Further modeling issues
Chapters 1 to 3 introduced the basic MSPC approach that is applied to the chemical reaction and the distillation processes in Chapters 4 and 5, respectively. This chapter extends the coverage of MSPC modeling methods by discussing the following and practically important aspects:
Section 6.1 introduces a maximum likelihood formulation for simultaneously estimating an unknown diagonal error covariance matrix and the model subspace, and covers cases where is known but not of the form .
Section 6.2 discusses the accuracy of estimating PLS models and compares them with OLS models with respect to the relevant case that the input variables are highly correlated. The section then extends the data structure in 2.23, 2.24 and 2.51 by including an error term for the input variable set, which yields an error-in-variable (Söderström 2007) or total least ...