Calibration designs

There are two points of view to take into account when setting up a trmning set for developing a predictive multivariate calibration model. One viewpoint is that the calibration set should be representative for the population for which future predictions are to be made. This will generally lead to a distribution of objects in experimental space that has a higher density towards the center, tailing out to the boundaries. Another consideration is that it is better to spread the samples more or 

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The expression for Vy = Sy = Vres/ is true if a = Xmean however, if x is different from Xmean, an extrapolation penalty is paid that is proportional to the square of the deviation. [See Eq. (2.16).] This results in the characteristic trumpet shape observed in Figures 2.6 and 2.8. The influence of the calibration design is shown in Figure 2.8, where the corresponding individ-... 

The calibration-design-dependent LOD approach, - namely the use of the confidence limit function, is endorsed here for reasons of logical consistency, response to optimization endeavors, and easy implementation. Fig. 2.14 gives a (highly schematic) overview ... 

Figure 4.29. Back-calculated results for files VALIDX.dat. The data are presented sequentially from left to right. The ordinate is in % of the nominal concentration. Numbers X = 1,2, and 3 indicate the data file. Each bracket indicates a day s worth of results (sorted by concentration). The log/log format tends to produce positive deviations at low concentrations, while the lin/lin format does the opposite, to the point of suggesting negative concentrations The reason is that the low concentration values are tightly clustered at the left end of the lin/lin depiction whereas the values are evenly spread in the log/log depiction, with commensurate effects on the position of Xmean, the sum Sxx< and the influence each coordinate has on the slope. The calibration design was optimized for the log/log format.

Figure 4.31. Key statistical indicators for validation experiments. The individual data files are marked in the first panels with the numbers 1, 2, and 3, and are in the same sequence for all groups. The lin/lin respectively log/log evaluation formats are indicated by the letters a and b. Limits of detection/quantitation cannot be calculated for the log/log format. The slopes, in percent of the average, are very similar for all three laboratories. The precision of the slopes is given as 100 t CW b)/b in [%]. The residual standard deviation follows a similar pattern as does the precision of the slope b. The LOD conforms nicely with the evaluation as required by the FDA. The calibration-design sensitive LOQ puts an upper bound on the estimates. The XI5% analysis can be high, particularly if the intercept should be negative.

LOD) calculate and display the limits of detection and quantitation LOD, LOQ. [Note This form of calculating the LOD or LOQ was chosen because the results are influenced not only by the noise on the baseline, but also by the calibration design from the educational point of view this is more important than the consideration whether any agency has officially adopted this or that LOD-model. For a comparison, see Figs. 2.14, 2.15, and 4.31]. 

Data) (Create New File) Define a new file, in which calibration designs can be stored. 

Hitchcock, K., Kalivas, J.H., and Sutter, J.M. (1992), Computer-Generated Multicomponent Calibration Designs for Optimal Analysis Sample Predictions, J. Chemom., 6, 85-96. 

Calibration design 62 spectra, 7 design points (collected with varying tem-perature>... 

As with the classical example, ail calculations are performed without knowledge about the presence of the interfercnt ( int" in Equation 5-21). It is only by chance that the interferent is represented in the calibration design. In practice, many samples would be collected in order to increase the likelihood that the interfering species would be adequately represented in the design. 

Calibration design for components A and B three-level flill factorial Calibration design for component C natural Validation design leave-one-out cross-validation Preproctjfiing none... 

Calibration Design 9 samples, selected using a mixture design Preprocessing baseline correction using the average of the first 10 measurement variables. 

Calibration design 25 samples, 5-level full factorial design... 

Calibration design 95 samples with var ing temperature and mixture design... 

Calibration design 22-sampIe mixture design Validation design leave-one-out cross-validation Preprocessing single-point baseline correction at 1100 nm Variable range 550 measurement variables 1100-2198 nra... 

The method for setting up a calibration design will be illustrated by a five-level, eight compound, 25 experiment, mixture, to give the design in Table 22. 

Table 22 Construction of an orthogonal calibration design for eight compounds and 25 levels...

Partial Factorials at Several Levels Calibration Designs... 

Table 2.30 Parameters for construction of a multilevel calibration design.

Two level factorial designs are primarily useful for exploratory purposes and calibration designs have special uses in areas such as multivariate calibration where we often expect an independent linear response from each component in a mixture. It is often important, though, to provide a more detailed model of a system. There are two prime reasons. The first is for optimisation - to find the conditions that result in a maximum or minimum as appropriate. An example is when improving die yield of synthetic reaction, or a chromatographic resolution. The second is to produce a detailed quantitative model to predict mathematically how a response relates to die values of various factors. An example may be how the near-infrared spectrum of a manufactured product relates to the nature of the material and processing employed in manufacturing. 

The aim is to construct a five level partial factorial (or calibration) design involving 25 experiments and up to 14 factors, each at levels —2, —1, 0, 1 and 2. Note that this design is only one of many possible such designs. 

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