Cross Model Validation

Anderssen, E., Dyrstad, K., Westad, F., Martens, H. Chemom. Intell. Lab. Syst. 84, 2006, 69-74. Reducing over-optimism in variable selection by cross-model validation. 

A widely used approach to establish model robustness is the randomization of response [25] (i.e., in our case of activities). It consists of repeating the calculation procedure with randomized activities and subsequent probability assessments of the resultant statistics. Frequently, it is used along with the cross validation. Sometimes, models based on the randomized data have high q values, which can be explained by a chance correlation or structural redundancy [26]. If all QSAR models obtained in the Y-randomization test have relatively high values for both and LOO (f, it implies that an acceptable QSAR model cannot be obtained for the given dataset by the current modeling method. 

Unlike test set validation methods, cross-validation methods attempt to validate a model using the calibration data only, without requiring the preparation and analysis of an additional test set of samples. This involves the execution of one or more internal validation procedures (hereby called subvalidations), where each subvalidation involves three steps ... 

L. Gidskehang, E. Anderssen and B.K. Alsberg, Cross model validation and optimisation of bihnear regression models, Chemom. Intell. Lab. Syst., 93, 1-10 (2008). 

One advantage of the cross-validation residuals is that they are more sensitive to outliers. Because the left out samples do not influence the construaion of the PCA models, unusual samples will have inflated residuals. The cross-validation PCA models are also less prone to modeling noise in the data and therefore the resulting residuals better reflect the inherent noise in the data set. The identification and removal of outliers and better estimation of noise can provide a more realistic estimate of the inherent dimensionaliw of a data set. 

The most robust analysis methods involve direct comparison of the AI (q) term with theoretical computations. Agreement between data and prediction then validate the models used. The application of inversion approaches involves taking Fourier transforms of the data to yield the set of vectors connecting scattering particles. However, one must be cautious when interpreting the results of these inversions. Experiments are currently underway to measure the Fj2ons term independently, which will allow us to extract the pure ion—DNA cross-term which is more straightforward to interpret. 

In the theory, it is possible to create new QSAR models with almost all datasets of compounds with known biological/toxicological activity. But practically it is a question of the quality and predictivity of a QSAR model to be applied in prediction of biological/toxicological activity. For this reason evaluation of each QSAR model is extremely important. The evaluation of a QSAR model can be preformed either by internal validation (cross validation) or external validation (use of a test-set). External validation is preferred, but is not always possible, e.g. because of the small size of a dataset (Dearden, 2003). 

Repeat questions 2 and 3, but instead of MLR use PLS1 (centred) for the prediction of the concentration of A retaining die first three PLS components. Note that to obtain a root mean square error it is best to divide by 21 rather than 25 if three components are retained. You are not asked to cross-validate the models. Why are the predictions much better ... 

The LOO cross-validated q oo values for the initial models was 0.875 using the water probe and 0.850 using the methyl probe. The application of the SRD/FFD variable selection resulted in an improvement of the significance of both models. The analysis yielded a correlation coefficient with a cross-validated q Loo of 0.937 for the water probe and 0.923 for the methyl probe. In addition we tested the reliability of the models by applying leave-20%-out and leave-50%-out cross-validation. Both models are also robust, indicated by high correlation coefficients of = 0.910 (water probe, SDEP = 0.409) and 0.895 (methyl probe, SDEP = 0.440) obtained by using the leave-50%-out cross-validation procedure. The statistical results gave confidence that the derived model could also be used for the prediction of novel compounds. 

Fit all the surfaces using kriging and validate the model. Once all the variables (surfaces) have been estimated by kriging, it is important validate the metamodel, i.e. using cross validation that allows us to asses the accuracy of the model without extra sampling [2], A kriging model can be considered correct if all the errors in cross validation are inside the interval [-3,+3] standard errors. 

External Validation versus Cross Validation A model fitted to the training set has minimal utility unless it can be generalized to predict unknown chemicals. Most experts in the QSAR held, as well as the present authors, concur that a model s predictive capability minimally needs to be demonstrated by some sort of cross validation or external validation procedure. Although both procedures share many common features, in principle, they are different in both ability and efficiency in assessing a model s overall prediction accuracy, applicability domain, and chance correlation during implementation. 

A variety of procedures are available to assess a model s true expected performance split sample validation, cross-validation, jackknifing, and bootstrapping. 

Principal components analysis of the set of 113 aldhydes (Table 15A.2) afforded two significant components according to cross validation. The model accounted for... 

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