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master's thesis
Analiza glavnih komponenti i faktorska analiza
Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2020. urn:nbn:hr:126:375879
Vilić, Ana
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics and Mathematics Teaching
Probability, Mathematical Statistics and Data Science Research Group

Institutional repository: Repository of School of Applied Mathematics and Informatics

Cite this document

Vilić, A. (2020). Analiza glavnih komponenti i faktorska analiza (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:375879

Vilić, Ana. "Analiza glavnih komponenti i faktorska analiza." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2020. https://urn.nsk.hr/urn:nbn:hr:126:375879

Vilić, Ana. "Analiza glavnih komponenti i faktorska analiza." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2020. https://urn.nsk.hr/urn:nbn:hr:126:375879

Vilić, A. (2020). 'Analiza glavnih komponenti i faktorska analiza', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 25 January 2025, https://urn.nsk.hr/urn:nbn:hr:126:375879

Vilić A. Analiza glavnih komponenti i faktorska analiza [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2020 [cited 2025 January 25] Available at: https://urn.nsk.hr/urn:nbn:hr:126:375879

A. Vilić, "Analiza glavnih komponenti i faktorska analiza", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2020. Available at: https://urn.nsk.hr/urn:nbn:hr:126:375879

Metadata
TitleAnaliza glavnih komponenti i faktorska analiza
Title (english)Principal Component Analysis and Factor Analysis
AuthorAna Vilić
MentorNenad Šuvak (mentor)
Committee memberMirta Benšić (predsjednik povjerenstva)
Committee memberNenad Šuvak (član povjerenstva)
Committee memberDanijel Grahovac (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Pure Mathematics and Mathematics Teaching)
(Probability, Mathematical Statistics and Data Science Research Group)
Osijek
Defense date and country2020-11-06, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Probability Theory and Statistics
Abstract
U ovom su radu opisane statističke metode analiza glavnih komponenti i faktorska analiza. U prvom dijelu rada navedeni su osnovni pojmovi i rezultati koji su potrebni u nastavku. U drugom poglavlju se bavimo analizom glavnih komponenti. Najprije definiramo i izvodimo glavne komponente, a zatim navodimo neka njihova algebarska svojstva i statističke implikacije tih svojstava. Nakon toga definiramo glavne komponente uzorka te se bavimo distribucijskim rezultatima za glavne komponente i procjenom parametara. Nadalje, osvrćemo se na nejedinstvenost glavnih komponenti za slučajan uzorak i njegove realizacije. Naime, glavne komponente nisu jedinstvena karakteristika podataka nego ovise o korištenim mjernim jedinicama i tipu matrice koja se koristi za izračun glavnih komponenti slučajnog uzorka. Zaključno, opisujemo jednu primjenu glavnih komponenti, primjenu glavnih komponenti u linearnoj regresiji. U trećem poglavlju se bavimo faktorskom analizom. U tom poglavlju prvo definiramo faktorski model, a nakon toga opisujemo procjenu parametara faktorskog modela. U tom poglavlju navodimo i usporedbu metoda, tj. navodimo sličnosti i razlike, analize glavnih komponenti i faktorske analize. U četvrtom poglavlju provodimo analizu glavnih komponenti i faktorsku analizu na primjerima. Kod primjera analize glavnih komponenti objašnjavamo kada ima smisla koristiti ovu metodu, kako odabrati broj glavnih komponenti za daljnju analizu, kako interpretirati zadržane glavne komponente te ilustriramo primjenu glavnih komponenti u linearnoj regresiji. Slično, kod primjera faktorske analize objašnjavamo kada su podaci prikladni za faktorsku analizu, kako odabrati broj faktora i kako interpretirati faktorsku strukturu.
Abstract (english)
In this thesis we describe two statistical methods, namely, principal component analysis and factor analysis. In the first chapter of this thesis we list basic concepts and results that are used throughout the thesis. In the second chapter we deal with principal component analysis. We first define and derive the principal components. In addition, we list some of their algebraic properties and the statistical implications of those properties. After that, we define the sample principal components and deal with distributional results and parameter estimation for the sample principal components. Furthermore, we look at the non-uniqueness of the principal components for random samples and their realizations. The principal components are not a unique characteristic of the data but depend on the units of measurement used and the type of matrix used to construct the sample principal components. To conclude this chapter, we describe one application of principal components and that is how to use prinicpal components in linear regression. In the third chapter, we first define the factor model and then describe the estimation of the factor model. In this chapter we also list the similarities and differences between principal component analysis and factor analysis. In the fourth chapter, we perform principal component analysis and factor analysis on examples. In this chapter, we explain when to use these methods, how to select the number of principal components or factors, how to interpret the principal components or factors and we illustrate the application of principal components in linear regression
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:375879
Study programmeTitle: Mathematics; specializations in: Financial and Statistical Mathematics, Mathematics and Computer Science, Industrial and Applied Mathematics
Course: Financial and Statistical Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2020-11-09 11:26:04