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:

• ﻧﻤﺎﺫﺝ ﺍﻧﺤﺪﺍﺭ ﺑﻮﺍﺳﻮﻥ ﺷﺒﻪ ﺍﻟﻤﻌﻠﻤﻲ ﺍﻟﺠﺰﺋﻲ ﺍﻟﻤﻌﻤﻢ (SPPO): ﻳﺴﺘﺨﺪﻡ ﻫﺬﺍ ﺍﻟﻨﻤﻮﺫﺝ ﻛﻼً ﻣﻦ ﺷﺮﺍﺋﺢ Pb ﻭ Ps ﻻﻟﺘﻘﺎﻁ
ﺎ ﻗﻮﻳًﺎ ﻭﻗﺎﺑﻼً ﻟﻠﺘﻔﺴﻴﺮ

ً

ﺍﻟﻌﻼﻗﺎﺕ ﻏﻴﺮ ﺍﻟﻤﻌﻠﻤﻴﺔ ﺑﻤﺮﻭﻧﺔ ﺑﻴﻦ ﺍﻟﻤﺘﻐﻴﺮﺍﺕ ﺍﻟﻤﺸﺘﺮﻛﺔ ﻭﺍﻻﺳﺘﺠﺎﺑﺔ ﺍﻟﻌﺪﺩﻳﺔ. ﻳﻮﻓﺮ SPPO ﻧﻬﺠ

.
ٍﻟﻠﺤﺎﻻﺕ ﺍﻟﺘﻲ ﻗﺪ ﻻ ﺗﺘﻤﻜﻦ ﻓﻴﻬﺎ ﺍﻟﻨﻤﺎﺫﺝ ﺍﻟﺨﻄﻴﺔ ﺍﻟﺘﻘﻠﻴﺪﻳﺔ ﻣﻦ ﺍﻟﺘﻘﺎﻁ ﻋﻤﻠﻴﺔ ﺗﻮﻟﻴﺪ ﺍﻟﺒﻴﺎﻧﺎﺕ ﺍﻟﻌﺪﺩﻳﺔ ﺍﻷﺳﺎﺳﻴﺔ ﺑﺸﻜﻞ ﻛﺎﻑ
SPPO ﻊ ﻫﺬﺍ ﺍﻟﻨﻤﻮﺫﺝ ﺇﻁﺎﺭ
ِّ• ﻧﻤﻮﺫﺝ ﺍﻧﺤﺪﺍﺭ ﺑﻮﺍﺳﻮﻥ ﺷﺒﻪ ﺍﻟﻤﻌﻠﻤﻲ ﺍﻟﺠﺰﺋﻲ ﺍﻟﻤﻌﻤﻢ ﻣﺘﻀﺨﻢ ﺍﻷﺻﻔﺎﺭ (SPZIP): ﻳُﻮﺳ
SPZIP ﻳﺘﻀﻤﻦ .Ps ﻭ Pb ﻟﻤﻌﺎﻟﺠﺔ ﺑﻴﺎﻧﺎﺕ ﺍﻟﻌﺪ ﺍﻟﺘﻲ ﺗﻌﺎﻧﻲ ﻣﻦ ﻣﺸﻜﻠﺔ ﺍﻟﺘﻀﺨﻢ ﺍﻟﺼﻔﺮﻱ، ﺑﺎﺳﺘﺨﺪﺍﻡ ﻛﻞ ﻣﻦ ﺷﺮﺍﺋﺢ
ﻣﻜﻮﻥ ﺗﻀﺨﻢ ﺻﻔﺮﻱ، ﻳﺘﻢ ﻧﻤﺬﺟﺘﻪ ﺑﺎﺳﺘﺨﺪﺍﻡ ﺩﺍﻟﺔ ﺍﻟﺮﺑﻂ (logit)، ﻟﺤﺴﺎﺏ ﻛﻞ ﻣﻦ ﺍﻷﺻﻔﺎﺭ ﺍﻟﻬﻴﻜﻠﻴﺔ ﻭﺍﻟﻌﺸﻮﺍﺋﻴﺔ. ﻳﻮﻓﺮ ﻫﺬﺍ
ﺃﻛﺜﺮ ﺩﻗﺔ ﻭﻭﺍﻗﻌﻴﺔ ﻟﻠﺒﻴﺎﻧﺎﺕ ﺫﺍﺕ ﺍﻷﺻﻔﺎﺭ ﺍﻟﺰﺍﺋﺪﺓ.
ًﺍﻟﻨﻬﺞ ﺗﻤﺜﻴﻼ
ﺎ ﻟﺘﺤﻠﻴﻞ
ً• ﻧﻤﻮﺫﺝ ﺍﻧﺤﺪﺍﺭ ﺑﻴﺘﺎ ﺷﺒﻪ ﺍﻟﻤﻌﻠﻤﻲ ﺍﻟﺠﺰﺋﻲ ﺍﻟﻤﻌﻤﻢ ﻣﺘﻀﺨﻢ ﺍﻷﺻﻔﺎﺭ (SPZIBE): ُﺻِّﻤﻢ ﻫﺬﺍ ﺍﻟﻨﻤﻮﺫﺝ ﺧﺼﻴﺼ
SPZIBE ﺷﺎﺋﻊ ﻓﻲ ﻣﺨﺘﻠﻒ ﺍﻟﻤﺠﺎﻻﺕ. ﻳﺴﺘﺨﺪﻡ
ﺍﻟﺒﻴﺎﻧﺎﺕ ﺍﻟﻨﺴﺒﻴﺔ ﺍﻟﺘﻲ ﺗﻌﺎﻧﻲ ﻣﻦ ﻣﺸﻜﻠﺔ ﺍﻟﺘﻀﺨﻢ ﺍﻟﺼﻔﺮﻱ، ﻭﻫﻮ ﺗﺤﺪ
ﻛﻼً ﻣﻦ ﺷﺮﺍﺋﺢ Pb ﻭ Ps ﻻﻟﺘﻘﺎﻁ ﺍﻟﻌﻼﻗﺎﺕ ﺍﻟﻤﻌﻘﺪﺓ ﺑﻴﻦ ﺍﻟﻤﺘﻐﻴﺮﺍﺕ ﺍﻟﻤﺸﺘﺮﻛﺔ ﻭﺍﻟﻤﺘﻐﻴﺮ ﺍﻟﺘﺎﺑﻊ. ﻳﺘﻢ ﺗﻄﻮﻳﺮ ﻧﺴﺨﺘﻴﻦ:
SPZIBE-Pb ﻭ SPZIBE-Ps، ﻣﻤﺎ ﻳﺴﻤﺢ ﺑﺘﻘﻴﻴﻢ ﻣﻘﺎﺭﻥ ﻷﺩﺍء ﻣﻨﺎﻫﺞ ﺍﻟﺸﺮﺍﺋﺢ ﺍﻟﻤﺨﺘﻠﻔﺔ.

Issues also as CD.

Text in English and abstract in Arabic & English.