The limit of quantification is the x value, where the relative error
of the quantification given the calibration model reaches a prespecified
value 1/k. Thus, it is the solution of the equation
$$L = k c(L)$$
where c(L) is half of the length of the confidence interval at the limit L
(DIN 32645, equivalent to ISO 11843). c(L) is internally estimated by
inverse.predict, and L is obtained by iteration.
loq(object, …, alpha = 0.05, k = 3, n = 1, w.loq = "auto",
var.loq = "auto", tol = "default")
| object | A univariate model object of class |
|---|---|
| alpha | The error tolerance for the prediction of x values in the calculation. |
| … | Placeholder for further arguments that might be needed by future implementations. |
| k | The inverse of the maximum relative error tolerated at the desired LOQ. |
| n | The number of replicate measurements for which the LOQ should be specified. |
| w.loq | The weight that should be attributed to the LOQ. Defaults
to one for unweighted regression, and to the mean of the weights
for weighted regression. See |
| var.loq | The approximate variance at the LOQ. The default value is calculated from the model. |
| tol | The default tolerance for the LOQ on the x scale is the value of the smallest non-zero standard divided by 1000. Can be set to a numeric value to override this. |
The estimated limit of quantification for a model used for calibration.
- IUPAC recommends to base the LOQ on the standard deviation of the signal where x = 0. - The calculation of a LOQ based on weighted regression is non-standard and therefore not tested. Feedback is welcome.
Examples for din32645
data(massart97ex3) attach(massart97ex3) m <- lm(y ~ x) loq(m)#> $x #> [1] 13.97764 #> #> $y #> 1 #> 30.6235 #># We can get better by using replicate measurements loq(m, n = 3)#> $x #> [1] 9.971963 #> #> $y #> 1 #> 22.68539 #>