This paper introduces a novel semiparametric Bayesian approach for bivariate meta-Regression. The method extends traditional binomial models to trinomial distributions, accounting for positive, neutral, and negative treatment effects. Using a conditional Dirichlet process, we develop a model to compare treatment and control groups across multiple clinical centers. This approach addresses the challenges posed by confounding factors in such studies. The primary objective is to assess treatment efficacy by modeling response outcomes as trinomial distributions. We employ Gibbs sampling and the Metropolis-Hastings algorithm for posterior computation. These methods generate estimates of treatment effects while incorporating auxiliary variables that may influence outcomes. Simulations across various scenarios demonstrate the model’s effectiveness. We also establish credible intervals to evaluate hypotheses related to treatment effects. Furthermore, we apply the methodology to real-world data on economic activity in Iran from 2009 to 2021. This application highlights the practical utility of our approach in meta-analytic contexts. Our research contributes to the growing body of literature on Bayesian methods in meta-analysis. It provides valuable insights for improving clinical study evaluations.

Statistical significance determines whether the relationship between two or more variables is caused by factors other than chance and randomness. Statistical hypothesis testing is a method by which statistical significance is determined. By introducing fuzzy Regression, several approaches were presented to estimate parameters of such the models. Now, most researches have conducted on the estimation method and little attention has been paid to the properties of estimators,, confidence intervals and significance tests. The main idea here is to investigate the significance of estimated parameters in an applied study with fuzzy-valued real data in the framework of fuzzy Regression modeling using $m$-estimators. For this purpose, by accessing the water and sewage data source of Ahvaz city, the required variables were first introduced. Since $m$-estimators use an algorithm based on reweighted method, we are looking to determine the weight of the users in terms of the consumption pattern, that is, the weight of high consumption users and low consumption users is determined. Now, the company can first identify and classify the consumption patterns of each user based on the determined weights, and then deal with the stepped pricing of each cubic meter of water for each user. This idea requires providing a significant model of fuzzy Regression. Since $m$-estimators of fuzzy Regression model do not have a closed form, bootstrap is used to present the numerical indices of the estimators, confidence intervals and the significance test of the model. By analyzing the results and keeping significant parameters a suitable model was introduced.

Both traditional and fuzzy Regression analyses have demonstrated the significant characteristics of the least-squares methodology as a method for parameter estimation.} The presence of outliers in the sample and/or minor variations in the dataset might impact the behaviour and characteristics of the least-squares estimators (LSE)‎. ‎In contrast‎, ‎robust approaches provide estimators of the parameters that are resilient to the aforementioned unfavourable effects‎. ‎This study aims to expand upon the Theil-Sen estimator in fuzzy Regression analysis‎, ‎with the objective of obtaining consistent findings even when outliers are present‎. ‎\rd{ We demonstrate the effectiveness of the suggested technique through simulation experiments and real-world examples‎, ‎comparing it to commonly used fuzzy Regression models‎. ‎The applicative examples are based on hydrology and atmospheric environment datasets‎. ‎We also show the sensitivity analysis of the estimated parameters using a Monte-Carlo simulation study‎, ‎demonstrating the effectiveness of the suggested estimators in comparison to other established approaches in the field of fuzzy Regression analysis‎. ‎The results showed that the Theil-Sen estimator (TSE) is very effective in cases where there are outliers‎, ‎and the calculation error is smaller compared to other methods.

In many applications we have to encountered with bounded dependent variables. Beta Regression model can be used to deal with these kinds of response variables. In this paper we aim to study spatially correlated responses in the unit interval. Initially we introduce spatial beta generalized linear mixed model in which the spatial correlation is captured through a random effect. Then the performances of the proposed model is evaluated via a simulation study, implementing Bayesian approach for parameter estimation.Finally the application of this model on two real data sets about migration rate and divorce rate in Iran are presented.

Background & Aim: One of the basic assumptions in simple linear Regression models is the statistical independence of observations. Sometimes this assumption is not true for study subject and consequently the use of general Regression models may not be appropriate. In this case, one of the leading methods is the use of multilevel models. The present study utilizes multivariate logistic Regression model using a multilevel model to exhibit the chance of having elbow, wrist and knee disorders over the past year based on elbow, wrist and disorders during the past week. Methods & Materials: This study is a cross-sectional study that was carried out from April 2015 to May 2016 in Mobarakeh Steel Company, Isfahan. The study population includes 300 male employees of Mobarakeh Steel Company, with a mean age of 41. 40± 8. 17 years and an average working experience of 16. 0± 7. 66 years. Data were analyzed using SPSS (version 24) and MLwiN software. Results: Based on this study, results obtained from single variable and multivariable Regression were different. Conclusion: Based on this study, it can be suggested that multivariable Regression cause a better and more accurate deduction compared to single variable method.

Evaluating the cutting rate (CR) of stones is important in the cost estimation and the planning of the stone processing plants. This research used Regression models to estimate the stones’ CR based on their physico-mechanical characteristics. Stone processing factories in Mahallat City (Markazi province, Iran) were visited, and the CR of diamond circular saws was recorded on six different travertine stones. Next, the stone block samples were collected from the quarries for laboratory tests. Stones’ porosity (n), uniaxial compressive strength (UCS), and Schmidt hammer hardness (SH) were determined in the laboratory as their physico-mechanical characteristics. Correlation relationships of CR with physico-mechanical characteristics were evaluated using simple and multiple Regression analyses, and estimator models were developed. Results showed that multiple Regression models are more reliable than simple Regression for estimating the stones’ CR. The validity of the developed multiple Regression models was verified with the published data of one researcher. The findings indicated that these models are accurate enough for estimating the CR of stones. Consequently, the multiple Regression models provide practical advantages for estimating the CR and save time and cost during the planning and design of the stone processing factories.

The Liu estimator has consistently been demonstrated to be an attractive shrinkage method for reducing the e ects of multicollinearity. The Poisson Regression model is a well-known model in applications when the response variable consists of count data. However, it is known that multicollinearity negatively a ects the variance of the maximum likelihood estimator (MLE) of the Poisson Regression coe cients. To address this problem, a Poisson Liu estimator has been proposed by numerous researchers. In this paper, a Jackknifed Liu-type Poisson estimator (JPLTE) is proposed and derived. The idea behind the JPLTE is to decrease the shrinkage parameter and, therefore, improve the resultant estimator by reducing the amount of bias. Our Monte Carlo simulation results suggest that the JPLTE estimator can bring significant improvements relative to other existing estimators. In addition, the results of a real application demonstrate that the JPLTE estimator outperforms both the Poisson Liu estimator and the maximum likelihood estimator in terms of predictive performance.