ﻣﺪﻝ ﮬﺎﯼ ﺭﮔﺮﺳﯿﻮﻥ ﺷﺒﻪ ﺑﺘﺎﯼ ﻣﻨﻌﻄﻒ ﺑﺮﺍﯼ ﺗﺤﻠﯿﻞ ﭘﺎﺳﺦ ﮬﺎﯼ ﭘﯿﻮﺳﺘﻪ ﮐﺮﺍﻧﺪﺍﺭ

This thesis presents the development an‎d assessment of pseudo-beta regression models for analyzing continuous data, such as ratios, rates, an‎d indices, constrained within the interval (0,1). These models establish a framework based on pseudo-likelihood that si multaneously accounts for the mean an‎d variance of the response variable. The variance function is parameterized using the expression ϕµp(1−µ)p, where µ represents the mean, ϕ is the dispersion parameter, an‎d p denotes the shape parameter. This approach not only generalizes stan‎dard Beta regression models but also inherently adapts to diverse patterns observed in bounded data. Furthermore, the framework extends naturally to multivariate an‎d longitudinal models by structuring the covariance matrix. The unknown parame ters are estimated through a combined methodology that utilizes pseudo-likelihood score equations for both the regression coefficients an‎d the dispersion parameter. Simulation studies confirm that these estimators exhibit consistency across various data generation designs, including those based on simplex an‎d beta distributions. To eva‎luate the practi cal effectiveness of the proposed method, four real-world datasets from distinct disciplines are analyzed. These applications include a multivariate analysis of body fat percentage, an investigation of water quality in hydroelectric power plants in both cross-sectional an‎d longitudinal scenarios, an exploration of the relationship between anxiety an‎d stress scores in psychometrics, an‎d an epidemiological study examining the impact of Body Mass Index (BMI) on the waist-to-hip ratio.

4

158863