Analiza vjerojatnosti pokrivanja Waldovih pouzdanih intervala za regresijske koeficijente u logističkoj regresijskoj analizi

master's thesis

• Author: Marija Špehar
• Mentor: Vesna Lužar-Stiffler (mentor)
• Committee member: Vesna Lužar-Stiffler (predsjednik povjerenstva)
• Committee member: Goran Radunović (član povjerenstva)
• Committee member: Ilja Gogić (član povjerenstva)
• Committee member: Marko Erceg (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2019-03-01, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu bavili smo se modelom logističke regresije, koja pripada široj klasi modela pod imenom generalizirani linearni modeli. Koristi se u analizi binarnih podataka, a može biti multinomna - u slučaju da varijabla odaziva poprima vrijednosti koje se mogu rasporediti u više od dvije kategorije te dihotomna, ako varijabla odaziva poprima samo dvije vrijednosti. Fokusirali smo se na dihotomnu logističku regresiju pri čemu smo prisustvo i odsustvo promatranog svojstva interpretirali jedinicom i nulom. Opisali smo način postavljanja modela te objasnili interpretaciju parametara, kao i metodu dobivanja procjene parametara. Koliko dobro model opisuje podatke te kako tumačimo određena svojstva pokazali smo na primjeru. Također, proveli smo analizu vjerojatnosti pokrivanja Waldovih pouzdanih intervala za regresijske koeficijente i iz rezultata zaključili da je primjena logističke regresije upitna za male uzorke (do duljine 200) i jednostavne modele s jednom do dvije prediktorske varijable zbog mogućeg problema s potpunom separacijom koji se često javlja pri izvođenju programa u SAS-u.

Abstract (english)

In this paper, we are dealing with a model of logistic regression, which belongs to a wider model class called generalized linear models. It is used in binary data analysis, and can be multinational - in case the dependent variable is taking values that can be deployed in more than two categories and dichotomous, if the responding variable getting only two values. We focused on the dichotomous logistic regression in which the presence and absence of the observed property interpreted by one and zero. We described the fitting model and explained the interpretation of parameters as well as the method of parameter estimation. How good a model describes the data and how we interpret some of the properties we showed in the example. Also, conducted an analysis of the coverage probability of Wald’s confidence intervals for regression coefficients and concluded that the application of logistic regression is questionable for small samples (to length 200) and simple models with one to two prediction variables due to a potential problem with complete separation often occurring when doing the program in SAS.

• Keywords: logistička regresija; generalizirani linearni model; Waldovi pouzdani intervali; SAS
• Keywords (english): logistic regression; generalized linear model; Wald’s confidence intervals; SAS
• Language: croatian
• URN:NBN: urn:nbn:hr:217:182343
• 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: 2019-09-05 11:21:12