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Population growth, urbanization, and land use change have increased disastrous floods. Iran is also among the countries at high risk of floods. The latest examples of flood damage are the devastating floods of the spring of 2019 with significant mortality and financial losses in more than ten provinces of the country. The purpose of this study is to prepare an urban flood risk map of District 4 City Shiraz. The vulnerability of the region was made using PROMETHEE Ⅱ and COPRAS multi-criteria decision-making models and urban flood hazard zones were prepared by partial least squares regression (PLSR) and ridge regression (RR) models and a risk map was obtained by multiplying the vulnerability and hazard in ArcGIS software. The highest percentage of the study area in the PROMETHEE Ⅱ and COPRAS models belongs to the moderate class of vulnerability. The evaluation of the vulnerability models using Boolean logic and RMSE and MAPE statistics, showed that the COPRAS model provided better results than the PROMETHEE model. The results of partial least square regression (PLSR) and ridge regression (RR) models in flood risk modeling were analyzed by the Taylor diagram, which showed the superiority of the ridge regression (RR) model and the accuracy of this model in preparing urban flood hazard maps. The risk map of the study area indicated that 34% of the area (973 ha) is in the range of high and very high flood risk.

Introduction Regression analysis is a common method for modeling relationships between variables. Usually Ordinary Least Squares method is applied to estimate regression model parameters. These estimators are unbiased and appropriate when design matrix is nonsingular. In presence of multicollinearity, design matrix is singular and Ordinary Least Squares estimates cannot be obtained. In this situation, other methods‎, ‎such as Lasso‎, ‎Ridge‎ and ‎Lars may be considered. Other hand, in many fields such as medicine, number of variables is greater than the number of observations‎ and usual methods such as Ordinary Least Squares are not proper and shrinkage methods‎, ‎such as Lasso‎, ‎Ridge‎ ‎and‎ ... ‎have a better performance to estimate regression model coefficients‎. ‎In the shrinkage methods‎, ‎tuning parameter plays an essential role in selecting variables and estimating parameters‎. ‎Bridge shrinkage estimators is an estimator that can be obtained by changing its tuning parameter‎. In other words, Bridge method is the extension of Ridge and Lasso regression methods. Selecting the appropriate amount of tuning parameter is important. There are many studies ‎on each of these methods under the assumed conditions. In this paper‎, performance of Bridge shrinkage estimators‎, ‎such as Lasso and Ridge‎ ‎are compared with Lars and Ordinary Least Squares estimators in a simulation study. Material and Methods A simulation study is applied to compare performance of the regression methods Ridge, Lasso, Lars and Ordinary Least Squares. MSE criterion is applied to evaluate the method performance. Statistical software R is applied for simulation and comparing the regression methods. Results and discussion In the presence of collinearity, Bridge regression estimators will result in appropriate estimators. These estimators are biased but their performance is better than unbiased estimators such as Ordinary Least Squares. Indeed, Bridge estimators have the best performance in the class of biased estimators. Conclusion In this article, Ridge and Lasso estimators as special cases of Bridge estimators are compared with Lasso and Ordinary Least Squares in a simulation study. This study shows that under the supposed conditions, Ridge, Lasso and Lars have better action than Ordinary Least Squares method. Lars method has the best performance and Ridge estimators is better than Lasso Regression.

Population growth, urbanization, and land use change have increased disastrous floods. Iran is also among the countries at high risk of floods. The latest examples of flood damage are the devastating floods of the spring of 2019 with significant mortality and financial losses in more than ten provinces of the country. The purpose of this study is to prepare an urban flood risk map of District 4 City Shiraz. The vulnerability of the region was made using PROMETHEE and COPRAS multi-criteria decision-making models and urban flood hazard zones were prepared by partial least squares regression (PLSR) and ridge regression (RR) models and a risk map was obtained by multiplying the vulnerability and hazard in ArcGIS software. The highest percentage of the study area in the PROMETHEE and COPRAS models belongs to the moderate class of vulnerability. The evaluation of the vulnerability models using Boolean logic and RMSE and MAPE statistics, showed that the COPRAS model provided better results than the PROMETHEE model. The results of partial least square regression (PLSR) and ridge regression (RR) models in flood risk modeling were analyzed by the Taylor diagram, which showed the superiority of the ridge regression (RR) model and the accuracy of this model in preparing urban flood hazard maps. The risk map of the study area indicated that 34% of the area (973 ha) is in the range of high and very high flood ri [ABSTRACT FROM AUTHOR]

The purpose of this research was to introduce the alternative model of regression algorithms and having it compared to linear regression. To do this, we need to use modern algorithms such as Ridge, Lasso, and Elastic net regression in which precision is maximized by regularizing the cost function. In this paper theoretical basis and practical implications have been explained.. The target population was patients diagnosed with Post Traumatic Stress Disorder (PTSD) in 2020 for the comparison. 97 PTSD patients (73 females and 24 males) in Tehran were measured in 8 variables related with the intensity of the trauma re-experience. The linear regression, Ridge, Lasso, and Elastic Regressions were used with R software. The results indicated that compared to linear regression, Elastic. LASSO and Ridge explained more variances and had more R square and less MSE respectively. When the main assumptions of Linear regression are not met, using shrinkage regressions seems to be reasonable and accurate.

The purpose of this study was to analyze the temporal variations of dust phenomenon and its relationship with the climatic elements in Yazd city, located near one of the critical centers of dust production in the center of Iran. For this purpose, the Dust Storm Index was first calculated. After the standardization of precipitation, temperature, maximum wind speed, average wind speed, relative humidity and, dust storm index, the co-linearity effect between variables was calculated by using inflation variance factor. Then, several regression models were prepared based on the optimal Ridge parameter. The performance of the models was evaluated based on the determination coefficient, F value and Root Mean Square Error. Finally, by using the most accurate model, the impact of climate parameters on the dust events changes was determined. The results showed that the incidence of dust events in the spring was more than the rest of the year. Based on the optimal model (Model 12), it was found that the main factor influencing the dust storm index variations in different seasons was the surface winds speed. It was also shown that 39%, 25%, 46% and 31% of dust storm index changes in winter, spring, summer, and autumn were due to the interaction of the five climatic parameters studied in this study.

The purpose of this study was to analyze the temporal variations of dust phenomenon and its relationship with the climatic elements in Yazd city, located near one of the critical centers of dust production in the center of Iran. For this purpose, the Dust Storm Index was first calculated. After the standardization of precipitation, temperature, maximum wind speed, average wind speed, relative humidity and, dust storm index, the co-linearity effect between variables was calculated by using inflation variance factor. Then, several regression models were prepared based on the optimal Ridge parameter. The performance of the models was evaluated based on the determination coefficient, F value and Root Mean Square Error. Finally, by using the most accurate model, the impact of climate parameters on the dust events changes was determined. The results showed that the incidence of dust events in the spring was more than the rest of the year. Based on the optimal model (Model 12), it was found that the main factor influencing the dust storm index variations in different seasons was the surface winds speed. It was also shown that 39%, 25%, 46% and 31% of dust storm index changes in winter, spring, summer, and autumn were due to the interaction of the five climatic parameters studied in this study. [ABSTRACT FROM AUTHOR]

Abstract Evapotranspiration is one of the most important parameters in the Planning and operation of reservoirs, designing of irrigation systems. The practical importance of accurate estimates of evaporation and the complexity of effect phenomenon, shows the use of new methods of data mining. In this study, the simulation of pan evaporation in Tabriz station using multiple regression models were investigated. Meteorological data, including maximum and minimum air temperature, dew point, maximum and minimum air relative humidity, number of sunshine hours and Daily wind speed during (1992-2012) were used in synoptic Tabriz stations. Various models of multiple linear regression and nonlinear one were derived for Tabriz station. The selected multiple linear regression model were tested by Ridge Regression method to be considered multi-collinearity among inputs in the model.Variance inflation factor, values for each variable were calculated. The results showed that all Variance inflation factor ,s had the value less than 10. In addition, the ratio for two- variable selected model was 3.34. Therefore, there was no multi-collinearity in the selected multiple linear regression model f (Tmin, n). Durbin-Watson statistic for the selected model was 1.45 that shows the reliability of the selected multiple linear regression model. RMSE and R 2 values of the selected models (multiple linear regression and Non- Linear Regression) was calculated as 2.45 and 0.67 and 2.58 and 0.65, respectively. This results demonstrate the ability of regression techniques to estimate Pan evaporation in Tabriz station.