Standard error of prediction

The Standard Error of Prediction (SEP) is supposed to refer uniquely to those situations when a calibration is generated with one data set and evaluated for its predictive performance with an independent data set. Unfortunately, there are times when the term SEP is wrongly applied to the errors in predicting y variables of the same data set which was used to generate the calibration. Thus, when we encounter the term SEP, it is important to examine the context in order to verify that the term is being used correctly. SEP is simply the square root of the Variance of Prediction, s2. The RMSEP (see below) is sometimes wrongly called the SEP. Fortunately, the difference between the two is usually negligible. 

The Root Mean Standard Error of Prediction (RMSEP) is simply the square root of the MSEP. The RMSEP is sometimes wrongly called the SEP. Fortunately, the difference between the two is usually negligible. 

RMSP Root mean standard error of prediction (6.128)... 

The results of PLS- and RBF calibration are compared in Fig. 6.23. It can be seen that the calibration points in case of the RBF net deviate slightly lower than that of PLS. This fact can be expressed quantitatively by means of the RMSP value (root mean standard error of prediction) ... 

The standard error of performance, also termed the standard error of prediction (SEP), which represents an estimate of the prediction error (1 sigma) for a regression line is given as ... 

You may be surprised that for our example data from Miller and Miller ([2], p. 106), the correlation coefficient calculated using any of these methods of computation for the r-value is 0.99887956534852. When we evaluate the correlation computation we see that given a relatively equivalent prediction error represented as (X - X), J2 (X - X), or SEP, the standard deviation of the data set (X) determines the magnitude of the correlation coefficient. This is illustrated using Graphics 59-la and 59-lb. These graphics allow the correlation coefficient to be displayed for any specified Standard error of prediction, also occasionally denoted as the standard error of estimate (SEE). It should be obvious that for any statistical study one must compare the actual computational recipes used to make a calculation, rather than to rely on the more or less non-standard terminology and assume that the computations are what one expected. 

Standard error of prediction Standard deviation of the predicted value obtained from linear regression. 

The classical standard deviation of prediction errors is widely used as a measure of the spread of the error distribution, and is called in this application standard error of prediction (SEP) defined by... 

FIGURE 4.6 Double CV with three segments (tout) in the outer CV and four segments (%) in the inner CV. In the outer CV, test sets are defined and the prediction performance for new cases is estimated (for instance the standard error of prediction, SEPtest). In the inner CV, the optimum complexity of the model is estimated from a calibration set as shown in Figure 4.5. 

Note Heating value in kJ/kg, others in mass %. The squared Pearson correlation coefficients, between experimental values and predicted values from leave-one-out CV and the standard error of prediction from leave-one-out CV (SEPCV, see Section 4.2.3) are given for a joint PLS2 model, and for separate PLS models developed for each variable seperately using the optimal number of components opt f°r each model. 

SEP Standard error of prediction, SEPCV for cross validation, SEPtest for an... 

In a paper that addresses both these topics, Gordon et al.11 explain how they followed a com mixture fermented by Fusarium moniliforme spores. They followed the concentrations of starch, lipids, and protein throughout the reaction. The amounts of Fusarium and even com were also measured. A multiple linear regression (MLR) method was satisfactory, with standard errors of prediction (SEP) for the constituents being 0.37% for starch, 4.57% for lipid, 4.62% for protein, 2.38% for Fusarium, and 0.16% for com. It may be inferred from the data that PLS or PCA (principal components analysis) may have given more accurate results. 

Given that the introduction of solvent obviously produces wet granules, the wet granulation process includes a drying step. Drying typically occurs in a fluid bed dryer. But there are other options, such as microwave vacuum dryers. In 1994, White applied on-line NIRS to monitor moisture content and predict drying end point in two TK Fielder microwave dryers. The NIR spectral data were correlated to off-line Karl Fischer measurements which resulted in a standard error of prediction equal to 0.6% when the samples... 

NIR models are validated in order to ensure quality in the analytical results obtained in applying the method developed to samples independent of those used in the calibration process. Although constructing the model involves the use of validation techniques that allow some basic characteristics of the model to be established, a set of samples not employed in the calibration process is required for prediction in order to conhrm the goodness of the model. Such samples can be selected from the initial set, and should possess the same properties as those in the calibration set. The quality of the results is assessed in terms of parameters such as the relative standard error of prediction (RSEP) or the root mean square error of prediction (RMSEP). 

RSEP relative standard error of prediction SVM support vector machine... 

SEP standard error of prediction TE/TEC thermoelectric/thermoelectric cooler... 

Fourier transform infrared (FTIR) spectroscopy of coal low-temperature ashes was applied to the determination of coal mineralogy and the prediction of ash properties during coal combustion. Analytical methods commonly applied to the mineralogy of coal are critically surveyed. Conventional least-squares analysis of spectra was used to determine coal mineralogy on the basis of forty-two reference mineral spectra. The method described showed several limitations. However, partial least-squares and principal component regression calibrations with the FTIR data permitted prediction of all eight ASTM ash fusion temperatures to within 50 to 78 F and four major elemental oxide concentrations to within 0.74 to 1.79 wt % of the ASTM ash (standard errors of prediction). Factor analysis based methods offer considerable potential in mineral-ogical and ash property applications. 

The third method for assessing accuracy is to calculate an elemental composition for each LTA s corresponding oxidized ash, based on the reference mineral elemental compositions. Reasonably close agreement between the actual (obtained by ICP-AES) and calculated elemental compositions would substantiate (but not prove) the mineral analysis. The standard error of prediction (SEP) for... 

TABLE 5.6. Standard Error of Prediction for Four-Component Organic Mixture DCLS, Example 2... 

The computer printouts are lengthy and filled with enough statistics to satisfy the most sophisticated user, but for purposes of illustration, we 11 limit our example to the highlights of the data from a 3-wavelength search on wheat samples for the constituent protein. It is noteworthy that such ill-defined molecules as proteins can be determined so rapidly, with so little sample preparation (a few seconds of grinding), with such low errors (typically with standard errors of prediction of about 0.2 over the range 9-18 percent protein). 

We can summarise some other ideas for evaluating the predictive ability of the PLS model. First, you can compare the average error (RMSEP) with the concentration levels of the standards (in calibration) and evaluate whether you (or your client) can accept the magnitude of this error (fit-for-purpose). Then, it is interesting to calculate the so-called "ratio of prediction to deviation", which is just RPD=SD/SEP, where, SD is the standard deviation of the concentrations of the validation samples and SEP is the bias-corrected standard error of prediction (for SEP, see Section 4.6 for more details). As a rule of thumb, an RPD ratio lower than 3 suggests the model has poor predictive capabilities [54]. 

As in univariate calibration, prediction intervals (Pis) can be constructed from the above estimated standard error of prediction, by means of a Student s /-statistic, as ... 

Other estimates of the standard error of prediction have been proposed. A fairly popular and user-friendly one, although with limited value for some data, is contained in the Unscrambler software (CAMO ASA, Oslo, Norway). 

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