Root-mean-square error of calibration RMSEC

Root mean square (RMS) granularity, 19 264 Root-mean-squared error of cross-validation (RMSECV), 6 50-51 Root-mean-squared error of calibration (RMSEC), 6 50-51... 

Root Mean Square Error of Calibration (RMSEC) Plot (Model Diagnostic) The RMSEC as a function of the number of variables included in the model is shown in Figure 5-77. It decreases as variables are added to the model and the largest decrease is observed between a one- and two-variable model. The reported error in the reference caustic concentration is approximately 0.033 vrt.% (la). The tentative conclusion is that four variables are appropriate because the RMSEC is less than the reference concentration error after five variables are included in the model. 

Root mean square error of calibration (RMSEC). 255 of cross validation for PC.A (RMSEC PCA). 93-94 of prediction IRMSEP) in DCLS. 200- 201 idealized behavior. 2SS-289 in MLR, 255 in PLS, 287-290 Row space, 58-59 Rsquare. 253 adjusted. 253... 

Table 1. Comparison of three PLS models in the Slurry-Fed Ceramic Melter data set. The variance in both blocks of data and the Root Mean Square Error of Calibration (RMSEC), Cross-validation (RMSECV) and Prediction (RMSEP) are compared.

The developed models should be tested using independent samples as validation sets to verify model accuracy and robustness. To evaluate model accuracy, the statistics used were the coefficient of correlation in calibration (rc i), coefficient of correlation in prediction (rpred), root mean square error of calibration (RMSEC), and root mean square error of prediction (RMSEP). 

The root mean square error of calibration (RMSEC) measures the average difference between the predicted and the reference values and, thus, gives an overall view of the fit of the model (how well the model predicts the same samples that were used to calculate the model). It is calculated as RMSEC = [E(y-yi.eference) /(f— — l)], whcrc I and A have the usual meanings, and the 1 takes account of the mean-centring or autoscaling of the... 

The root mean squared error of calibration (RMSEC) has been defined above. The leverage, ha, quantifies the distance of the predicted sample (at zero concentration level) to the mean of the calibration set in the -dimensional space Hq can be estimated as an average value of the leverages of a set of validation samples having zero concentration of the analyte. For a model calculated from mean-centred spectra its calculation was presented in Section 5.3 in matrix notation /zo=l//+to (T T) 4o, where to is the (.4x1) score vector of the predicted sample and T is the (7x4) matrix of scores for the calibration set. Finally, A(a,p,v) is a statistical parameter that takes into account the a and (3 probabilities of falsely stating the presence/absence of analyte, respectively, as recommended elsewhere. When the number of degrees of freedom i.e. the number of calibration samples) is high (v>25), as is usually the case in multivariate calibration models, and a =) , then A(a,(S,v) can be safely approximated to 2 ... 

Figure 6.7 The root mean square error of calibration (RMSEC), leave-one-out cross validation (RMSECV) and prediction (RMSEP) are plotted as a function of the signal-to-noise ratio (SNR). While the intrinsic SNR amounts to 3000, random noise was artificially added to mid-IR spectra of 247 serum samples (which decreases the SNR) and the concentration of glucose was recalculated by means of partial least squares (PLS) based on the noisy spectra. The open symbols refer to assessing the quality of quantification within the teaching set, while the filled symbols relate to an external validation set. The data show that the noise can be increased by more than an order of magnitude before the prediction accuracy of the independent external validation set (RMSEP) is affected. In addition, it can clearly be observed that the RMSEC is a poor measure of accuracy since it suggests delivering seemingly better results for lower SNRs, while in fact the calibration simply tends to fit the noise for low values of SNR (see section 6.7).

In GA-PLS, model vahdation was achieved through leave-one-out cross-validation (LOO CV) to find the best number of latent variables (Lv) to be used in calibration and prediction. External validation (for a test set), and the predictive ability was statistically evaluated through the root mean square errors of calibration (RMSEC) and vahdation (RMSECV). The results indicate that four latent variables are the best number to make a model. The following equation represents the best model achieved by GA-PLS ... 

RMSEC root mean square error of calibration... 

Root mean square error of calibration (RMSEQ plot (RMSEC vs. number of variables)... 

NC = number of components selected by cross-validation, = determination coefficient, RMSEC = Root Mean Square Error of Calibration, RMSEP = Root Mean Square Error of Prediction... 

The goodness of a calibration can be summarized by two values, the percentage of variance explained by the model and the Root Mean Square Error in Calibration (RMSEC). The former, being a normalized value, gives an initial idea about how much of the variance of the data set is captured by the model the latter, being an absolute value to be interpreted in the same way as a standard deviation, gives information about the magnitude of the error. 

The root mean squared error (RMSE) is the square root of MSE, and can again be given for calibration (RMSEC or RMSECAL), CV (RMSECV or RMSECv) or for prediction/test (RMSEP, or RMSEtest). In the case of a negligible bias, RMSEP and SEP are almost identical, as well as MSEniST and SEP2. 

Figure 6.13 The root mean square error (RMSE) as derived from the calibration within the teaching set (RMSEC) or from evaluating the independent validation set (RMSEP) as a function of the ratio between the number of samples used to teach the algorithm and the number of parameters (latent variables) 5, 10, or 20 samples out of the teaching set were used for teaching. The dashed line indicates that the ratio should be larger than 5 in order to obtain reasonable values for independent validation. For Nteach/Npara < 5 the RMSEC decreases due to overfitting, but the RMSEP reveals that in fact only random variations had been fitted, which were not found in the independent validation set.

Table 3. Results of PLS models for fresh Duke berry samples (r = coefficient of correlation RMSEC = root mean square of the standard error in calibration RMSEGV = root mean square of the standard error in cross-validation LV = latent variables). All data were preprocessed by second derivative of reduced and smoothed data.

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