Root mean square error method

Step 1. Determination of IDL and IQL following the Root Mean Square Error method... 

The root-mean-square error in the kinetic fit was an acceptable 2.83% and was minimized by the SIMPLEX method discussed elsewhere (8). An... 

Publication Date March 13, 2007 doi 10.1021/bk-2007-0958.ch009 Table 5. Mean Unsigned Errors (kcal/mol), Root-Mean-Square Errors, and Times for hybrid DFT and DPT Methods and AMI at QCISD/MG3 Geometries ... 

It should be mentioned that another validation technique, called leverage correction [1], is available in some software packages. This method, unlike cross validation, does not involve splitting of the calibration data into model and test sets, but is simply an altered calculation of the RMSEE fit error of a model. This alteration involves the weighting of the contribution of the root mean square error from each calibration... 

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). 

Additional examination of the model s fit is performed through the comparison of the experimental and predicted bioactivities and is needed to statistically ensure that the models are sound. The methods of chi (%) and root-mean squared error (RMSE) are performed to determine if the model possesses the predictive quality reflected in the R2. The use of RMSE shows the error between the mean of the experimental values and predicted activities. The chi value exhibits the difference between the experimental and predicted bioactivities ... 

Root Mean Square Error of Prediction (RMSEP) Plot (Model Diagnostic) The RMSEP plot for the MCB model is shown in Figure 5.127. Although the shape of this RMSEP plot is not ideal, it does not exhibit erratic behavior. Tlie first minimum in this plot is at four factors with a lower minimum at six factors. In Section 5.2.1.2, nonlinear behavior was suspected as the root cause of the failure of the DCLS method. Tlicreforc, it is reasonable that a PLS model re-... 

At this point, it is worth noting that the same validation methods that are used to avoid overfitting of quantitative models (Section 8.3.7) can also be used to avoid overfitting in qualitative models. The only difference is that the figure of merit in this case is not the Root Mean Squared Error of Prediction (RMSEP), but rather the percent correct classification or %CC ... 

An important issue in PCR is the selection of the optimal number of principal components kopt, for which several methods have been proposed. A popular approach consists of minimizing the root mean squared error of cross-validation criterion RMSECV,. For one response variable (q = 1), it equals... 

The NRL tight-binding method has been used to address the adsorption of 02 on Pt(l 1 1) [99]. The Pt-Pt interactions were taken from a large data base of TB parameter for the elements which are posted on the world wide web [100]. These parameters were obtained from a fit to DFT bulk calculations. Still, it has been demonstrated that the pure Pt surface is also well-described by this parametrization [42], For the Pt-O and the 0-0 TB parameters a new fit had to be performed. They were adjusted in order to reproduce the GGA-DFT results of the 02/Pt(l 1 1) potential energy surface [91, 92], The root mean square error of the fit is below 0.1 eV [41] which is in the range of the error of the GGA-DFT calculations. The spin state of the oxygen molecule was not explicitly considered in the... 

Figures 11 and 12 illustrate the performance of the pR2 compared with several of the currently popular criteria on a specific data set resulting from one of the drug hunting projects at Eli Lilly. This data set has IC50 values for 1289 molecules. There were 2317 descriptors (or covariates) and a multiple linear regression model was used with forward variable selection the linear model was trained on half the data (selected at random) and evaluated on the other (hold-out) half. The root mean squared error of prediction (RMSE) for the test hold-out set is minimized when the model has 21 parameters. Figure 11 shows the model size chosen by several criteria applied to the training set in a forward selection for example, the pR2 chose 22 descriptors, the Bayesian Information Criterion chose 49, Leave One Out cross-validation chose 308, the adjusted R2 chose 435, and the Akaike Information Criterion chose 512 descriptors in the model. Although the pR2 criterion selected considerably fewer descriptors than the other methods, it had the best prediction performance. Also, only pR2 and BIC had better prediction on the test data set than the null model.

If the function may be made linear with respect to its unknown parameters by a suitable transformation, then it may be fitted by the Linearized Least Squares method (10) so as to minimize the root mean square error in the original (untransformed) space. The essence of this technique is to use weighted (linear) least squares to effect a non-linear least squares fit. Assume that the equation has been transformed into an equal variance space and let... 

Experimental values obtained in this way must be compared with those calculated according to Equation (21). Predicted versus experimental values are compared in Figure 10. The root mean square error (RMSE) is less than 5.6%. It should be noted that no adjustable parameters have been employed and the method can be used for any reacfor size without limitations. 

Figure 9.2 The root mean squared error (RMSE) of models for prediction of aqueous solubility of chemical compounds shown as a function of the number of molecules, n, used for model development and validation. The results of methods developed using quantum chemical (3D), topological descriptors (2D/1D), and methods based on other physicochemical descriptors (PhysChem) are shown.

The residuals may also be obtained from cross-validation. With the methods described in this book, both the X part and the y part of Equation (7.7) are modeled and hence have associated residuals. The residual ey of y is usually summed to a number of regression statistics such as percentage variance explained, the coefficient of determination, root mean squared error of prediction etc. Diagnostics based on y-residuals are well covered in standard regression literature [Atkinson 1985, Beebe et al. 1998, Cook 1996, Cook Weisberg 1980, Cook Weisberg 1982, Martens Ntes 1989, Weisberg 1985],... 

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