# Fit Rocke-Lorenzato profile model to residuals This routine fits the Rocke-Lorenzato precision profile model to the residuals from the fit. ```r PWD_resi(true, resi, epsilon=1e-8, printem=FALSE) ``` ## Arguments - `true`: the vector of values used to predict the precision – commonly X. - `resi`: the vector of residuals whose variance is thought to be a function of “true”. - `epsilon`: **optional** (default of 1e-8) - convergence tolerance limit. - `printem`: **optional** (default of FALSE) - if TRUE, routine will print out results as a `message`. ## Returns A list containing the following components: - **sigmar**: the estimate of $\sigma_r$ - **kappar**: the estimate of $\kappa_r$ - **L**: the -2 log likelihood - **scalr**: the scaled residuals - **poolsig**: the maximum likelihood estimate of $\sigma_r$ if $\kappa_r$ = 0 - **poolkap**: the maximum likelihood estimate of $\kappa_r$ if $\sigma_r$ = 0 ## 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). ## Examples ```r # 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, printem=TRUE) ``` ## References Hawkins DM and Kraker JJ (in press). Precision Profile Weighted Deming Regression for Methods Comparison. **The Journal of Applied Laboratory Medicine**. [doi:10.1093/jalm/jfaf183](doi: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 ## Author(s) Douglas M. Hawkins, Jessica J. Kraker [krakerjj@uwec.edu](mailto:krakerjj@uwec.edu)

PWD_resi function