PLS multi-step regressions in data paths

Here is presented a procedure that extends standard PLS Regression to several data matrices in a path. The basic idea is to convert the path of data matrices into interconnected regressions. Forecasts by PLS are extended to multi-step forecasts for each data matrix in the path. We study how far we can make forecasts, i.e., how far we can ‘see’ in the path. It is shown how data paths are divided into parts, where multi-step forecasting can be carried out within each part. The principles of PLS are used to suggest criteria for estimation in the regressions. These methods can be used to supervise a complex path of industrial chemical/biological processes. It is shown how expanding and contracting paths, which is common for industrial processes, can be handled. These methods can be used to carry out analysis of general path models. It is shown briefly by an example how a Structural Equations Model, SEM, can be converted into a collection of sequential paths that can be analyzed by present methods. The results suggest that conclusions made at SEM analysis may not always be reliable. The theory is applied to process data. It is shown how we work with the analysis of each regression in a similar way as in PLS.