, Y, K=5)
summary(outliers_assess)

Summary information of output from PWD_resi

Description

The function, invisible to the user, is called by summary() to display the formatted results of output from PWD_resi.

Usage

## S3 method for class 'pwdresi'
summary(object, digits = 4, ...)

Arguments

Value

object is returned invisibly per generic summary method conventions.

Examples

# library
library(ppwdeming)

# parameter specifications
sigma <- 1
kappa <- 0.08
alpha <- 1
beta  <- 1.1
true  <- 8*10^((0:99)/99)
truey <- alpha+beta*true
# simulate single sample - set seed for reproducibility
set.seed(1039)
# specifications for predicate method
X     <- sigma*rnorm(100)+true *(1+kappa*rnorm(100))
# specifications for test method
Y     <- sigma*rnorm(100)+truey*(1+kappa*rnorm(100))

# fit the model and store output
RL_gh_fit  <- PWD_get_gh(X,Y)
# run the residual analysis from the model output
post  <- PWD_resi(X, RL_gh_fit$resi)
summary(post)