Regression RMSEP

Parameter Units Concentration range Wavelength range (nm) Number of PLSl factors Regression coefficient RMSEC RMSEP... 

Regardless of potential collection efficiency improvements, they obtained an RMSEP of 0.38 mM. However, the PLS calibration model was obtained using 30 samples with 12 factors retained for the development of the regression vector. Without reported evidence of glucose spectral features, it is difficult to determine whether the data were overfit. The model was applied to 24 samples that were not in the calibration set, giving some justification to the analysis. 

Common practice is to use only RMSEC, RMSEP, or RMSECV to assess the optimum number of basis vectors. However, these diagnostics only evaluate the bias of the model with respect to prediction error. As Figure 5.13 shows, there is a tradeoff of variance for prediction estimates with respect to bias. As more basis vectors are utilized to generate the regression vector, the bias decreases at a sacrifice of a variance increase. 

The scale-error-complexity (SEC) surfaces. Instead of observing the prediction error with respect to resolution, it is also possible to monitor the complexity of the calibration/classification model. In PLS this can be measured by the number of PLS factors needed. How the error (e.g. RMSECV, RMSEP, PRESS) changes with varying the added scale and model complexity can be observed in scale-error-complexity (SEC) surfaces. In this case the first axis is the scales, the second axis is the model complexity (for PLS this is the number factors) and the third axis is the error. The complexity dimension is not limited to the number of PLS factors. For example classification and regression trees (CART) a measure based on tree depth and branching could be used [45],... 

PLS performed on the Fourier Domain spectra (FDS) (or delay domain spectra) produced an RMSEP of 4.12% with 7 regression factors. PLS similarly performed on the FDS from the 0-5000pg ml" ampicillin data set produced an RMSEP of 4.28% (8 factors data not shown). 

First, a percentage, say 80%, from the m samples with variables in Vi and V2 is randomly selected to build two regression models using a preselected modeling method such as PLS [11] or support vector machines (SVMs) [12], respectively. Then an RMSEP value can be computed for each model by using the remaining 20% samples as the test set. Denote the two RMSEP values as RMSEPi and RMSEP2, of which the difference can be calculated as... 

In a multivariate calibration, where a set of NIR spectra (Xnxk, N samples and K variables) is regressed onto a continuous variable (yivxi) such as the fat or moisture content, the statistical errors, the accuracy, are most often used as a quality measure of the calibration. The absolutely most common quality measure of a multivariate calibration is the prediction error, expressed either as root mean square error of prediction (RMSEP) or standard error of performance (SEP). Both are calculated and are the result of a validation process, such as test set or cross-validation. These prediction errors are defined as ... 

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