Graphical criterion for assessing trilinearity and selecting the optimal number of factors in the generalized rank annihilation method using liquid chromatography–diode array detection data Original Research Article

A weight parameter (α) was introduced into the generalized rank annihilation method (GRAM) to calculate and reduce the bias in the predicted concentration. Here we show that α can be used as an indicator to determine whether the trilinearity assumptions are met and to select the right number of factors to calculate the model. The procedure is to calculate several GRAM models by varying α and the number of factors. When the experimental data are trilinear and the right number of factors is used, α does not affect the predicted concentration. If the condition of trilinearity is not met or the correct number of factors is not used, the predicted concentration changes when α changes. A graph shows this behavior. Both simulated and real data were checked for trilinearity. Deviations from the ideal mathematical model, such as the time shift or different shape of the chromatographic profiles, were simulated. These parameters have an effect but the greatest effect was produced by the selection of the number of factors.