A comparative study between shrinkage methods (ridge-lasso) using simulation

The general linear model is widely used in many scientific fields, especially biological ones. The Ordinary Least Squares (OLS) estimators for the coefficients of the general linear model are characterized by good specifications symbolized by the acronym BLUE (Best Linear Unbiased Estimator), provided that the basic assumptions for building the model under study are met. The failure to achieve one of the basic assumptions or hypotheses required to build the model can lead to the emergence of estimators with low bias and high variance, which results in poor performance in both prediction and explanation of the model in question. The hypothesis that there are no multiple linear relationships between the explanatory variables is considered one of the leading hypotheses on which the model is based. Thus, the emergence of this problem leads to misleading results and high (Wide) confidence limits for the estimators associated with those variables due to problems characterizing the model. Shrinkage methods are considered one of the most effective and preferable ways to eliminate the multicollinearity problem. These methods are based on addressing the multicollinearity problems by reducing the variance of estimators in the model. Ridge and Lasso methods represent the most and most common of these methods of shrinkage. The simulation was carried out for different sample sizes (40, 120, 200) and some variables (P=30, 60) in the first and second experiments arbitrarily and at the level of low, medium, and high correlation coefficients (0.2, 0.5, 0.8). When (p=30, 60) Lasso method has the smallest (MSE) than the Ridge method. The Lasso method proved its efficiency by obtaining the least MSE. Optimal Penalty parameter (λ) chosen from Cross-Validation through minimizing (MSE) of prediction. We see a rapid increase for (MSE) for both (Ridge-Lasso) where the top axis indicates the number of model variables, and when the correlation between variables increases and sample size too, we can see the (MSE) values increase in the Ridge method than the Lasso method. A ridge method gives greater efficiency when the sample size is more significant than variables (

A new shrinkage method for higher dimensions regression model to remedy of multicollinearity problem

This research seeks to present new method of shrinking variables to select some basic variables from large data sets. This new shrinkage estimator is a modification of (Ridge and Adaptive Lasso) shrinkage regression method in the presence of the mixing parameter that was calculated in the Elastic-Net. The Proposed estimator is called (Improved Mixed Shrinkage Estimator (IMSHE)) to handle the problem of multicollinearity. In practice, it is difficult to achieve the required accuracy and efficiency when dealing with a big data set, especially in the case of multicollinearity problem between the explanatory variables. By using Basic shrinkage methods (Lasso, Adaptive Lasso and Elastic Net) and comparing their results with the New shrinkage method (IMSH) was applied to a set of obesity -related data containing (52) variables for a sample of (112) observations. All shrinkage methods have also been compared for efficiency through Mean Square Error (MSE) criterion and Cross Validation Parameter (CVP). The results showed that the best shrinking parameter among the four methods (Lasso, Adaptive Lasso, Elastic Net and IMSH) was for the IMSH shrinkage method, as it corresponds to the lowest (MSE) based on the cross-validation parameter test (CVP). The new proposed method IMSH achieved the optimal shrinking parameter (λ = 0.6932827) according to the (CVP) test, that leads to have minimum value of mean square error (MSE) equal (0.2576002). The results showed when the value of the regularization parameter increases, the value of the shrinkage parameter decreases to become equal to zero, so the ideal number of variables after shrinkage is (p=6)

Estimation of COVID-19 infections in Iraqi governorates using generalized moments method in spatial autoregressive model

At the end of 2019, a new type of virus that infects the human respiratory system was discovered in China, and it was briefly called COVID-19. In March 2020, the world Health Organization (WHO) declared Corona Virus a global pandemic. The Corona Virus is transmitted through air or through contact. The possibility of infection increases in the area or areas neighboring to the area that witnessed a community spread of the virus or when individuals return from that affected area to their areas of residence. Given the limited studies on the impact of affected neighboring areas or countries, this study focused on using the spatial autoregression model, one of the econometric models. Model parameters have been estimated using the Generalized Moment Method (GMM) which has the ability to correct the Endogeneity that occurs by the spatial regression variable as well as due to the endogenous variables. The results showed that the number of infections (Yn) of Corona epidemic increases as there are infections in the surrounding areas and vice versa. This confirms the impact of spatial neighborhood on the spread of infections among neighboring governorates

Measuring the Impact of Environmental Sustainability on Tuberculosis Rates Using the Two-Stage Least Squares Method in the Polled Model

Iraq has witnessed several changes that directly and negatively affected the nature of society and the environment, such as an increase in the population over the past two decades. Hence, an increase in demand for food, energy, housing, and water means an increase in solid and liquid waste as a result of weak environmental awareness. Tuberculosis is one of the infectious diseases, and Iraq is witnessing a noticeable increase in the rate of infections at the governorates level. The explanatory variables that were chosen are among the variables of the sustainable environment adopted by the Ministry of health in Iraq. Therefore, it was essential to know their effect on the phenomenon under study (number of tuberculosis cases). The results of estimating the model parameters using the two-stage least squares method and the transformations method show that the explanatory variables significantly affect the dependent variable, as explained above. This study focused on the effect of some sustainable environment variables (the population, the number of health institutions, the proportion of the population that uses clean drinking water, and the percentage of the population with access to sanitation) on tuberculosis rates based on the polled model at the governorates level for the period (2013–2017). The two-stage least squares method was used to estimate model parameters. The results showed that increasing environmental awareness represented by sustainable environment variables positively impacts lower rates of tuberculosis at the governorates level