Plot calibration graphs from univariate linear models

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

m <- lm(y ~ x, data = din32645) +

m <- lm(y ~ x, data = din32645)
 calplot(m)

 ## Prediction of x with confidence interval
 prediction <- inverse.predict(m, 3500, alpha = 0.01)
 
 # This should give 0.07434 according to test data from Dintest, which 
 # was collected from Procontrol 3.1 (isomehr GmbH) in this case
-round(prediction$Confidence, 5)
#> [1] 0.07434

+round(prediction$Confidence, 5)
#> [1] 0.07434

 ## Critical value:
 crit <- lod(m, alpha = 0.01, beta = 0.5)
 
 # According to DIN 32645, we should get 0.07 for the critical value
 # (decision limit, "Nachweisgrenze")
-round(crit$x, 2)
#> [1] 0.07
# and according to Dintest test data, we should get 0.0698 from
-round(crit$x, 4)
#> [1] 0.0698

+round(crit$x, 2)
#> [1] 0.07
# and according to Dintest test data, we should get 0.0698 from
+round(crit$x, 4)
#> [1] 0.0698

 ## Limit of detection (smallest detectable value given alpha and beta)
 # In German, the smallest detectable value is the "Erfassungsgrenze", and we
 # should get 0.14 according to DIN, which we achieve by using the method 
 # described in it:
 lod.din <- lod(m, alpha = 0.01, beta = 0.01, method = "din")
-round(lod.din$x, 2)
#> [1] 0.14

+round(lod.din$x, 2)
#> [1] 0.14

 ## Limit of quantification
 # This accords to the test data coming with the test data from Dintest again, 
 # except for the last digits of the value cited for Procontrol 3.1 (0.2121)
 loq <- loq(m, alpha = 0.01)
-round(loq$x, 4)
#> [1] 0.212

+round(loq$x, 4)
#> [1] 0.212

 # A similar value is obtained using the approximation 
 # LQ = 3.04 * LC (Currie 1999, p. 120)
 3.04 * lod(m, alpha = 0.01, beta = 0.5)$x
#> [1] 0.2122306

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. @@ -126,19 +139,18 @@ 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.

Arguments

object	A univariate model object of class `lm` or - `rlm` +	A univariate model object of class `lm` or + `rlm` with model formula `y ~ x` or `y ~ x - 1`.
A vector of observed y values for one sample.
…	...	Placeholder for further arguments that might be needed by future implementations.

Value

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

Note

The function was validated with examples 7 and 8 from Massart et al. (1997). @@ -180,17 +191,15 @@ 0.2.1. Confidence intervals for x values obtained from calibrations with replicate measurements did not take the variation about the means into account. Please refer to the vignette for details.

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

The decision limit (German: Nachweisgrenze) is defined as the signal or analyte concentration that is significantly different from the blank signal with a first order error alpha (one-sided significance test). @@ -122,23 +135,22 @@ concentration where the probability that the signal is not detected although the analyte is present (type II or false negative error), is beta (also a one-sided significance test).

Arguments

object	A univariate model object of class `lm` or - `rlm` +	A univariate model object of class `lm` or + `rlm` with model formula `y ~ x` or `y ~ x - 1`, optionally from a weighted regression.
…	...	Placeholder for further arguments that might be needed by future implementations.

Value

A list containig the corresponding x and y values of the estimated limit of detection of a model used for calibration.

Note

- The default values for alpha and beta are the ones recommended by IUPAC. @@ -178,9 +189,8 @@ xD from the LOD in the signal domain SD is done by simply inverting the calibration function (i.e. assuming a known calibration function). - The calculation of a LOD from weighted calibration models requires - a weights argument for the internally used predict.lm + a weights argument for the internally used predict.lm function, which is currently not supported in R.

References

Massart, L.M, Vandenginste, B.G.M., Buydens, L.M.C., De Jong, S., Lewi, P.J., @@ -192,14 +202,12 @@

Currie, L. A. (1997) Nomenclature in evaluation of analytical methods including detection and quantification capabilities (IUPAC Recommendations 1995). Analytica Chimica Acta 391, 105 - 126.

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