PWD_RL: Weighted Deming - Rocke-Lorenzato - known sigma, kappa

In ppwdeming: Precision Profile Weighted Deming Regression

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, epsilon=1e-6)

Arguments

X	the vector of predicate readings,
Y	the vector of test readings,
sigma	the RL sigma parameter,
kappa	the RL kappa parameter,
lambda	optional (default of 1) - the ratio of the X to the Y precision profile,
epsilon	optional - convergence tolerance limit.

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:

alpha	the fitted intercept
beta	the fitted slope
fity	the vector of predicted Y
mu	the vector of estimated latent true values
resi	the vector of residuals
like	the -2 log likelihood L
innr	the number of inner refinement loops executed
error	an error code if the iteration fails

Author(s)

Douglas M. Hawkins, Jessica J. Kraker [e-mail]

References

Hawkins DM and Kraker JJ. Precision Profile Weighted Deming Regression for Methods Comparison, on Arxiv (2025) doi:10.48550/arXiv.2508.02888

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

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 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")

ppwdeming documentation built on Sept. 9, 2025, 5:37 p.m.