Regresijska analiza višekategorijskih varijabli odziva

master's thesis

• Author: Ivana Barišić Lučić
• Mentor: Miljenko Huzak (mentor)
• Committee member: Miljenko Huzak (predsjednik povjerenstva)
• Committee member: Sonja Štimac (član povjerenstva)
• Committee member: Marko Erceg (član povjerenstva)
• Committee member: Siniša Slijepčević (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2018-11-27, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Logistička regresija korisna je metoda u istraživačkim problemima u kojima želimo opisati zavisnu varijablu s dvije ili više kategorija pomoću nezavisnih varijabli. Područja u kojima možemo koristiti logističku regresiju su raznolika (biomedicina, osiguranje, itd.), te upravo to logističku regresiju čini praktičnom. U ovom radu logističku regresiju objašnjavamo od najjednostavnijeg modela, odnosno kada pomoću jedne nezavisne varijable opisujemo dihotomnu zavisnu varijablu. Zatim preko složenog logističkog modela u kojem imamo \(k\) nezavisnih varijabli pomoću kojih želimo opisati dihotomnu zavisnu varijablu dolazimo do polinomnog logističkog modela u kojem imamo \(k\) nezavisnih varijabli pomoću kojih želimo opisati kategorijsku (\(m\) kategorija) zavisnu varijablu. Glavna zadaća logističke regresije, složene i polinomne, je pronaći koje nezavisne varijable najbolje opisuju zavisnu. Naravno, moramo imati na umu da će uvijek puni model logističke regresije bolje opisivati zavisnu varijablu, no od interesa je pronaći što je moguće manje varijabli koji će biti dobri prediktori zavisne varijable. Polinomnu logističku regresiju provodimo na podacima o 61-om bolesniku s Crohnovom bolesti. Iako je analiza u ovom radu pokazala kako niti jedan od prediktora (dob, spol, sedimentacija, CRP, kalprotektin, te BMI) značajno ne opisuju stupanj aktivnosti Crohnove bolesti (remisija, blaga upala, te jaka upala) preporučit ćemo ponovnu analizu na većem uzorku.

Abstract (english)

Logistic regression is useful method in researches which analyze categorical (two or more categories) dependent variable using independent variables. The areas where we can use logistic regression are diverse (biomedicine, insurance, etc.), and this makes logistic regression practical. This thesis explain the logistic regression from the simplest model, ie when using an independent variable we describe a dichotomous dependent variable. Then, through a multiple logistic model in which we have \(k\) independent variables by which we want to describe a dichotomous dependent variable, we come to a polynomial logistic model in which we have \(k\) independent variables by which we want to describe the categorical (\(m\) category) dependent variables. The main task of logistic regression, multiple and polynomial, is to find which independent variables best describe the dependent variable. Of course, we must keep in mind that a full logistic regression model will always better describe the dependent variable, but it is of interest to find as less as possible variables which will be good predictors. Polynomial logistic regression is performed on data of 61 patients with Crohn’s disease. Although the analysis in this thesis did not get any predictor (age, gender, sedimentation, CRP, calprotectin, and BMI) which significantly describe the degree of Crohn’s disease activity (remission, mild and severe disease), we would recommend re-analysis on a larger sample.

• Keywords: logistička regresija; istraživački problemi
• Keywords (english): logistic regression; research problems
• Language: croatian
• URN:NBN: urn:nbn:hr:217:597654
• 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: 2019-03-04 10:18:57