A proposed estimatoro f generalized semiparametric regression model /
مقدرمقترح لنموذج الإنحدار شبه المعلمي المُعَمَّم
by Muhammad El- Metwally Muhammad Seliem ; Supervisors Prof. Sayed Mesheal El-Sayed, Prof. Mohamed Reda Abonaze.
- 164 Leaves : illustrations ; 30 cm. + CD.
Thesis (Ph.D)-Cairo University, 2025.
Bibliography: pages 119-133.
This dissertation develops three generalized semiparametric regression models (GSPRMs) as an extension of parametric generalized linear models (GLMs) to address the dual chal- lenges of excess zeros and nonlinear covariate effects in count data and proportion data. Two estimators are developed for these models: penalized smoothing splines (Ps) and P-splines (Pb). Within the GSPRMs framework, three specific models are developed, each estimated using both developed estimators. First, the semiparametric partially Poisson (SPPO) regres- sion model captures nonparametric covariate effects in standard count data. Second, the semiparametric partially zero-inflated Poisson (SPZIP) regression model incorporates logis- tic regression components to address excess zeros in count data. Third, the semiparametric partially zero-inflated Beta (SPZIBE) regression model handles proportion data with zero- inflation.
To evaluate the performance and applicability of these developed models, extensive sim- ulation studies and real-world applications were conducted, demonstrating their robustness and practical utility. The Pb estimator of the extended models (SPPO-Pb, SPZIP-Pb, SPZIBE- Pb) show superior performance across evaluation metrics, including Akaike Information Cri- terion (AIC), Bayesian Information Criterion (BIC), and root mean square error (RMSE), achieving RMSE reductions of 40–58 % compared to standard Poisson, zero-inflated Poisson (ZIP) and zero-inflated Beta (ZIBE) regression models estimated via maximum likelihood (ML). Real-world applications to the Biochemists dataset (count data) and the Varieties of Democracy (V-Dem) dataset, a global socio-political dataset (proportion data), validate their utility across scientific and socio-political contexts. These models provide researchers in economics, political science, and social sciences with robust, interpretable tools for analyz- ing zero-inflated (ZI) data with enhanced predictive accuracy. ﺗﻌﺎﻟﺞ ﻫﺬﻩ ﺍﻷﻁﺮﻭﺣﺔ، ﺍﻟﺘﺤﺪﻳﺎﺕ ﺍﻟﻤﻨﻬﺠﻴﺔ ﻓﻲ ﻧﻤﺬﺟﺔ ﺑﻴﺎﻧﺎﺕ ﺍﻟﻌﺪ ﻭﺑﻴﺎﻧﺎﺕ ﺍﻟﻨﺴﺐ ﺍﻟﺘﻲ ﺗﻌﺎﻧﻲ ﻣﻦ ﻣﺸﻜﻠﺔ ﺍﻟﺘﻀﺨﻢ ﺍﻟﺼﻔﺮﻱ، ﻭﻫﻲ ﻣﺸﻜﻠﺔ ﺷﺎﺋﻌﺔ ﻓﻲ ﺍﻟﺒﻴﺎﻧﺎﺕ ﺍﻟﻮﺍﻗﻌﻴﺔ ﺍﻟﺘﻲ ﺗﺘﻤﺜﻞ ﻓﻲ ﻣﺠﺎﻻﺕ ﻣﺜﻞ ﺍﻻﻗﺘﺼﺎﺩ، ﺍﻟﻌﻠﻮﻡ ﺍﻟﺴﻴﺎﺳﻴﺔ، ﻋﻠﻢ ﺍﻷﻭﺑﺌﺔ، ﻭﺍﻟﻌﻠﻮﻡ ﺍﻻﺟﺘﻤﺎﻋﻴﺔ. ﻏﺎﻟﺒًﺎ ﻣﺎ ﺗﻔﺸﻞ ﻧﻤﺎﺫﺝ ﺍﻟﻤﻌﻠﻤﻴﺔ ﺍﻟﺘﻘﻠﻴﺪﻳﺔ، ﻣﺜﻞ ﺍﻧﺤﺪﺍﺭ ﺑﻮﺍﺳﻮﻥ (PO)، ﻭﺍﻧﺤﺪﺍﺭ ﺑﻮﺍﺳﻮﻥ ﻣﺘﻀﺨﻢ ﺍﻷﺻﻔﺎﺭ (ZIP)، ﻭﺍﻧﺤﺪﺍﺭ ﺑﻴﺘﺎ ﻣﺘﻀﺨﻢ ﺍﻷﺻﻔﺎﺭ (ZIBE)، ﻓﻲ ﺍﻟﺘﻘﺎﻁ ﺍﻟﻌﻼﻗﺎﺕ ﻏﻴﺮ ﺍﻟﺨﻄﻴﺔ ﺑﻴﻦ ﺍﻟﻤﺘﻐﻴﺮﺍﺕ ﺍﻟﺘﻔﺴﻴﺮﻳﺔ ﻭﺍﻟﻤﺘﻐﻴﺮﺍﺕ ﺍﻟﺘﺎﺑﻌﺔ، ﻣﻤﺎ ﻳﺆﺩﻱ ﺇﻟﻰ ﺍﻧﺤﻴﺎﺯ ﻓﻲ ﺍﻟﺘﻘﺪﻳﺮﺍﺕ ﻭﺍﻧﺨﻔﺎﺽ ﺍﻟﺪﻗﺔ ﺍﻟﺘﻨﺒﺆﻳﺔ. ﻛﻤﺎ ﺗﻔﺘﻘﺮ ﺍﻟﻨﻤﺎﺫﺝ ﺷﺒﻪ ﺍﻟﻤﻌﻠﻤﻴﺔ ﺍﻟﺤﺎﻟﻴﺔ ﺇﻟﻰ ﺁﻟﻴﺎﺕ ﻣﺪﻣﺠﺔ ﻟﻠﺘﻌﺎﻣﻞ ﻣﻊ ﺍﻟﺘﻀﺨﻢ ﺍﻟﺼﻔﺮﻱ، ﺍ ﺟﺪﻳﺪًﺍ ﻟﻨﻤﺎﺫﺝ ﺧﺎﺻﺔً ﻋﻨﺪ ﺍﻟﺘﻌﺎﻣﻞ ﻣﻊ ﺑﻴﺎﻧﺎﺕ ﺍﻟﻌﺪ ﻭﺍﻟﻨﺴﺐ ﻓﻲ ﺇﻁﺎﺭ ﻣﻮﺣﺪ. ﻟﻤﻌﺎﻟﺠﺔ ﻫﺬﻩ ﺍﻟﻔﺠﻮﺍﺕ، ﺗﺆﺳﺲ ﻫﺬﻩ ﺍﻷﻁﺮﻭﺣﺔ ﺇﻁﺎﺭ Penalized Smoothing) ﻳﻌﺘﻤﺪ ﻋﻠﻰ ﻣﻘﺪﺭﻳﻦ: ﺍﻟﺸﺮﺍﺋﺢ ﺍﻟﺘﻤﻬﻴﺪﻳﺔ ﺍﻟﻤﻌﺎﻗﺒﺔ ،(GSPRMs) ﻌﻤﻤﺔ ﺍﻻﻧﺤﺪﺍﺭ ﺷﺒﻪ ﺍﻟﻤﻌﻠﻤﻴﺔ ﺍﻟﻤ ،GSPRMs ﺍﻟﻤﻌﺎﻗﺒﺔ، ﺍﻟﻠﺬﻳﻦ ﻳﻌﺰﺯﺍﻥ ﺍﻟﻜﻔﺎءﺓ ﺍﻟﺤﺴﺎﺑﻴﺔ ﻭﺍﻟﻤﺮﻭﻧﺔ ﻓﻲ ﺍﻟﻨﻤﺬﺟﺔ. ﺿﻤﻦ ﻧﻤﺎﺫﺝ (B-spline) ﻭﺷﺮﺍﺋﺢ (Splines ُﻁﻮﺭﺕ ﺛﻼﺛﺔ ﻧﻤﺎﺫﺝ ﺟﺪﻳﺪﺓ ﻟﺘﻠﺒﻴﺔ ﺍﺣﺘﻴﺎﺟﺎﺕ ﺗﺤﻠﻴﻞ ﺍﻟﺒﻴﺎﻧﺎﺕ ﺍﻟﻤﻌﻘﺪﺓ:
Applied Statistics and Econometrics الإحصاء التطبيقي والاقتصاد القياسي
Semiparametric Regression Models Parametric Models Generalized Linear Models Count Data Proportion Data P-Splines Smoothing Splines Excess Zeros Problem نماذج العد نماذج شبه معلمية