Faktorska analiza

master's thesis

• Title (english): Factor analysis
• Author: Ozana Jurić
• Mentor: Anamarija Jazbec (mentor)
• Committee member: Anamarija Jazbec (predsjednik povjerenstva)
• Committee member: Hrvoje Šikić (član povjerenstva)
• Committee member: Vedran Krčadinac (član povjerenstva)
• Committee member: Marko Tadić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2022-03-04, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom diplomskom radu vidjeli smo teorijsku pozadinu faktorske analize te samu primjenu iste. Na početku smo definirali faktorski model. Vidjeli smo da težine faktorskog modela služe za pridruživanje početnih varijabli faktorima te za interpretaciju dobivenih faktora. Također smo vidjeli da modeliranje započinjemo pretpostavkom da su početne varijable korelirane, a kao izlaz te analize su nekorelirani faktori, odnosno odvojene grupe varijabli. Upoznali smo se sa raznim tehnikama ekstrakcije faktora koje uglavnom imaju isti cilj, a to je ekstrakcija maksimalne varijance iz skupa podataka sa svakim faktorom. Vidjeli smo i kriterije za odabir broja faktora, a u idealnim slučajevima svi kriteriji ishode jednaki brojem. Nakon toga smo vidjeli kako se možemo koristiti različitim tipovima rotacija kako bi poboljšali interpretabilnost i korist rješenja. Na kraju smo na primjeru pokazali kako se provodi faktorska analiza.

Abstract (english)

In this thesis, we saw the theoretical background of factor analysis and the application of it. At the beginning, we defined a factor model. We have seen that models factor weights are used to associate initial variables with factors and to interpret the obtained factors. We have also seen that we start modeling by assuming that the initial variables are correlated, and the output of that analysis are uncorrelated factors, i.e. separate groups of variables. We have introduced various factor extraction techniques whom mostly have the same goal, to extract the maximum variance from the data set with each factor. We have also seen the criteria for selecting a number of factors, and ideally all the criteria give the same number as an outcome. After that, we saw how we can use different types of rotation to improve the interpretability and usefulness of the solution. In the end, we showed by example how factor analysis is conducted.

• Keywords: faktorski model; nekorelirani faktori; ekstrakcija maksimalne varijance
• Keywords (english): factor model; uncorrelated factors; maximum variance
• Language: croatian
• URN:NBN: urn:nbn:hr:217:574418
• 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: 2022-03-28 11:18:27