The inverse prediction works in a variety of cases and is

tested with Examples 7 and 8 from Massart!

I need to compare with the DIN and draper examples, and finish
the package vignette.



git-svn-id: http://kriemhild.uft.uni-bremen.de/svn/chemCal@6 5fad18fb-23f0-0310-ab10-e59a3bee62b4

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+\name{inverse.predict}
+\alias{inverse.predict}
+\alias{inverse.predict.lm}
+\alias{inverse.predict.default}
+\title{Predict x from y for a linear calibration}
+\usage{inverse.predict(object, newdata, 
+  ws = ifelse(length(object$weights) > 0, mean(object$weights), 1),
+  alpha=0.05, ss = "auto")
+}
+\arguments{
+  \item{object}{
+    A univariate model object of class \code{\link{lm}} with model formula
+    \code{y ~ x} or \code{y ~ x - 1}.
+  }
+  \item{newdata}{ 
+    A vector of observed y values for one sample.
+  }
+  \item{ws}{ 
+    The weight attributed to the sample. The default is to take the 
+    mean of the weights in the model, if there are any.
+  }
+  \item{alpha}{
+    The confidence level for the confidence interval to be reported.
+  }
+  \item{ss}{
+    The estimated standard error of the sample measurements. The 
+    default is to take the residual standard error from the calibration.
+  }
+}
+\value{
+  A list containing the predicted x value, its standard error and a
+  confidence interval.
+}
+\description{
+  This function predicts x values using a univariate linear model that has been
+  generated for the purpose of calibrating a measurement method. Prediction
+  intervals are given at the specified confidence level.
+  The calculation method was taken from Massart et al. (1997). In particular,
+  Equations 8.26 and 8.28 were combined in order to yield a general treatment
+  of inverse prediction for univariate linear models, taking into account 
+  weights that have been used to create the linear model, and at the same
+  time providing the possibility to specify a precision in sample measurements
+  differing from the precision in standard samples used for the calibration.
+  This is elaborated in the package vignette.
+}
+\note{
+  The function was validated with examples 7 and 8 from Massart et al. (1997).
+}
+\references{
+  Massart, L.M, Vandenginste, B.G.M., Buydens, L.M.C., De Jong, S., Lewi, P.J.,
+  Smeyers-Verbeke, J. (1997) Handbook of Chemometrics and Qualimetrics: Part A,
+  p. 200
+}
+\examples{
+data(massart97ex3)
+attach(massart97ex3)
+yx <- split(y,factor(x))
+s <- round(sapply(yx,sd),digits=2)
+w <- round(1/(s^2),digits=3)
+weights <- w[factor(x)]
+m <- lm(y ~ x,w=weights)
+
+inverse.predict(m,c(15))
+}
+\keyword{manip}