Multivariate standard addition method solved by net analyte signal calculation and rank annihilation factor analysis.

This article describes the use of the net analyte signal (NAS) concept and rank annihilation factor analysis (RAFA) for building two different multivariate standard addition models called "SANAS" and "SARAF." In the former, by the definition of a new subspace, the NAS vector of the analyte of interest in an unknown sample as well as the NAS vectors of samples spiked with various amounts of the standard solutions are calculated and then their Euclidean norms are plotted against the concentration of added standard. In this way, a simple linear standard addition graph similar to that in univariate calibration is obtained, from which the concentration of the analyte in the unknown sample and the analytical figures of merit are readily calculated. In the SARAF method, the concentration of the analyte in the unknown sample is varied iteratively until the contribution of the analyte in the response data matrix is completely annihilated. The proposed methods were evaluated by analyzing simulated absorbance data as well as by the analysis of two indicators in synthetic matrices as experimental data. The resultant predicted concentrations of unknown samples showed that the SANAS and SARAF methods both produced accurate results with relative errors of prediction lower than 5% in most cases.