| Although multivariate statistical methods were originally developed in the social sciences, they are now used as almost routine procedures for the analysis of data in science and engineering. Multivariate techniques are useful for summarizing the information contained in large datasets, which in chemical engineering are often products of the large volume of data generated by highly instrumented processes and by computerized analytical instruments. In this thesis, we investigate the use of some multivariate methods for exploratory data analysis and in regression analysis. In addition to carrying out a comparative analysis of principal component regression, canonical correlation analysis, redundancy analysis, and partial least squares (PLS) for the exploratory analysis of two large industrial datasets, we also address the question of the usefulness of the idea of latent variables. To clarify the mechanics of partial least squares, we develop a geometric framework that is useful for understanding exactly what PLS does. In addition, the issue of interval estimation in partial least squares is considered, and we develop an approximation that allows us to construct approximate confidence intervals from calibration models based on PLS. Finally, the close correspondence between factor analysis and errors-in-variables models is discussed, and we then consider how these methods might be adapted to incorporate dimensional reduction in a regression situation where there is error in all the variables. |
