From 91a5834dd701211f929fd25419dc34561ce3b4e7 Mon Sep 17 00:00:00 2001 From: Johannes Ranke Date: Fri, 14 Feb 2025 09:15:20 +0100 Subject: Initialize dev docs --- docs/dev/reference/sigma_twocomp.html | 169 ++++++++++++++++++++++++++++++++++ 1 file changed, 169 insertions(+) create mode 100644 docs/dev/reference/sigma_twocomp.html (limited to 'docs/dev/reference/sigma_twocomp.html') diff --git a/docs/dev/reference/sigma_twocomp.html b/docs/dev/reference/sigma_twocomp.html new file mode 100644 index 00000000..12af9e8a --- /dev/null +++ b/docs/dev/reference/sigma_twocomp.html @@ -0,0 +1,169 @@ + +Two-component error model — sigma_twocomp • mkin + Skip to contents + + +
+
+
+ +

Two-component error model

+ Source: R/sigma_twocomp.R +
sigma_twocomp.Rd
+
+ +
+

Function describing the standard deviation of the measurement error in +dependence of the measured value \(y\):

+
+ +
+

Usage

+ 
sigma_twocomp(y, sigma_low, rsd_high)
+
+ +
+

Arguments

+ + +
y
+

The magnitude of the observed value

+ + +
sigma_low
+

The asymptotic minimum of the standard deviation for low +observed values

+ + +
rsd_high
+

The coefficient describing the increase of the standard +deviation with the magnitude of the observed value

+ +
+
+

Value

+

The standard deviation of the response variable.

+
+
+

Details

+

$$\sigma = \sqrt{ \sigma_{low}^2 + y^2 * {rsd}_{high}^2}$$ sigma = +sqrt(sigma_low^2 + y^2 * rsd_high^2)

+

This is the error model used for example by Werner et al. (1978). The model +proposed by Rocke and Lorenzato (1995) can be written in this form as well, +but assumes approximate lognormal distribution of errors for high values of +y.

+
+
+

References

+

Werner, Mario, Brooks, Samuel H., and Knott, Lancaster B. (1978) +Additive, Multiplicative, and Mixed Analytical Errors. Clinical Chemistry +24(11), 1895-1898.

+

Rocke, David M. and Lorenzato, Stefan (1995) A two-component model for +measurement error in analytical chemistry. Technometrics 37(2), 176-184.

+

Ranke J and Meinecke S (2019) Error Models for the Kinetic Evaluation of Chemical +Degradation Data. Environments 6(12) 124 +doi:10.3390/environments6120124 +.

+
+ +
+

Examples

+ 
times <- c(0, 1, 3, 7, 14, 28, 60, 90, 120)
+d_pred <- data.frame(time = times, parent = 100 * exp(- 0.03 * times))
+set.seed(123456)
+d_syn <- add_err(d_pred, function(y) sigma_twocomp(y, 1, 0.07),
+  reps = 2, n = 1)[[1]]
+f_nls <- nls(value ~ SSasymp(time, 0, parent_0, lrc), data = d_syn,
+ start = list(parent_0 = 100, lrc = -3))
+library(nlme)
+f_gnls <- gnls(value ~ SSasymp(time, 0, parent_0, lrc),
+  data = d_syn, na.action = na.omit,
+  start = list(parent_0 = 100, lrc = -3))
+if (length(findFunction("varConstProp")) > 0) {
+  f_gnls_tc <- update(f_gnls, weights = varConstProp())
+  f_gnls_tc_sf <- update(f_gnls_tc, control = list(sigma = 1))
+}
+f_mkin <- mkinfit("SFO", d_syn, error_model = "const", quiet = TRUE)
+f_mkin_tc <- mkinfit("SFO", d_syn, error_model = "tc", quiet = TRUE)
+plot_res(f_mkin_tc, standardized = TRUE)
+
+AIC(f_nls, f_gnls, f_gnls_tc, f_gnls_tc_sf, f_mkin, f_mkin_tc)
+#>              df      AIC
+#> f_nls         3 114.4817
+#> f_gnls        3 114.4817
+#> f_gnls_tc     5 103.6447
+#> f_gnls_tc_sf  4 101.6447
+#> f_mkin        3 114.4817
+#> f_mkin_tc     4 101.6446
+
+
+
+ + +
+ + + + + + + -- cgit v1.2.1