Estimate a limit of quantification (LOQ)

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.

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")

loq(
+  object,
+  ...,
+  alpha = 0.05,
+  k = 3,
+  n = 1,
+  w.loq = "auto",
+  var.loq = "auto",
+  tol = "default"
+)

Arguments

object: A univariate model object of class lm or - rlm - with model formula y ~ x or y ~ x - 1, - optionally from a weighted regression. If weights are specified - in the model, either w.loq or var.loq have to - be specified.
alpha: The error tolerance for the prediction of x values in the calculation.; A univariate model object of class lm or +rlm with model formula y ~ x or y ~ x - +1, optionally from a weighted regression. If weights are specified in the +model, either w.loq or var.loq have to be specified.
...: Placeholder for further arguments that might be needed by - future implementations.; Placeholder for further arguments that might be needed by +future implementations.
alpha: The error tolerance for the prediction of x values in the +calculation.
k: The inverse of the maximum relative error tolerated at the - desired LOQ.; 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 massart97ex3 for - an example how to take advantage of knowledge about the - variance function.; 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 massart97ex3 for an example how to take +advantage of knowledge about the variance function.
var.loq: The approximate variance at the LOQ. The default value is - calculated from the model.; 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 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.

Value

The estimated limit of quantification for a model used for calibration.

The estimated limit of quantification for a model used for +calibration.

Note

- 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.

* 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

m <- lm(y ~ x, data = massart97ex1)
+    
+m <- lm(y ~ x, data = massart97ex1)
 loq(m)
 #> $x
 #> [1] 13.97764
@@ -141,6 +147,7 @@
 #> $y
 #> [1] 22.68539
 #> 
+


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Estimate a limit of quantification (LOQ)

Arguments

Value

Note

See also

Examples