PWD_inference: Weighted Deming Regression - Inference

In ppwdeming: Precision Profile Weighted Deming Regression

Weighted Deming Regression – Inference

Description

This routine fits the regression, uses the jackknife to get its precision, and optionally prints it out. Currently implements Rocke-Lorenzato as the variance profile model.

Usage

PWD_inference(X, Y, lambda=1, MDL=NA, epsilon=1e-8, printem=FALSE)

Arguments

X	the vector of predicate readings,
Y	the vector of test readings,
lambda	optional (default of 1) - the ratio of the X to the Y precision profile.
MDL	optional (default to missing) - medical decision level(s),
epsilon	optional (default of 1.e-8) - convergence tolerance limit,
printem	optional - if TRUE, routine will print out results as a message.

Details

For the linear model relating the predicate and test readings, the standard errors of the estimators \hat{\alpha}, \hat{\beta}, and their covariance are estimated by the jackknife. The 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.

Value

A list containing the following components:

alpha	the fitted intercept
beta	the fitted slope
cor	the Pearson correlation between X and Y
fity	the vector of predicted Y
mu	the vector of estimated latent true values
resi	the vector of residuals
preresi	the vector of leave-one-out predicted residuals
sigma	the estimate of the Rocke-Lorenzato \sigma
kappa	the estimate of the Rocke-Lorenzato \kappa
like	the -2 log likelihood L
sealpha	the jackknife standard error of alpha
sebeta	the jackknife standard error of beta
covar	the jackknife covariance between alpha and beta
preMDL	the predictions at the MDL(s)
preMDLl	the lower confidence limit(s) of preMDL
preMDLu	the upper confidence limit(s) of preMDL

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

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

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,printem=TRUE)

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