chemCal 0.1-37

Calibration data from Massart et al. (1997), example 3

Usage

data(massart97ex3)

Description

Sample dataset from p. 188 to test the package.

Format

A dataframe containing 6 levels of x values with 5 observations of y for each level.

Source

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, Chapter 8.

Examples

data(massart97ex3)
attach(massart97ex3)

The following objects are masked from massart97ex3 (pos = 3):

    x, y


yx <- split(y, x)
ybar <- sapply(yx, mean)
s <- round(sapply(yx, sd), digits = 2)
w <- round(1 / (s^2), digits = 3)
weights <- w[factor(x)]
m <- lm(y ~ x, w = weights)
calplot(m)

Warning message:
Assuming constant prediction variance even though model fit is weighted





# The following concords with the book p. 200
inverse.predict(m, 15, ws = 1.67)  # 5.9 +- 2.5


$Prediction
[1] 5.865367

$`Standard Error`
[1] 0.8926109

$Confidence
[1] 2.478285

$`Confidence Limits`
[1] 3.387082 8.343652




inverse.predict(m, 90, ws = 0.145) # 44.1 +- 7.9


$Prediction
[1] 44.06025

$`Standard Error`
[1] 2.829162

$Confidence
[1] 7.855012

$`Confidence Limits`
[1] 36.20523 51.91526





# The LOD is only calculated for models from unweighted regression
# with this version of chemCal
m0 <- lm(y ~ x)
lod(m0)


$x
[1] 5.407085

$y
       1 
13.63911 





# Limit of quantification from unweighted regression
loq(m0)


$x
[1] 13.97764

$y
      1 
30.6235 





# For calculating the limit of quantification from a model from weighted
# regression, we need to supply weights, internally used for inverse.predict
# If we are not using a variance function, we can use the weight from
# the above example as a first approximation (x = 15 is close to our
# loq approx 14 from above).
loq(m, w.loq = 1.67)


$x
[1] 7.346195

$y
       1 
17.90777 




# The weight for the loq should therefore be derived at x = 7.3 instead
# of 15, but the graphical procedure of Massart (p. 201) to derive the 
# variances on which the weights are based is quite inaccurate anyway.