In order to investigate a series of data scenarios and determine the model governing the changes of a random variable over time‎, ‎according to the variables affecting it‎, ‎efficient methods have been developed in recent decades‎. ‎One of these methods is the generalized additive model‎. ‎By this modeling for data‎, ‎it is possible to check the behavior of the non-linear data and even predict the future‎. ‎In this article‎, ‎we intend to express this method non-parametrically‎, ‎in cases such as when the variable is independent‎, ‎time series‎, ‎or has a lag and implement the estimation of model parameters‎. ‎Moreover‎, ‎we will demonstrate the power and effectiveness of this method by presenting some examples.

Flood control and management is a fundamental issue for hydrology researchers and managers. Regarding the design and construction of different hydraulic structures such as reservoirs and dams, as effective techniques for flood control, accurate estimation of the magnitude and return periods of flood is required for appropriate estimation of the dimension and resilience of structures. Design flood estimation is done through frequency analysis with the key stationary assumption. Nowadays, factors such as land use change, inappropriate management and climate change has influenced stationary conditions of flood peaks. Therefore, in the presence of nonstationary conditions, the estimation based on stationary assumption is not confident and may lead to large errors. In this study for non-stationary flood frequency analysis, the GAMLESS model for location, scale and shape parameter estimation are introduced while visual inspection of nonstationary are as well presented and developed for quantile estimation. Six hydrometery stations in different provinces in the north of Iran were selected. Frequency analysis in stationary and non-stationary conditions was performed for each station. Results indicated that location and scale parameters have linear and quadratic trend. In addition, in Nodekhormalo station the design flood estimated by nonstationary assumption was around 3 times higher than of that obtained for the stationary conditions. Results also demonstrated that in stations with increasing non-stationary trend, return period of large floods was decreasing and for the same return periods, flood quantiles has increased.

In this paper, the focus is on additive models with interval data. An additive model can be converted to a multi-objective linear problem if information about preferences of the consumption of inputs and the production of outputs are taken into account. Here in this study, data are not exact and are of interval kind. Moreover, the most preferred solutions with available information by interval additive models are sought. It has also been shown that if additional information is available, an axial solution can be applied.Also, the most preferred target settings will be computed too. In this study twenty bank branches in Iran are evaluated, and target settings and efficiency are compared with the original case and significant decisions are made.

Extended Abstract Background: Deforestation poses a serious threat to ecosystems by reducing biodiversity, disrupting hydrological cycles, and exacerbating climate change. In addition to undermining natural resources, it adversely impacts local economies and ecotourism. The Hyrcanian forests, among the most valuable temperate biomes, harbor numerous endemic species. However, anthropogenic pressures, such as urban expansion, unsustainable agriculture, and unregulated exploitation, have led to severe degradation of these forests. The Peymot Forest region in Noor County, Mazandaran Province, is no exception and is currently facing a significant decline in forest cover. Methods: In total, 107 deforested plots were recorded to identify key drivers and spatial patterns of deforestation in the study area. Deforested sites were coded as “1” and non-deforested sites as “0.” In this research, deforestation is defined as the permanent or long-term conversion of forested areas into non-forested land due to anthropogenic activities or natural disturbances, where forest recovery within a reasonable timeframe is improbable. Fourteen environmental and anthropogenic predictor variables—including slope aspect, slope gradient, elevation, landform shape, profile curvature, slope length, wind exposure, minimum temperature, mean temperature, maximum temperature, precipitation, distance to roads, distance to settlements, and proximity to agricultural land—were extracted from multiple sources and integrated into two statistical modeling frameworks: Generalized Linear Model (GLM) and Generalized Additive Model (GAM). GLM, an extension of classical linear regression adapted for binary outcomes, and GAM, an advanced nonparametric extension of GLM that effectively captures nonlinear relationships, were employed for spatial modeling. The GLM framework began with variable selection based on ecological knowledge and multicollinearity analysis, followed by stepwise model refinement using likelihood ratio tests to eliminate non-significant predictors. Appropriate smoothing functions were selected in the GAM approach, and optimal degrees of freedom were determined for each smoother. Model performance was enhanced through the estimation of smoothing parameters and significance testing for each smooth term. Model validation was conducted using the Akaike Information Criterion (AIC) and the Area Under the Curve (AUC) of the Receiver Operating Characteristic. Deforestation risk maps were generated for both models independently, and final susceptibility maps were classified into four risk categories (low, moderate, high, and very high) using natural breaks. Results: Results from the GLM indicated that elevation, wind exposure, distance to roads, distance to settlements, and mean temperature were statistically significant predictors of deforestation. The final model achieved a notable reduction in deviance (from 207.94 to 81.68) and an AIC value of 93.68, reflecting strong model fit and predictive capacity. According to the GAM results, the most influential factors included elevation, wind exposure, distance to roads, distance to settlements, and proximity to agricultural land,with human-related variables showing the highest contribution to deforestation probability. Specifically, increased distances from settlements (25.6%), agricultural land (22.1%), and roads (18.3%) were associated with decreased deforestation likelihood. The GAM outperformed the GLM, achieving an AIC of 21.07 and an AUC of 0.947. Final susceptibility maps from both models revealed that a substantial portion of the study area would fall within the "very high" risk category, indicating critical vulnerability in the near future. Conclusion: The findings underscore the applicability of deforestation risk modeling using GLM and GAM in supporting sustainable forest management. The outputs can serve as a decision-support tool for regional planning and targeted resource allocation. Moreover, advanced modeling frameworks, such as GAM, allow for more accurate estimation of nonlinear and complex interactions among predictors. The resulting deforestation zoning maps offer a scientific foundation for implementing proactive strategies, including legal restrictions in high-risk areas, community-based awareness programs, and the promotion of sustainable land-use practices. Integration of local data with robust global models enhances predictive performance and improves the effectiveness of policy interventions. Ultimately, this study not only contributes practical and theoretical insights into deforestation dynamics but also provides a transferable methodology for application in other ecologically sensitive regions.

Background: Survival rates for breast cancer (BC) are often based on the outcomes of this disease. The aim of this study was to compare the performance of three survival models, namely Cox regression, Aalen’ s, and Lin and Ying’ s additive hazards (AH) models for identifying the prognostic factors regarding the survival time of BC patients. Materials and Methods: This study was a historical cohort study which used 1025 females’ medical records that underwent modified radical mastectomy or breast saving. These patients were admitted to Besat and Chamran Hospitals, Tehran, Iran, during 2010– 2015 and followed until 2017. The Aalen’ s and Lin and Ying’ s AH models and also traditional Cox model were applied for analysis of time to death of BC patients using R 3. 5. 1 software. Results: In Aalen’ s and also Lin and Ying’ s AH models, age at diagnosis, history of disease, number of lymph nodes, metastasis, hormonal therapy, and evacuation lymph nodes were prognostic factors for the survival of BC patients (P < 0. 05). In addition, in the Lin and Ying’ s AH model tumor size (P = 0. 048) was also identified as a significant factor. According to Aalen’ s plot, metastasis, age at diagnosis, and number of lymph nodes had a time‑ varying effect on survival time. These variables had a different slope as the times go on. Conclusion: AH model may yield new insights in prognostic studies of survival time of patients with BC over time. Because of the positive slope of estimated cumulative regression function in Aalen’ s plot, metastasis, higher age at diagnosis, and high number of lymph nodes are important factors in reducing the survival BC, and then based on these factors, the therapists should consider a special therapeutic protocol for BC patients.

This study aimed to estimate the genetic parameters of body weight traits in Markhoz goats, using B-spline random regression models. The data used in this study included 19549 records collected during 29 years (1992-2021) in Markhoz goat Breeding Research Station, located in Sanandaj, Iran. The model used to analyze data included fixed effects (year of birth, sex, type of birth and age of dam) and random effects including direct additive genetic, maternal additive genetic, permanent environmental and maternal permanent environmental assuming homogeneous and heterogeneous residual variance during the time. Akaike (BIC) and Bayesian (BIC) information criteria were used to compare the models and bspq.4.4.4.4 was selected as the best model. The direct heritability values for birth, 3-month, 6-month, 9-month and 12-month weights were estimated to be 0.14, 0.16, 0.08, 0.28 and 0.26, respectively. Genetic correlation between body weights at birth and 3-month, birth and 6-month, birth and 9-month, birth and 12-month, 3-month and 6-month, 3-month and 9-month, 3-month and 12-month, 6-months and 9-month and 9-month and 12-month were 0.22, 0.38, 0.21, 0.56, -0.26, 0.30, 0.62, 0.86 and 0.77, respectively. The highest phenotypic correlation was between the weight of 9-month and 12-month (0.82) and the lowest correlation was between birth weight and 3-month and 6-month (0.12). The results showed that the 9-month weight is a good criterion for selection in Markhoz goats.

ABSTRACTThe purpose of this research was to compare different statistical methods such as GBLUP, BayesA, BayesB, BayesC, BayesL, Ridge regression, Boosting and SVM for genomic evaluation of traits with additive and dominance genetic architecture. A genome consisting of 5 chromosomes was simulated, with 1000 single nucleotide polymorphism markers (SNP) uniformly distributed on each chromosome. In two different scenarios, 50 and 500 quantitative trait loci (QTL) were considered and in each scenario of QTL number, 0.00, 10, 20, 50 and 100% of QTLs were given dominance genetic effect. The prediction accuracy, bias and reliability of genomic breeding values were used for analyzing the results and comparing the methods. The results showed that not separating the dominance effects from the additive effects lead to a decrease in the accuracy and reliability and an increase in the bias of the predicted genomic breeding values. In all examined scenarios of the QTL number and percentages of QTLs with dominance effect, the Bayesian methods had higher prediction accuracy and reliability and their predictions had the least bias. Boosting predicted the genomic breeding values with the lowest accuracy and reliability and highest bias. The performance of SVM and Ridge regression was better than Boosting, but lower than Bayesian methods and GBLUP. In terms of computing speed, GBLUP and Boosting were, respectively, the fastest and the slowest method. It can be concluded that to increase the efficiency of genomic selection, first, the dominance genetic effects need to be included in the model and, second, methods with the highest predictive performance should be used.