Standard spress value

The maximum number of latent variables is the smaller of the number of x values or the number of molecules. However, there is an optimum number of latent variables in the model beyond which the predictive ability of the model does not increase. A number of methods have been proposed to decide how many latent variables to use. One approach is to use a cross-validation method, which involves adding successive latent variables. Both leave-one-out and the group-based methods can be applied. As the number of latent variables increases, the cross-validated will first increase and then either reach a plateau or even decrease. Another parameter that can be used to choose the appropriate number of latent variables is the standard deviation of the error of the predictions, SpREss ... 

SDEP (the standard deviation of the error of predictions) corresponds to jpress but the number of degrees of freedom is not considered in the calculation of the SDEP value. The smallest -spress or SDEP value should be taken as the criterion for the optimum number of components. Alternatively, an increase of the value by a certain percentage, e.g., 5%, may be defined as the criterion to accept a further PLS component. As long as only significant components are extracted in the PLS analysis, PRESS, SDEP and Jpress will decrease if too many components are derived, overprediction results and PRESS, SDEP and spress increase. 

Another alternative to training and test selections is cross-validation. In this approach, many models are derived where one or several compounds are excluded from the data set and are predicted by the corresponding model. In the most common leave-one-out cross-validation, every compound is eliminated once. Thus, n models (n = number of compounds) are derived and the n predictions are compared with the experimental values the cross-correlation coefficient, and spREss. the standard deviation of predictions, are calculated from the sum of the squared deviations of the predicted values (PRESS), in the same manner as the squared correlation coefficient and the standard deviation s are calculated if no cross-validation is performed. For theoretical reasons, cannot be larger than p- and ipRESS cannot be smaller than 5 may even be negative which means that the predictions by the model are worse than taking the average of all biological data as the predicted values. 

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