Metoda parcijalnih najmanjih kvadrata: Regresijski model

master's thesis

• Author: Tamara Sente
• Mentor: Miljenko Huzak (mentor)
• Committee member: Miljenko Huzak (predsjednik povjerenstva)
• Committee member: Vjekoslav Kovač (član povjerenstva)
• Committee member: Nela Bosner (član povjerenstva)
• Committee member: Zvonko Iljazović (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2016-09-27, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

PLS metoda (metoda parcijalnih najmanjih kvadrata) je statistička metoda koju je 1966. godine predstavio Herman Wold kao algoritam sličan metodi potencija na polju ekonometrije. U današnjici se dana metoda više koristi na području kemometrije, gdje se koristi u kombinaciji s regresijskim modelom za predviđanje nezavisne varijable. Cilj metode je reducirati dimenziju broja komponenti kojima ćemo ući u regresijski model, zbog čega nas podsjeća na PCA (metoda glavnih komponenti). Iako je PCA poznatiji u teoriji, u praksi se češće koristi PLS metoda jer pri redukciji komponenti u regresijskom modelu uzima u obzir zavisnu i nezavisnu varijablu. Osim samog modela, važna je i implementacija te se u radu spominju i dva najpoznatija algoritma: NIPALS i SIMPLS.

Abstract (english)

PLS method (partial least squares method) is a statistical method that was originated in 1966 by Herman Wold as an algorithm alike to the power method in the field of econometrics. In the present, given method is being used in the field of chemometrics, where is used in combination with the regression model to predict the independent variable. The aim is to reduce the dimension of the number of components and performs least squares regression on these components, instead of on the original data – which is similar to the PCA (Principal Component Analysis). Although PCA is much more known in theory, PLS method is used more often in practice, because in the reduction of components and regression model combines components from dependent and independent variable. In addition to the modelling, implementation takes the important part in real life, that is why the two most famous algorithm NIPALS and SIMPLS are mentioned in this paper.

• Keywords: PLS metoda; metoda parcijalnih najmanjih kvadrata; metoda glavnih komponenti; redukcija komponenti u regresijskom modelu; NIPALS; SIMPLS
• Keywords (english): PLS method; partial least squares method; Principal Component Analysis; reduction of components in regression model; NIPALS; SIMPLS
• Language: croatian
• URN:NBN: urn:nbn:hr:217:915875
• Study programme: Title: Mathematical Statistics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-02-06 14:57:15