Principal components regression (PCR) and partial least squares regression (PLS) are widely used in multivariate calibration in the fields of chemometrics, econometrics, social science and so forth, serving as alternative solutions to the problems which arise in ordinary least squares regression when explanatory variables are either collinear, or there are hundreds of explanatory variables with a relatively small sample size. Both PCR and PLS tackle the problems by constructing lower dimensional factors based on the explanatory variables. The extra step of factor construction makes the standard prediction uncertainty theory of ordinary least squares regression not directly applicable to the two reduced dimension methods. In the thesis, we start by reviewing the ordinary least squares regression prediction uncertainty theory, and then investigate how the theory performs when it extends to PCR and PLS, aiming at potentially better approaches. The first main contribution of the thesis is to clarify the quantification of prediction uncertainty for PLS. We rephrase existing methods with consistent mathematical notations in the hope of giving a clear guidance to practitioners. The second main contribution is to develop a new linearisation method for PLS. After establishing the theory, simulation and real data studies have been employed to understand and compare the new method with several commonly used methods. From the studies of simulations and a real dataset, we investigate the properties of simple approaches based on the theory of ordinary least squares theory, the approaches using resampling of data, and the local linearisation approaches including a classical and our improved new methods. It is advisable to use the ordinary least squares type prediction variance with the estimated regression error variance from the tuning set in both PCR and PLS in practice.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:631903 |
| Date | January 2014 |
| Creators | Zhang, Y. |
| Publisher | University College London (University of London) |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://discovery.ucl.ac.uk/1433990/ |
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