Estimation of fuzzy Multivariate Monotonic Regression Function with an Application

A thesis

Submitted to the council of the college of Administration & Economics\ University of Karbala as partial fulfillment of the requirements for the degree of Philosophy of Statistics

By
 Ali Mohammed Obaid Al-Sakmani

Supervision
Prof.  Dr . Mahdi Wahab Nea’ama

Abstract

In this thesis, the Fuzzy Isotonic Regression Model was proposed considering that the dependent variable is fuzzy by extracting the degrees of non-affiliation for the observations of this variable with the aim of excluding the observations of little importance from the model and thus increasing the accuracy of the model. The proposed model was estimated using three methods: the fuzzy monotonic maximum likelihood method, the fuzzy monotonic least squares method (FILSR) and the fuzzy monotonic M estimator (FIM). These methods were compared with the same methods in the absence of fuzziness using Monte-Carlo simulation experiments for different models that include independent variables (p=5, 10, 15, 30) and sample sizes (n=50, 100, 250, 300). It was concluded that the best method for estimating the monotonic regression function is the fuzzy monotonic maximum likelihood method, followed by the fuzzy monotonic least squares method and finally the fuzzy monotonic M method. The fuzzy monotonic maximum likelihood and fuzzy monotonic least squares method are close in estimation. Also, real data representing (250) patients with chronic kidney disease ((CKD) for the years (2023-2019) from the Karbala Health Department – Al-Hussein Teaching Hospital were used, as the dependent variable (y) was the glomerular filtration rate (GFR) and a set of variables affecting the incidence of the disease with twenty-one independent variables, which are X₁ Age (Age), X₂ Sex (Sex), X₃ Family History (Family Historical), X4 Body Mass Index (BMI)) k, X₅ Blood Pressure (Blood Pressure), X₆ Diabetes (Diabetic), X₇ Smoking (Smoking), X₈ Cholesterol levels (Cholesterol levels), X₉ Diet (Diet), X₁₀ Protein levels in the urine (Proteinuria) (an indicator of kidney damage) (Proteinuria), and X₁₁ Taking nonsteroidal anti-inflammatory drugs NSAIDs, X₁₂ Cardiac functions, X₁₃ Phosphorus levels, X₁₄ Calcium levels, X₁₅ Potassium levels, X₁₆ Proteinuria, X₁₇ Uric acid levels, X₁₈ Vitamin D levels, X₁₉ Chronic exposure to dehydration, X₂₀ Exposure to x-rays and radioactive materials. It was found that the method was effective in estimating the monotonic regression model under data with a monotonic increasing trend, as the actual values ​​were consistent with the estimated values.