Predict x from y for a linear calibration — inverse.predict • chemCal

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

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 + + 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

- + overrides ws.

Value

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

Note

- +

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.

References

- +

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)
-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
-#> 

-# 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)
-  ybar <- sapply(yx, mean)
-  s <- round(sapply(yx, sd), digits = 2)
-  w <- round(1 / (s^2), digits = 3)
-})
-
-massart97ex3.means <- aggregate(y ~ x, massart97ex3, mean)
-
-m3.means <- lm(y ~ x, w = weights, data = massart97ex3.means)
-
-inverse.predict(m3.means, 15, ws = 1.67)  # 5.9 +- 2.5
-
#> $Prediction
-#> [1] 5.865367
-#> 
-#> $`Standard Error`
-#> [1] 0.8926109
-#> 
-#> $Confidence
-#> [1] 2.478285
-#> 
-#> $`Confidence Limits`
-#> [1] 3.387082 8.343652
-#> 
inverse.predict(m3.means, 90, ws = 0.145) # 44.1 +- 7.9
-
#> $Prediction
-#> [1] 44.06025
-#> 
-#> $`Standard Error`
-#> [1] 2.829162
-#> 
-#> $Confidence
-#> [1] 7.855012
-#> 
-#> $`Confidence Limits`
-#> [1] 36.20523 51.91526
-#> 

-

Examples

# 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
+#> [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
+#> 
+
+# 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)
+  ybar <- sapply(yx, mean)
+  s <- round(sapply(yx, sd), digits = 2)
+  w <- round(1 / (s^2), digits = 3)
+})
+
+massart97ex3.means <- aggregate(y ~ x, massart97ex3, mean)
+
+m3.means <- lm(y ~ x, w = weights, data = massart97ex3.means)
+
+inverse.predict(m3.means, 15, ws = 1.67)  # 5.9 +- 2.5
+#> $Prediction
+#> [1] 5.865367
+#> 
+#> $`Standard Error`
+#> [1] 0.8926109
+#> 
+#> $Confidence
+#> [1] 2.478285
+#> 
+#> $`Confidence Limits`
+#> [1] 3.387082 8.343652
+#> 
+inverse.predict(m3.means, 90, ws = 0.145) # 44.1 +- 7.9
+#> $Prediction
+#> [1] 44.06025
+#> 
+#> $`Standard Error`
+#> [1] 2.829162
+#> 
+#> $Confidence
+#> [1] 7.855012
+#> 
+#> $`Confidence Limits`
+#> [1] 36.20523 51.91526
+#> 
+
+