# Weighted Deming Regression -- general weights This code is used for the setting of known precision profiles implemented in user-provided R functions called `gfun` and `hfun`. ```r PWD_known(X, Y, gfun, hfun, gparms, hparms, epsilon=1e-8, MDL=NA, getCI=TRUE, printem=FALSE) ``` ## Arguments - `X`: the vector of predicate readings. - `Y`: the vector of test readings. - `gfun`: a function with two arguments, a vector of size **n** and a vector of parameters. - `hfun`: a function with two arguments, a vector of size **n** and a vector of parameters. - `gparms`: a numeric vector containing any parameters referenced by `gfun`. - `hparms`: a numeric vector containing any parameters referenced by `hfun`. - `epsilon`: **optional** (default of 1.e-8) - convergence tolerance limit. - `MDL`: **optional** (default of NA) - medical decision level(s). - `getCI`: **optional** (default of TRUE) - allows for jackknifed standard errors on the regression and MDL. - `printem`: **optional** (default of FALSE) - if TRUE, routine will print out results as a `message`. ## Returns 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 - **scalr**: the vector of scaled residuals using the specified g and h - **L**: 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 ## 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. ## Examples ```r # 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, printem=TRUE) ``` ## Author(s) Douglas M. Hawkins, Jessica J. Kraker [krakerjj@uwec.edu](mailto:krakerjj@uwec.edu)

PWD_known function