chemCal (version 0.2.3)

inverse.predict: Predict x from y for a linear calibration

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.

Usage

inverse.predict(
  object,
  newdata,
  ...,
  ws = "auto",
  alpha = 0.05,
  var.s = "auto"
)

Arguments

object

A univariate model object of class lm or rlm with model formula y ~ x or y ~ x - 1.

newdata

A vector of observed y values for one sample.

…

Placeholder for further arguments that might be needed by future implementations.

ws

The weight attributed to the sample. This argument is obligatory if object has weights.

alpha

The error tolerance level for the confidence interval to be reported.

var.s

The estimated variance of the sample measurements. The default is to take the residual standard error from the calibration and to adjust it using ws, if applicable. This means that var.s overrides ws.

Value

A list containing the predicted x value, its standard error and a confidence interval.

Details

This is an implementation of Equation (8.28) in the Handbook of Chemometrics and Qualimetrics, Part A, Massart et al (1997), page 200, validated with Example 8 on the same page, extended as specified in the package vignette

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

# NOT RUN {
# This is example 7 from Chapter 8 in Massart et al. (1997)
m <- lm(y ~ x, data = massart97ex1)
inverse.predict(m, 15)        #  6.1 +- 4.9
inverse.predict(m, 90)        # 43.9 +- 4.9
inverse.predict(m, rep(90,5)) # 43.9 +- 3.2

# For reproducing the results for replicate standard measurements in example 8,
# we need to do the calibration on the means when using chemCal > 0.2
weights <- with(massart97ex3, {
  yx <- split(y, x)
  ybar <- sapply(yx, mean)
  s <- round(sapply(yx, sd), digits = 2)
  w <- round(1 / (s^2), digits = 3)
})

massart97ex3.means <- aggregate(y ~ x, massart97ex3, mean)

m3.means <- lm(y ~ x, w = weights, data = massart97ex3.means)

inverse.predict(m3.means, 15, ws = 1.67)  # 5.9 +- 2.5
inverse.predict(m3.means, 90, ws = 0.145) # 44.1 +- 7.9


# }