Russolillo, Giorgio
(2009)
Partial Least Squares Methods for NonMetric Data.
[Tesi di dottorato]
(Inedito)
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Tipologia del documento: 
Tesi di dottorato

Lingua: 
English 
Titolo: 
Partial Least Squares Methods for NonMetric Data 
Autori: 
Autore  Email 

Russolillo, Giorgio  giorgio.russolillo@unina.it 

Data: 
30 Novembre 2009 
Numero di pagine: 
240 
Istituzione: 
Università degli Studi di Napoli Federico II 
Dipartimento: 
Matematica e statistica 
Scuola di dottorato: 
Scienze economiche e statistiche 
Dottorato: 
Statistica 
Ciclo di dottorato: 
22 
Coordinatore del Corso di dottorato: 
nome  email 

Lauro, Carlo Natale  clauro@unina.it 

Tutor: 
nome  email 

Lauro, Carlo Natale  clauro@unina.it 

Data: 
30 Novembre 2009 
Numero di pagine: 
240 
Parole chiave: 
PLS methods, NIPALS, PLS Regression, PLS Path Modeling Optimal Scaling, nonmetric data, nonlinearity 
Settori scientificodisciplinari del MIUR: 
Area 13  Scienze economiche e statistiche > SECSS/01  Statistica 
Depositato il: 
11 Dic 2009 18:33 
Ultima modifica: 
30 Apr 2014 19:40 
URI: 
http://www.fedoa.unina.it/id/eprint/4216 
DOI: 
10.6092/UNINA/FEDOA/4216 
Abstract
Partial Least Squares (PLS) methods embrace a suite of data analysis techniques based on algorithms belonging to PLS family. These algorithms consist in various extensions of the Nonlinear estimation by Iterative PArtial Least Squares (NIPALS) algorithm, which was proposed by Herman Wold as an alternative algorithm for implementing a Principal Component Analysis. The peculiarity of this algorithm is that it calculates principal components by means of an iterative sequence of simple ordinary least squares regressions. This feature allows overcoming computational problems due to missing data or landscape data matrices, i.e. matrix having more columns than rows.
PLS methods were born to handle data sets forming metric spaces. This involves that all the variables embedded in the analysis are observed on interval or ratio scales.
In this work we evidenced how NIPALS based algorithms, properly adjusted, can work as optimal scaling algorithms. This new feature of PLS, which had been until now totally unexplored, allowed us to device a new suite of PLS methods: the NonMetric PLS (NMPLS) methods.
NMPLS methods can be used with different aims:
 to analyze at the same time variables observed on different measurement scales;
 to investigate non linearity;
 to discard the hard assumption of linearity in favor of a milder assumption of monotonicity.
In particular, these methods generalize standard NIPALS, PLS Regression and PLS Path Modeling in such a way to handle variables observed on a variety of measurement scales, as well as to cope with non linearity problems.
Three new algorithms are been proposed to implement NMPLS methods: the NonMetric NIPALS algorithm, the NonMetric PLS Regression algorithm, and the NonMetric PLS Path Modeling algorithm.
All these algorithms provide at the same time specific PLS model parameters as well as scaling values for variables to be scaled.
Scaling values provided by these algorithms are been proved to be optimal, in the sense that they optimize the same criterion of the model in which they are involved. Moreover, they are suitable, since they respect the constraints depending on which among the properties of the original measurement scale we want to preserve.
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