On some beta ridge regression estimators: method, simulation and application

Performance evaluation of different regression models: application in a breast cancer patient data

This paper provides a comprehensive analysis of linear regression models, focusing on addressing multicollinearity challenges in breast cancer patient data. Linear regression methodologies, including GAM, Beta, GAM Beta, Ridge, and Beta Ridge, are compared using two statistical criteria. The study, conducted with R software, showcases the Beta regression model's exceptional performance, achieving a BIC of - 5520.416. Furthermore, the Ridge regression model demonstrates remarkable results with the best AIC at - 8002.647. The findings underscore the practical application of these models in real-world scenarios and emphasize the Beta regression model's superior ability to handle multicollinearity challenges. The preference for AIC over BIC in Generalized Additive Models (GAMs) is rooted in the AIC's calculation framework, highlighting its effectiveness in capturing the complexity and flexibility inherent in GAMs.

Biased proportional hazard regression estimator in the existence of collinearity

This paper proposed a new biased proportional hazard regression (PHR) estimator which is the combination of elastic net proportional hazard regression (ENPHR) and principal components proportional hazard regression (PCPHR) estimator. Comparison of proposed estimator with ENPHR, PCPHR, ridge PHR, lasso PHR, r - k class PHR and maximum likelihood (ML) estimators is done in terms of scalar mean square error (MSE). Simulation study is conducted to examine the performance of each estimator. Furthermore, the developed estimator is utilized to analyze the infant mortality in Delhi, India.

Effect of geographical factors on reference values of creatine kinase isoenzyme

The aim of this study was to investigate the geographical spatial distribution of creatine kinase isoenzyme (CK-MB) in order to provide a scientific basis for clinical examination. The reference values of CK-MB of 8697 healthy adults in 137 cities in China were collected by reading a large number of literates. Moran index was used to determine the spatial relationship, and 24 factors were selected, which belonged to terrain, climate, and soil indexes. Correlation analysis was conducted between CK-MB and geographical factors to determine significance, and 9 significance factors were extracted. Based on R language to evaluate the degree of multicollinearity of the model, CK-MB Ridge model, Lasso model, and PCA model were established, through calculating the relative error to choose the best model PCA, testing the normality of the predicted values, and choosing the disjunctive kriging interpolation to make the geographical distribution. The results show that CK-MB reference values of healthy adults were generally correlated with latitude, annual sunshine duration, annual mean relative humidity, annual precipitation amount, and annual range of air temperature and significantly correlated with annual mean air temperature, topsoil gravel content, topsoil cation exchange capacity in clay, and topsoil cation exchange capacity in silt. The geospatial distribution map shows that on the whole, it is higher in the north and lower in the south, and gradually increases from the southeast coastal area to the northwest inland area. If the geographical factors are obtained in a location, the CK-MB model can be used to predict the CK-MB of healthy adults in the region, which provides a reference for us to consider regional differences in clinical diagnosis.

Improved shrinkage estimators in the beta regression model with application in econometric and educational data

Although beta regression is a very useful tool to model the continuous bounded outcome variable with some explanatory variables, however, in the presence of multicollinearity, the performance of the maximum likelihood estimates for the estimation of the parameters is poor. In this paper, we propose improved shrinkage estimators via Liu estimator to obtain more efficient estimates. Therefore, we defined linear shrinkage, pretest, shrinkage pretest, Stein and positive part Stein estimators to estimate of the parameters in the beta regression model, when some of them have not a significant effect to predict the outcome variable so that a sub-model may be sufficient. We derived the asymptotic distributional biases, variances, and then we conducted extensive Monte Carlo simulation study to obtain the performance of the proposed estimation strategy. Our results showed a great benefit of the new methodologies for practitioners specifically in the applied sciences. We concluded the paper with two real data analysis from economics and education.

Batch Process Monitoring Based on Quality-Related Time-Batch 2D Evolution Information

This paper proposed a quality-related online monitoring strategy based on time and batch two-dimensional evolution information for batch processes. In the direction of time, considering the difference between each phase and the steady part and the transition part in the same phase, the change trend of the regression coefficient of the PLS model is used to divide each batch into phases, and each phase into parts. The phases, the steady parts, and the transition parts are finally distinguished and dealt with separately in the subsequent modeling process. In the batch direction, considering the slow time-varying characteristics of batch evolution, sliding windows are used to perform mode division by analyzing the evolution trend of the score matrix T in the PLS model on the base of phase division and within-phase part division. Finally, an online monitoring model that comprehensively considers the evolution information of time and batch is obtained. In a typical batch operation process, injection molding is used as an example for experimental analysis. The results show that the proposed algorithm takes advantage of mixing the time-batch two-dimensional evolution information. Compared with the traditional methods, the proposed method can overcome the shortcomings caused by the single dimension analysis and has better monitoring results.

Slow Time-Varying Batch Process Quality Prediction Based on Batch Augmentation Analysis

In this paper, focusing on the slow time-varying characteristics, a series of works have been conducted to implement an accurate quality prediction for batch processes. To deal with the time-varying characteristics along the batch direction, sliding windows can be constructed. Then, the start-up process is identified and the whole process is divided into two modes according to the steady-state identification. In the most important mode, the process data matrix, used to establish the regression model of the current batch, is expanded to involve the process data of previous batches, which is called batch augmentation. Thus, the process data of previous batches, which have an important influence on the quality of the current batch, will be identified and form a new batch augmentation matrix for modeling using the partial least squares (PLS) method. Moreover, considering the multiphase characteristic, batch augmentation analysis and modeling is conducted within each phase. Finally, the proposed method is applied to a typical batch process, the injection molding process. The quality prediction results are compared with those of the traditional quality prediction method based on PLS and the ridge regression method under the proposed batch augmentation analysis framework. The conclusion is obtained that the proposed method based on the batch augmentation analysis is superior.