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

massart97ex3

- - -

Format

massart97ex3

Format

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

Source

- +

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

# 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)
-
-# The following concords with the book p. 200
-inverse.predict(m3.means, 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(m3.means, 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, data = massart97ex3) 
-lod(m0)
-
#> $x
-#> [1] 5.407085
-#> 
-#> $y
-#> [1] 13.63911
-#> 

-# Limit of quantification from unweighted regression
-loq(m0)
-
#> $x
-#> [1] 9.627349
-#> 
-#> $y
-#> [1] 22.00246
-#> 

-# 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(m3.means, 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. 
-

Examples

# 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)
+
+# The following concords with the book p. 200
+inverse.predict(m3.means, 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(m3.means, 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, data = massart97ex3) 
+lod(m0)
+#> $x
+#> [1] 5.407085
+#> 
+#> $y
+#> [1] 13.63911
+#> 
+
+# Limit of quantification from unweighted regression
+loq(m0)
+#> $x
+#> [1] 9.627349
+#> 
+#> $y
+#> [1] 22.00246
+#> 
+
+# 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(m3.means, 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. 
+