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

Sample dataset from p. 188 to test the package.

data(massart97ex3)

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: 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.