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")



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.


The error tolerance for the prediction of x values in the calculation.

Placeholder for further arguments that might be needed by future implementations.


The inverse of the maximum relative error tolerated at the desired LOQ.


The number of replicate measurements for which the LOQ should be specified.


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 approximate variance at the LOQ. The default value is calculated from the model.


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.

See also

Examples for din32645


m <- lm(y ~ x, data = massart97ex1) 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 #>