inverse.predict. chemCal 0.1-35.900

Usage

inverse.predict(object, newdata, ..., ws, 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. +
newdata: + A vector of observed y values for one sample. +
...: + 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. +
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. +

+ +

Value

+ +

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

+ +

Description

+ +

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.

+ +

Note

+ +

The function was validated with examples 7 and 8 from Massart et al. (1997).

+ +

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

+ +

Examples

# This is example 7 from Chapter 8 in Massart et al. (1997)
+data(massart97ex1)
+m <- lm(y ~ x, data = massart97ex1)
+inverse.predict(m, 15)        #  6.1 +- 4.9
+
+$Prediction
+[1] 6.09381
+
+$`Standard Error`
+[1] 1.767278
+
+$Confidence
+[1] 4.906751
+
+$`Confidence Limits`
+[1]  1.187059 11.000561
+
+
+inverse.predict(m, 90)        # 43.9 +- 4.9
+
+$Prediction
+[1] 43.93983
+
+$`Standard Error`
+[1] 1.767747
+
+$Confidence
+[1] 4.908053
+
+$`Confidence Limits`
+[1] 39.03178 48.84788
+
+
+inverse.predict(m, rep(90,5)) # 43.9 +- 3.2
+
+$Prediction
+[1] 43.93983
+
+$`Standard Error`
+[1] 1.141204
+
+$Confidence
+[1] 3.168489
+
+$`Confidence Limits`
+[1] 40.77134 47.10832
+
+

+ + + +