Principal Components Against Collinearity Problems in Regression Models and Discriminant Analysis

الموضوعات

إحصاء

الملخص

In this thesis, we studied the collinearity problem in multivariate regression and discriminant analysis using the principal component as a solution for this problem. In particular, we investigated the collinearity assumption among the independent variables in both models. Then we investigated the use of principal components to solve the collinearity problems in both models. The subject of using principal components in linear regression models may be a straightforward subject, but using it in multivariate linear regression when their exist several responses and several independent variables is theoretically tedious. We build the multivariate linear regression model using principal component to establish the Principal Component Regression (PCR) model, and the linear discriminant model to establish the Discriminant Analysis Principal Components (DAPC) model. We used Latent Root Regression (LRR) and Least Absolute Shrinkage and Selection Operator (LASSO) to select components for each dependent variable. To estimate the parameters for PCR we used Ordinary Least Squares (OLS) which assumes that the residuals are multivariate normally distributed. Unfortunately, the estimates of the parameters are biased, resulting in a problem which does not allow to use the well-known criteria, such as Mean Squares Error (MSE) or Root Mean Squares Error (RMSE). All methods were applied on a real medical data set with fourteen variables including three dependent variables indicating the severity of both diabetes and hypertension on patients in the Gaza Strip. Collinearity in the data was diagnosed, and one independent variable had to be excluded. PCA was applied to only ten predictors, and we found that the first Six components have 81.5% of the total variance. By using LRR with Cross Validation we selected the most predictive components for regression models. For PCR and after using LRR, the study identified the most predictive PCs and the independent variables with significant loadings for severity of both diabetes and hypertension in the medical data set. In the application of DAPC, a categorical response variable with four categories to indicate the severity of diabetes was created and three discriminant functions were estimated. The results identified the most important variables that have high loadings on the three linear discriminant functions.

روابط وملفات

التعريف والنوع

رقم الوثيقة

fea3e703-936f-4a06-9ca9-2dc841ba81ba

رقم العقد

0

نوع الوسائط

Crawler

نوع المحتوى

الرسائل العلمية

صيغة المصدر

رسائل ماجيستير

نوع الملف

pdf text

أسماء الملفات

2103207_1.pdf

بيانات النشر

ترجمة العنوان

استخدام المركبات الأساسية لمعالجة الازدواج الخطي في نماذج الانحدار والتحليل التمييزي

ألقاب المؤلفين

[{"name_ar":"Mahmoud K. Okasha","title_ar":"اشراف","title_en":"Supervision"},{"name_ar":"وعد حسن علي عابد","title_ar":"اعداد","title_en":"Preparation"}]

اللغة

English

المصدر والدورية

اسم المصدر

Principal Components Against Collinearity Problems in Regression Models and Discriminant Analysis

المحتوى والصفحات

عدد الصفحات

0

إشراف وإعداد

الإشراف

Mahmoud K. Okasha

الإعداد

وعد حسن علي عابد

الاقتباسات الببليوغرافية