| One difficulty that faces many chemometricians is determining how many factors exist in any data set and how many factors should be included in an analysis. Including too many factors in the analysis may overfit the data, yielding false positives or artificially lower errors. Too few factors in the model will underfit the data, depriving the analysis of statistically important chemical information. Unfortunately, no universal method exists to determine the number of factors that should be included for the best possible analysis. Accordingly, this presents a challenge because there is no way to determine if the optimally complex model has been chosen.; This research investigates several different approaches to determine the optimal complexity of models for multivariate analysis. In one approach, a statistical method has been developed to determine the number of significant factors in a set of data as well as to examine the magnitude of inherent errors in calibration data. Window evolving factor analysis (WEFA) has been used in a second approach to determine the optimal complexity of data indirectly via examination of the resulting spectra. A third approach investigates the design of a chemical sensor array for the optimal discrimination of a mixture.; While each of the different methods has different advantages, the overall goal is to achieve the most accurate analysis possible. Additionally, the different approaches undertaken in this research yield important benefits. These benefits include the ability to perform real-time analysis and robust analyses. Many of these approaches have increased sensitivity and lowered prediction errors. |
