Plot calibration graphs from univariate linear models

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. - The calculation method was taken from Massart et al. (1997). In particular, - Equations 8.26 and 8.28 were combined in order to yield a general treatment - of inverse prediction for univariate linear models, taking into account - weights that have been used to create the linear model, and at the same - 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.

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. The +calculation method was taken from Massart et al. (1997). In particular, +Equations 8.26 and 8.28 were combined in order to yield a general treatment +of inverse prediction for univariate linear models, taking into account +weights that have been used to create the linear model, and at the same 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.

inverse.predict(object, newdata, ...,
-  ws, alpha=0.05, var.s = "auto")

inverse.predict(
+  object,
+  newdata,
+  ...,
+  ws = "auto",
+  alpha = 0.05,
+  var.s = "auto"
+)

Arguments

object: A univariate model object of class lm or - rlm - with model formula y ~ x or y ~ x - 1.; A univariate model object of class lm or +rlm with model formula y ~ x or y ~ x - +1.
newdata: A vector of observed y values for one sample.
...: Placeholder for further arguments that might be needed by - future implementations.; Placeholder for further arguments that might be needed by +future implementations.
ws: The weight attributed to the sample. This argument is obligatory - if object has weights.
alpha: The error tolerance level for the confidence interval to be reported.; The error tolerance level for the confidence interval to be +reported.
var.s: The estimated variance of the sample measurements. The default is to take - the residual standard error from the calibration and to adjust it - using ws, if applicable. This means that var.s - overrides ws.; The estimated variance of the sample measurements. The default +is to take the residual standard error from the calibration and to adjust it +using ws, if applicable. This means that var.s overrides +ws.

Value

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

+confidence interval.

Details

This is an implementation of Equation (8.28) in the Handbook of Chemometrics +and Qualimetrics, Part A, Massart et al (1997), page 200, validated with +Example 8 on the same page, extended as specified in the package vignette

Note

The function was validated with examples 7 and 8 from Massart et al. (1997). - Note that the behaviour of inverse.predict changed with chemCal version - 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.

The function was validated with examples 7 and 8 from Massart et al. +(1997). Note that the behaviour of inverse.predict changed with chemCal +version 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

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

# This is example 7 from Chapter 8 in Massart et al. (1997)
+    
+# This is example 7 from Chapter 8 in Massart et al. (1997)
 m <- lm(y ~ x, data = massart97ex1)
 inverse.predict(m, 15)        #  6.1 +- 4.9
 #> $Prediction
@@ -204,6 +218,7 @@
 #> [1] 36.20523 51.91526
 #> 
 
+


diff --git a/docs/reference/lod.html b/docs/reference/lod.html
index a2d66ce..1fbae76 100644
--- a/docs/reference/lod.html
+++ b/docs/reference/lod.html
@@ -1,12 +1,12 @@
 
 Estimate a limit of detection (LOD) — lod • chemCal
@@ -54,76 +54,81 @@
   
     
     Estimate a limit of detection (LOD)
-    
+    Source: R/lod.R
     lod.Rd
     
 
     
     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).
-  The detection limit, or more precise, the minimum detectable value 
-  (German: Erfassungsgrenze), is then defined as the signal or analyte
-  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).
+analyte concentration that is significantly different from the blank signal
+with a first order error alpha (one-sided significance test).  The detection
+limit, or more precise, the minimum detectable value (German:
+Erfassungsgrenze), is then defined as the signal or analyte 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).
     
 
     
-    lod(object, ..., alpha = 0.05, beta = 0.05, method = "default", tol = "default")
+    lod(
+  object,
+  ...,
+  alpha = 0.05,
+  beta = 0.05,
+  method = "default",
+  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.
+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.
+Placeholder for further arguments that might be needed by
+future implementations.
 alpha
 The error tolerance for the decision limit (critical value).
 beta
 The error tolerance beta for the detection limit.
 method
-The “default” method uses a prediction interval at the LOD
-    for the estimation of the LOD, which obviously requires
-    iteration. This is described for example in Massart, p. 432 ff.
-    The “din” method uses the prediction interval at
-    x = 0 as an approximation.
+The “default” method uses a prediction interval at the
+LOD for the estimation of the LOD, which obviously requires iteration. This
+is described for example in Massart, p. 432 ff.  The “din” method
+uses the prediction interval at x = 0 as an approximation.
 tol
 When the “default” method is used, the default tolerance
-    for the LOD 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.
+for the LOD 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
-    A list containig the corresponding x and y values of the estimated limit of
-  detection of a model used for calibration.
+    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.
-  - The estimation of the LOD in terms of the analyte amount/concentration
-    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
-    function, which is currently not supported in R.
+    * The default values for alpha and beta are the ones recommended by IUPAC.
+* The estimation of the LOD in terms of the analyte amount/concentration 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
+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., 
-  Smeyers-Verbeke, J. (1997) Handbook of Chemometrics and Qualimetrics: Part A,
-  Chapter 13.7.8
+    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, Chapter 13.7.8
 J. Inczedy, T. Lengyel, and A.M. Ure (2002) International Union of Pure and
-  Applied Chemistry Compendium of Analytical Nomenclature: Definitive Rules.
-  Web edition.
-Currie, L. A. (1997) Nomenclature in evaluation of analytical methods including
-  detection and quantification capabilities (IUPAC Recommendations 1995). 
-  Analytica Chimica Acta 391, 105 - 126.
+Applied Chemistry Compendium of Analytical Nomenclature: Definitive Rules.
+Web edition.
+Currie, L. A. (1997) Nomenclature in evaluation of analytical methods
+including detection and quantification capabilities (IUPAC Recommendations
+1995).  Analytica Chimica Acta 391, 105 - 126.
     
     
     See also
@@ -132,7 +137,8 @@
 
     
     Examples
-    m <- lm(y ~ x, data = din32645)
+    
+m <- lm(y ~ x, data = din32645)
 lod(m) 
 #> $x
 #> [1] 0.08655484
@@ -150,6 +156,7 @@
 #> $y
 #> [1] 3155.393
 #> 
+
 
     

   

diff --git a/docs/reference/loq.html b/docs/reference/loq.html
index 0960251..86c8f43 100644
--- a/docs/reference/loq.html
+++ b/docs/reference/loq.html
@@ -1,11 +1,10 @@
 
-Estimate a limit of quantification (LOQ) — loq • chemCalEstimate a limit of quantification (LOQ) — loq • chemCal
@@ -53,69 +52,75 @@
   
     
     Estimate a limit of quantification (LOQ)
-    
+    Source: R/loq.R
     loq.Rd
     
 
     
-    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.
+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.
     
     
     See also
@@ -124,7 +129,8 @@
 
     
     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
 #> 
+
 
     

   

diff --git a/docs/reference/massart97ex1.html b/docs/reference/massart97ex1.html
index e5dd85a..a02dfe0 100644
--- a/docs/reference/massart97ex1.html
+++ b/docs/reference/massart97ex1.html
@@ -47,7 +47,7 @@
   
     
     Calibration data from Massart et al. (1997), example 1
-    
+    Source: R/chemCal-package.R
     massart97ex1.Rd
     
 
@@ -55,9 +55,6 @@
     Sample dataset from p. 175 to test the package.
     
 
-    
-    data(massart97ex1)
-    
 
     
     Format
@@ -65,9 +62,9 @@
     
     
     Source
-    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,
-  Chapter 8.
+    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, Chapter 8.
     
 
   

diff --git a/docs/reference/massart97ex3.html b/docs/reference/massart97ex3.html
index 4196882..5cbdbd6 100644
--- a/docs/reference/massart97ex3.html
+++ b/docs/reference/massart97ex3.html
@@ -47,7 +47,7 @@
   
     
     Calibration data from Massart et al. (1997), example 3
-    
+    Source: R/chemCal-package.R
     massart97ex3.Rd
     
 
@@ -55,25 +55,23 @@
     Sample dataset from p. 188 to test the package.
     
 
-    
-    massart97ex3
-    
 
     
     Format
-    A dataframe containing 6 levels of x values with 5
-  observations of y for each level.
+    A dataframe containing 6 levels of x values with 5 observations of y
+for each level.
     
     
     Source
-    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,
-  Chapter 8.
+    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, Chapter 8.
     
 
     
     Examples
-    # For reproducing the results for replicate standard measurements in example 8,
+    
+# For reproducing the results for replicate standard measurements in example 8,
 # we need to do the calibration on the means when using chemCal > 0.2
 weights <- with(massart97ex3, {
   yx <- split(y, x)
@@ -149,6 +147,7 @@
 # The weight for the loq should therefore be derived at x = 7.3 instead
 # of 15, but the graphical procedure of Massart (p. 201) to derive the 
 # variances on which the weights are based is quite inaccurate anyway. 
+
 
     

   

diff --git a/docs/reference/rl95_cadmium.html b/docs/reference/rl95_cadmium.html
index da9294d..4ddb8e4 100644
--- a/docs/reference/rl95_cadmium.html
+++ b/docs/reference/rl95_cadmium.html
@@ -1,5 +1,7 @@
 
-Cadmium concentrations measured by AAS as reported by Rocke and Lorenzato (1995) — rl95_cadmium • chemCalCadmium concentrations measured by AAS as reported by Rocke and Lorenzato
+(1995) — rl95_cadmium • chemCal
@@ -46,8 +48,9 @@
       
   
     
-    Cadmium concentrations measured by AAS as reported by Rocke and Lorenzato (1995)
-    
+    Cadmium concentrations measured by AAS as reported by Rocke and Lorenzato
+(1995)
+    Source: R/chemCal-package.R
     rl95_cadmium.Rd
     
 
@@ -58,13 +61,13 @@
 
     
     Format
-    A dataframe containing four replicate observations for each 
-  of the six calibration standards.
+    A dataframe containing four replicate observations for each of the
+six calibration standards.
     
     
     Source
-    Rocke, David M. und Lorenzato, Stefan (1995) A two-component model for
-  measurement error in analytical chemistry. Technometrics 37(2), 176-184.
+    Rocke, David M. und Lorenzato, Stefan (1995) A two-component model
+for measurement error in analytical chemistry. Technometrics 37(2), 176-184.
     
 
   
diff --git a/docs/reference/rl95_toluene.html b/docs/reference/rl95_toluene.html
index fb071e1..4c8c7d2 100644
--- a/docs/reference/rl95_toluene.html
+++ b/docs/reference/rl95_toluene.html
@@ -1,7 +1,7 @@
 
 Toluene amounts measured by GC/MS as reported by Rocke and Lorenzato (1995) — rl95_toluene • chemCal
@@ -49,26 +49,26 @@
   
     
     Toluene amounts measured by GC/MS as reported by Rocke and Lorenzato (1995)
-    
+    Source: R/chemCal-package.R
     rl95_toluene.Rd
     
 
     
     Dataset reproduced from Table 4 in Rocke and Lorenzato (1995). The toluene
-  amount in the calibration samples is given in picograms per 100 µL.
-  Presumably this is the volume that was injected into the instrument.
+amount in the calibration samples is given in picograms per 100 µL.
+Presumably this is the volume that was injected into the instrument.
     
 
 
     
     Format
-    A dataframe containing four replicate observations for each
-  of the six calibration standards.
+    A dataframe containing four replicate observations for each of the
+six calibration standards.
     
     
     Source
-    Rocke, David M. und Lorenzato, Stefan (1995) A two-component model for
-  measurement error in analytical chemistry. Technometrics 37(2), 176-184.
+    Rocke, David M. und Lorenzato, Stefan (1995) A two-component model
+for measurement error in analytical chemistry. Technometrics 37(2), 176-184.
     
 
   
diff --git a/docs/reference/utstats14.html b/docs/reference/utstats14.html
index 78d2604..1ffc224 100644
--- a/docs/reference/utstats14.html
+++ b/docs/reference/utstats14.html
@@ -1,6 +1,6 @@
 
-Example data for calibration with replicates from University of Toronto — utstats14 • chemCalExample data for calibration with replicates from University of Toronto — utstats14 • chemCal
@@ -48,26 +48,27 @@
   
     
     Example data for calibration with replicates from University of Toronto
-    
+    Source: R/chemCal-package.R
     utstats14.Rd
     
 
     
-    Dataset read into R from 
-  https://sites.chem.utoronto.ca/chemistry/coursenotes/analsci/stats/files/example14.xls.
+    Dataset read into R from
+https://sites.chem.utoronto.ca/chemistry/coursenotes/analsci/stats/files/example14.xls.
     
 
 
     
     Format
-    A tibble containing three replicate observations of the response for five
-  calibration concentrations.
+    A tibble containing three replicate observations of the response for
+five calibration concentrations.
     
     
     Source
-    David Stone and Jon Ellis (2011) Statistics in Analytical Chemistry. Tutorial website
-  maintained by the Departments of Chemistry, University of Toronto.
-  https://sites.chem.utoronto.ca/chemistry/coursenotes/analsci/stats/index.html
+    David Stone and Jon Ellis (2011) Statistics in Analytical Chemistry.
+Tutorial website maintained by the Departments of Chemistry, University of
+Toronto.
+https://sites.chem.utoronto.ca/chemistry/coursenotes/analsci/stats/index.html
     
 
   
-- 
cgit v1.2.1

- All functions + Main functions
- `calplot()` + `calplot()`	Plot calibration graphs from univariate linear models
- `din32645` -	Calibration data from DIN 32645
- `inverse.predict()` -	Predict x from y for a linear calibration
`lod()`	Estimate a limit of quantification (LOQ)
+ `inverse.predict()` +	Predict x from y for a linear calibration
+ Datasets + +
+ `din32645` +	Calibration data from DIN 32645
`massart97ex1`
`rl95_cadmium`	Cadmium concentrations measured by AAS as reported by Rocke and Lorenzato (1995)	Cadmium concentrations measured by AAS as reported by Rocke and Lorenzato +(1995)
`rl95_toluene`

Plot calibration graphs from univariate linear models

Arguments

Value

Note

Author

Examples

Calibration data from DIN 32645

Format

References

Examples

All functions

Main functions

Datasets

Predict x from y for a linear calibration

Arguments

Value

Details

Note

References

Examples

Estimate a limit of detection (LOD)

Arguments

Value

Note

References

See also

Examples

Estimate a limit of quantification (LOQ)

Arguments

Value

Note

See also

Examples

Calibration data from Massart et al. (1997), example 1

Format

Source

Calibration data from Massart et al. (1997), example 3

Format

Source

Examples

Cadmium concentrations measured by AAS as reported by Rocke and Lorenzato (1995)

Cadmium concentrations measured by AAS as reported by Rocke and Lorenzato +(1995)

Format

Source

Toluene amounts measured by GC/MS as reported by Rocke and Lorenzato (1995)

Format

Source

Example data for calibration with replicates from University of Toronto

Format

Source