MULTIDIMENSIONAL SIMPLEX INTERPOLATION - AN APPROACH TO LOCAL MODELS FOR PREDICTION

The use of local linear models for prediction is investigated. A number of calibration samples, constituting a prediction set, in the neighbourhood of the unknown sample is selected from a given set. The extreme case of local models, where the prediction set forms a simplex, is given particular consideration. Two methods for selection of the prediction set in this case are introduced, ensuring interpolation within the simplex. These methods are compared to multiple linear regression, using a larger prediction set. The prediction error is divided into two contributions: (i) the data error emanating from random and systematic errors in both the dependent and the independent variables; (ii) the interpolation error due to lack-of-fit for the linear model. The properties of both these contributions as a function of the size of the prediction set are studied by simulations. The results are compared to theoretical relations. Simulated experiments in size exclusion chromatography are used as an application. A refinement step in the prediction, using a recalculated distance measure for the selection of the prediction set, is introduced leading to a substantial decrease in the prediction error.