Analiza korespodencije - metoda glavnih komponenti kategorijskih podataka

master's thesis

• Author: Jelena Mađarević
• Mentor: Anamarija Jazbec (mentor)
• Committee member: Anamarija Jazbec (predsjednik povjerenstva)
• Committee member: Miljenko Marušić (član povjerenstva)
• Committee member: Vjekoslav Kovač (član povjerenstva)
• Committee member: Nela Bosner (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2015-07-13, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics; Probability Theory and Statistics

Abstract

Korespondencijska analiza primarno je multivarijatna deskriptivna metoda koja prezentira veze između redaka i stupaca u tablici frekvencija pomoću grafičkog prikaza točaka u zajedničkom niskodimenzionalnom prostoru. Ukoliko želimo maksimalno iskoristiti prednosti korespondencijske analize podaci bi trebali zadovoljavati neke od sljedećih kriterija: 1. Matrica podataka trebala bi biti velika, tj. takva da je otežano otkrivanje struktura pomoću jednostavnih statističkih analiza. 2. Varijable bi trebale biti homogene, tako da ima smisla računati udaljenosti između pojedinih kategorija 3. Metoda je najprikladnija za podatke čija je struktura nepoznata. Analiza korespondencije vrlo je fleksibilna metoda. Kao prvo, nameće minimalne zahtjeve nad samim podacima, a kao drugo dopusta korištenje suplementarnih informacija. Metoda je eksplorativna tehnika i kao takva može poslužiti kao korisna dopuna drugim metodama koje se baziraju na testiranju hipoteza. Korespondencijska analiza je od bitnog značaja znanstvenicima za analizu kategorijskih podataka, ima široku primjenu u raznim područjima od ekologije, društvenih znanosti, biomedicini... Grafički prikaz je vrlo djelotvoran za komunikaciju kompleksnih odnosa između varijabli/kategorija. Štoviše, komplementaran je novim važnim metodama poput log linearnih modela. Nedostaci ove metode su nemogućnost dobivanja udaljenosti između točaka koje pripadaju različitim skupovima (nisu definirane), te nedostatak testa značajnosti za otkrivene veze medu kategorijama.

Abstract (english)

Correspondence analysis is primary a multivariate descriptive method of analysis that presents the relations between rows and columns in a frequency table graphically as point in a common low-dimensional space. Some of following criteria should be satisfied if the advantages of the method are to be exploited to the full: 1. The data matrix should be large, making it difficult to discover the structure by means of simple statistical analyses. 2. The variables need to be homogenous, so that it is meaningful to calculate distances between categories. 3. The method is most suitable for the data for which the structure is unknown. Correspondence analysis is a very flexible method. First it imposes few requirements as regards the dana themselves and, second, it allows the use of supplementary information. The method is an exploratory technique and thus serves as useful supplement to other methods based on hypothesis testing. Correspondence analysis is a very useful method for different kind of sciences in fields like ecology, social, biomedical sciences etc. The graphical display is very beneficial for communication complex relations between variables/categories. Furthermore, it complements other new important methods such as loglinear models. The disadvantages of the method are that the distances between the points of different sets is not defined and it does not include significance tests for effects or interactions.

• Keywords: Korespondencijska analiza
• Keywords (english): Correspondence analysis
• Language: croatian
• URN:NBN: urn:nbn:hr:217:808917
• 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: Access restricted to students and staff of home institution
• Created on: 2019-01-17 11:12:10