<p> Functional Data Analysis (FDA) has attracted substantial attention for the last two decades. Within FDA, classifying curves into two or more categories is consistently of interest to scientists, but multi-class prediction within FDA is challenged in that most classification tools have been limited to binary response applications. The functional logistic regression (FLR) model was developed to forecast a binary response variable in the functional case. In this study, a functional nominal multinomial logit regression (F-NM-LR) model was developed that shifts the FLR model into a multiple logit model. However, the model generates inaccurate parameter function estimates due to multicollinearity in the design matrix. A generalized partial least squares (GPLS) approach with cubic B-spline basis expansions was developed to address the multicollinearity and high dimensionality problems that preclude accurate estimates and curve discrimination with the F-NM-LR model. The GPLS method extends partial least squares (PLS) and improves upon current methodology by introducing a component selection criterion that reconstructs the parameter function with fewer predictors. The GPLS regression estimates are derived via Iteratively ReWeighted Partial Least Squares (IRWPLS), defining a set of uncorrelated latent variables to use as predictors for the F-GPLS-NM-LR model. This methodology was compared to the classic alternative estimation method of principal component regression (PCR) in a simulation study. The performance of the proposed methodology was tested via simulations and applications on a spectrometric dataset. The results indicate that the GPLS method performs well in multi-class prediction with respect to the F-NM-LR model. The main difference between the two approaches was that PCR usually requires more components than GPLS to achieve similar accuracy of parameter function estimates of the F-GPLS-NM-LR model. The results of this research imply that the GPLS method is preferable to the F-NM-LR model, and it is a useful contribution to FDA techniques. This method may be particularly appropriate for practical situations where accurate prediction of a response variable with fewer components is a priority.</p><p>
| Identifer | oai:union.ndltd.org:PROQUEST/oai:pqdtoai.proquest.com:10599676 |
| Date | 30 November 2017 |
| Creators | Albaqshi, Amani Mohammed H. |
| Publisher | University of Northern Colorado |
| Source Sets | ProQuest.com |
| Language | English |
| Detected Language | English |
| Type | thesis |
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