Introduction to chemCal

Johannes Ranke

2020-05-20

2021-04-08

Source: vignettes/chemCal.Rmd

chemCal.Rmd

@@ -99,25 +99,29 @@ Usage

When calibrating an analytical method, the first task is to generate a suitable model. If we want to use the chemCal functions, we have to restrict ourselves to univariate, possibly weighted, linear regression so far.

Once such a model has been created, the calibration can be graphically shown by using the calplot function:

library(chemCal)
-m0 <- lm(y ~ x, data = massart97ex3)
-calplot(m0)

+library(chemCal)
+m0 <- lm(y ~ x, data = massart97ex3)
+calplot(m0)

As we can see, the scatter increases with increasing x. This is also illustrated by one of the diagnostic plots for linear models provided by R:

plot(m0, which=3)

+plot(m0, which=3)

Therefore, in Example 8 in Massart et al. (1997), weighted regression is proposed which can be reproduced by the following code. Note that we are building the model on the mean values for each standard in order to be able to reproduce the results given in the book with the current version of chemCal.

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

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

If we now want to predict a new x value from measured y values, we use the inverse.predict function:

inverse.predict(m, 15, ws=1.67)

+inverse.predict(m, 15, ws=1.67)

## $Prediction
 ## [1] 5.865367
 ## 
@@ -129,7 +133,8 @@
 ## 
 ## $`Confidence Limits`
 ## [1] 3.387082 8.343652

inverse.predict(m, 90, ws = 0.145)

+inverse.predict(m, 90, ws = 0.145)

## $Prediction
 ## [1] 44.06025
 ## 
@@ -170,7 +175,7 @@ s_{\hat{x_s}} = \frac{1}{b_1} \sqrt{\frac{{s_s}^2}{w_s m} +
             {{b_1}^2 \left( \sum{w_i} \sum{w_i {x_i}^2} - {\left( \sum{ w_i x_i } \right)}^2 \right) } \right) }
 \end{equation}\]
 where I interpret \(\frac{{s_s}^2}{w_s}\) as an estimator of the variance at location \(\hat{x_s}\), which can be replaced by a user-specified value using the argument var.s of the function inverse.predict.
-
+
 
 Analytical Methods Committee. 1989. “Robust Statistics — How Not to Reject Outliers. Part 1. Basic Concepts.” The Analyst 114: 1693–7.
 
@@ -202,7 +207,7 @@ s_{\hat{x_s}} = \frac{1}{b_1} \sqrt{\frac{{s_s}^2}{w_s m} +
 
 
 
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+  Site built with pkgdown 1.6.1.
 
 
       
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