Chapter 6

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:

1. how to estimate PCA models if the error covariance matrix ;

2. how to estimate PLS/MRPLS models if the input variable sets are also corrupted by an error vector;

3. how to estimate MSPC models if the reference data contain outliers; and

4. how to estimate MSPC models if only small reference sets are available.

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 ...*

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