A comparison of model choice strategies for logistic regression

Purpose:The purpose of this study is to develop and compare model choice strategies in context of logistic regression.Model choice means the choice of the covariates to be included in the model.Design/methodology/approach:The study is based on Monte Carlo simulations.The methods are compared in terms of three measures of accuracy:specificity and two kinds of sensitivity.A loss function combining sensitivity and specificity is introduced and used for a final comparison.Findings:The choice of method depends on how much the users emphasize sensitivity against specificity.It also depends on the sample size.For a typical logistic regression setting with a moderate sample size and a small to moderate effect size,either BIC,BICc or Lasso seems to be optimal.Research limitations:Numerical simulations cannot cover the whole range of data-generating processes occurring with real-world data.Thus,more simulations are needed.Practical implications:Researchers can refer to these results if they believe that their data-generating process is somewhat similar to some of the scenarios presented in this paper.Alternatively,they could run their own simulations and calculate the loss function.Originality/value:This is a systematic comparison of model choice algorithms and heuristics in context of logistic regression.The distinction between two types of sensitivity and a comparison based on a loss function are methodological novelties.

Comparison of isotope-based linear and Bayesian mixing models in determining moisture recycling ratio

Stable water isotopes are natural tracers quantifying the contribution of moisture recycling to local precipitation,i.e.,the moisture recycling ratio,but various isotope-based models usually lead to different results,which affects the accuracy of local moisture recycling.In this study,a total of 18 stations from four typical areas in China were selected to compare the performance of isotope-based linear and Bayesian mixing models and to determine local moisture recycling ratio.Among the three vapor sources including advection,transpiration,and surface evaporation,the advection vapor usually played a dominant role,and the contribution of surface evaporation was less than that of transpiration.When the abnormal values were ignored,the arithmetic averages of differences between isotope-based linear and the Bayesian mixing models were 0.9%for transpiration,0.2%for surface evaporation,and–1.1%for advection,respectively,and the medians were 0.5%,0.2%,and–0.8%,respectively.The importance of transpiration was slightly less for most cases when the Bayesian mixing model was applied,and the contribution of advection was relatively larger.The Bayesian mixing model was found to perform better in determining an efficient solution since linear model sometimes resulted in negative contribution ratios.Sensitivity test with two isotope scenarios indicated that the Bayesian model had a relatively low sensitivity to the changes in isotope input,and it was important to accurately estimate the isotopes in precipitation vapor.Generally,the Bayesian mixing model should be recommended instead of a linear model.The findings are useful for understanding the performance of isotope-based linear and Bayesian mixing models under various climate backgrounds.

Country-based modelling of COVID-19 case fatality rate:A multiple regression analysis

BACKGROUND The spread of the severe acute respiratory syndrome coronavirus 2 outbreak worldwide has caused concern regarding the mortality rate caused by the infection.The determinants of mortality on a global scale cannot be fully understood due to lack of information.AIM To identify key factors that may explain the variability in case lethality across countries.METHODS We identified 21 Potential risk factors for coronavirus disease 2019(COVID-19)case fatality rate for all the countries with available data.We examined univariate relationships of each variable with case fatality rate(CFR),and all independent variables to identify candidate variables for our final multiple model.Multiple regression analysis technique was used to assess the strength of relationship.RESULTS The mean of COVID-19 mortality was 1.52±1.72%.There was a statistically significant inverse correlation between health expenditure,and number of computed tomography scanners per 1 million with CFR,and significant direct correlation was found between literacy,and air pollution with CFR.This final model can predict approximately 97%of the changes in CFR.CONCLUSION The current study recommends some new predictors explaining affect mortality rate.Thus,it could help decision-makers develop health policies to fight COVID-19.

Remaining useful life prediction based on nonlinear random coefficient regression model with fusing failure time data

Remaining useful life(RUL) prediction is one of the most crucial elements in prognostics and health management(PHM). Aiming at the imperfect prior information, this paper proposes an RUL prediction method based on a nonlinear random coefficient regression(RCR) model with fusing failure time data.Firstly, some interesting natures of parameters estimation based on the nonlinear RCR model are given. Based on these natures,the failure time data can be fused as the prior information reasonably. Specifically, the fixed parameters are calculated by the field degradation data of the evaluated equipment and the prior information of random coefficient is estimated with fusing the failure time data of congeneric equipment. Then, the prior information of the random coefficient is updated online under the Bayesian framework, the probability density function(PDF) of the RUL with considering the limitation of the failure threshold is performed. Finally, two case studies are used for experimental verification. Compared with the traditional Bayesian method, the proposed method can effectively reduce the influence of imperfect prior information and improve the accuracy of RUL prediction.

Modeling of Total Dissolved Solids (TDS) and Sodium Absorption Ratio (SAR) in the Edwards-Trinity Plateau and Ogallala Aquifers in the Midland-Odessa Region Using Random Forest Regression and eXtreme Gradient Boosting

Efficient water quality monitoring and ensuring the safety of drinking water by government agencies in areas where the resource is constantly depleted due to anthropogenic or natural factors cannot be overemphasized. The above statement holds for West Texas, Midland, and Odessa Precisely. Two machine learning regression algorithms (Random Forest and XGBoost) were employed to develop models for the prediction of total dissolved solids (TDS) and sodium absorption ratio (SAR) for efficient water quality monitoring of two vital aquifers: Edward-Trinity (plateau), and Ogallala aquifers. These two aquifers have contributed immensely to providing water for different uses ranging from domestic, agricultural, industrial, etc. The data was obtained from the Texas Water Development Board (TWDB). The XGBoost and Random Forest models used in this study gave an accurate prediction of observed data (TDS and SAR) for both the Edward-Trinity (plateau) and Ogallala aquifers with the R2 values consistently greater than 0.83. The Random Forest model gave a better prediction of TDS and SAR concentration with an average R, MAE, RMSE and MSE of 0.977, 0.015, 0.029 and 0.00, respectively. For the XGBoost, an average R, MAE, RMSE, and MSE of 0.953, 0.016, 0.037 and 0.00, respectively, were achieved. The overall performance of the models produced was impressive. From this study, we can clearly understand that Random Forest and XGBoost are appropriate for water quality prediction and monitoring in an area of high hydrocarbon activities like Midland and Odessa and West Texas at large.

A Hybrid Model Evaluation Based on PCA Regression Schemes Applied to Seasonal Precipitation Forecast

Possible changes in the structure and seasonal variability of the subtropical ridge may lead to changes in the rainfall’s variability modes over Caribbean region. This generates additional difficulties around water resource planning, therefore, obtaining seasonal prediction models that allow these variations to be characterized in detail, it’s a concern, specially for island states. This research proposes the construction of statistical-dynamic models based on PCA regression methods. It is used as predictand the monthly precipitation accumulated, while the predictors (6) are extracted from the ECMWF-SEAS5 ensemble mean forecasts with a lag of one month with respect to the target month. In the construction of the models, two sequential training schemes are evaluated, obtaining that only the shorter preserves the seasonal characteristics of the predictand. The evaluation metrics used, where cell-point and dichotomous methodologies are combined, suggest that the predictors related to sea surface temperatures do not adequately represent the seasonal variability of the predictand, however, others such as the temperature at 850 hPa and the Outgoing Longwave Radiation are represented with a good approximation regardless of the model chosen. In this sense, the models built with the nearest neighbor methodology were the most efficient. Using the individual models with the best results, an ensemble is built that allows improving the individual skill of the models selected as members by correcting the underestimation of precipitation in the dynamic model during the wet season, although problems of overestimation persist for thresholds lower than 50 mm.

Utilization of Logistical Regression to the Modified Sine-Gordon Model in the MST Experiment

In this paper, a logistical regression statistical analysis (LR) is presented for a set of variables used in experimental measurements in reversed field pinch (RFP) machines, commonly known as “slinky mode” (SM), observed to travel around the torus in Madison Symmetric Torus (MST). The LR analysis is used to utilize the modified Sine-Gordon dynamic equation model to predict with high confidence whether the slinky mode will lock or not lock when compared to the experimentally measured motion of the slinky mode. It is observed that under certain conditions, the slinky mode “locks” at or near the intersection of poloidal and/or toroidal gaps in MST. However, locked mode cease to travel around the torus;while unlocked mode keeps traveling without a change in the energy, making it hard to determine an exact set of conditions to predict locking/unlocking behaviour. The significant key model parameters determined by LR analysis are shown to improve the Sine-Gordon model’s ability to determine the locking/unlocking of magnetohydrodyamic (MHD) modes. The LR analysis of measured variables provides high confidence in anticipating locking versus unlocking of slinky mode proven by relational comparisons between simulations and the experimentally measured motion of the slinky mode in MST.

Integrating Multiple Linear Regression and Infectious Disease Models for Predicting Information Dissemination in Social Networks

Social network is the mainstream medium of current information dissemination,and it is particularly important to accurately predict its propagation law.In this paper,we introduce a social network propagation model integrating multiple linear regression and infectious disease model.Firstly,we proposed the features that affect social network communication from three dimensions.Then,we predicted the node influence via multiple linear regression.Lastly,we used the node influence as the state transition of the infectious disease model to predict the trend of information dissemination in social networks.The experimental results on a real social network dataset showed that the prediction results of the model are consistent with the actual information dissemination trends.

Smoothed Empirical Likelihood Inference for Nonlinear Quantile Regression Models with Missing Response

In this paper, three smoothed empirical log-likelihood ratio functions for the parameters of nonlinear models with missing response are suggested. Under some regular conditions, the corresponding Wilks phenomena are obtained and the confidence regions for the parameter can be constructed easily.

Selection of the Linear Regression Model According to the Parameter Estimation

In this paper, based on the theory of parameter estimation, we give a selection method and, in a sense of a good character of the parameter estimation, we think that it is very reasonable. Moreover, we offer a calculation method of selection statistic and an applied example.

COVID‑19 and tourism sector stock price in Spain:medium‑term relationship through dynamic regression models

The global pandemic,coronavirus disease 2019(COVID-19),has significantly affected tourism,especially in Spain,as it was among the first countries to be affected by the pandemic and is among the world’s biggest tourist destinations.Stock market values are responding to the evolution of the pandemic,especially in the case of tourist companies.Therefore,being able to quantify this relationship allows us to predict the effect of the pandemic on shares in the tourism sector,thereby improving the response to the crisis by policymakers and investors.Accordingly,a dynamic regression model was developed to predict the behavior of shares in the Spanish tourism sector according to the evolution of the COVID-19 pandemic in the medium term.It has been confirmed that both the number of deaths and cases are good predictors of abnormal stock prices in the tourism sector.

Nonlinear free vibration of piezoelectric semiconductor doubly-curved shells based on nonlinear drift-diffusion model

In this paper, the nonlinear free vibration behaviors of the piezoelectric semiconductor(PS) doubly-curved shell resting on the Pasternak foundation are studied within the framework of the nonlinear drift-diffusion(NLDD) model and the first-order shear deformation theory. The nonlinear constitutive relations are presented, and the strain energy, kinetic energy, and virtual work of the PS doubly-curved shell are derived.Based on Hamilton's principle as well as the condition of charge continuity, the nonlinear governing equations are achieved, and then these equations are solved by means of an efficient iteration method. Several numerical examples are given to show the effect of the nonlinear drift current, elastic foundation parameters as well as geometric parameters on the nonlinear vibration frequency, and the damping characteristic of the PS doublycurved shell. The main innovations of the manuscript are that the difference between the linearized drift-diffusion(LDD) model and the NLDD model is revealed, and an effective method is proposed to select a proper initial electron concentration for the LDD model.

Combined model based on optimized multi-variable grey model and multiple linear regression

The construction method of background value is improved in the original multi-variable grey model （MGM（1,m）） from its source of construction errors. The MGM（1,m） with optimized background value is used to eliminate the random fluctuations or errors of the observational data of all variables, and the combined prediction model together with the multiple linear regression is established in order to improve the simulation and prediction accuracy of the combined model. Finally, a combined model of the MGM（1,2） with optimized background value and the binary linear regression is constructed by an example. The results show that the model has good effects for simulation and prediction.

EMPIRICAL BAYES ESTIMATION FOR ESTIMABLE FUNCTION OF REGRESSION COEFFICIENT IN A MULTIPLE LINEAR REGRESSION MODEL

In this paper we consider the empirical Bayes (EB) estimation problem for estimable function of regression coefficient in a multiple linear regression model Y=Xβ+e. where e with given β has a multivariate standard normal distribution. We get the EB estimators by using kernel estimation of multivariate density function and its first order partial derivatives. It is shown that the convergence rates of the EB estimators are under the condition where an integer k > 1 . is an arbitrary small number and m is the dimension of the vector Y.

ON CONFIDENCE REGIONS OF SEMIPARAMETRIC NONLINEAR REGRESSION MODELS(A GEOMETRIC APPROACH)

A geometric framework is proposed for semiparametric nonlinear regression models based on the concept of least favorable curve, introduced by Severini and Wong (1992). The authors use this framework to drive three kinds of improved approximate confidence regions for the parameter and parameter subset in terms of curvatures. The results obtained by Hamilton et al. (1982), Hamilton (1986) and Wei (1994) are extended to semiparametric nonlinear regression models.

A LARGE SAMPLE ESTIMATE IN MEDIAN LINEAR REGRESSION MODEL Ⅰ: NONTRUNCATED CASE

This paper uses a grouping-adjusting procedure to the data from a median linear regression model, and estimtes the regression coefficients by the method of weighted least squares. This method simplifies computation and in the meantime, preserves the same asymptotic normal distribution for the estimator, as in the ordinary minimum L_1-norm estimates.

Quantum Fuzzy Regression Model for Uncertain Environment

In the era of big data,traditional regression models cannot deal with uncertain big data efficiently and accurately.In order to make up for this deficiency,this paper proposes a quantum fuzzy regression model,which uses fuzzy theory to describe the uncertainty in big data sets and uses quantum computing to exponentially improve the efficiency of data set preprocessing and parameter estimation.In this paper,data envelopment analysis(DEA)is used to calculate the degree of importance of each data point.Meanwhile,Harrow,Hassidim and Lloyd(HHL)algorithm and quantum swap circuits are used to improve the efficiency of high-dimensional data matrix calculation.The application of the quantum fuzzy regression model to smallscale financial data proves that its accuracy is greatly improved compared with the quantum regression model.Moreover,due to the introduction of quantum computing,the speed of dealing with high-dimensional data matrix has an exponential improvement compared with the fuzzy regression model.The quantum fuzzy regression model proposed in this paper combines the advantages of fuzzy theory and quantum computing which can efficiently calculate high-dimensional data matrix and complete parameter estimation using quantum computing while retaining the uncertainty in big data.Thus,it is a new model for efficient and accurate big data processing in uncertain environments.

Federated Learning Model for Auto Insurance Rate Setting Based on Tweedie Distribution

In the assessment of car insurance claims,the claim rate for car insurance presents a highly skewed probability distribution,which is typically modeled using Tweedie distribution.The traditional approach to obtaining the Tweedie regression model involves training on a centralized dataset,when the data is provided by multiple parties,training a privacy-preserving Tweedie regression model without exchanging raw data becomes a challenge.To address this issue,this study introduces a novel vertical federated learning-based Tweedie regression algorithm for multi-party auto insurance rate setting in data silos.The algorithm can keep sensitive data locally and uses privacy-preserving techniques to achieve intersection operations between the two parties holding the data.After determining which entities are shared,the participants train the model locally using the shared entity data to obtain the local generalized linear model intermediate parameters.The homomorphic encryption algorithms are introduced to interact with and update the model intermediate parameters to collaboratively complete the joint training of the car insurance rate-setting model.Performance tests on two publicly available datasets show that the proposed federated Tweedie regression algorithm can effectively generate Tweedie regression models that leverage the value of data fromboth partieswithout exchanging data.The assessment results of the scheme approach those of the Tweedie regressionmodel learned fromcentralized data,and outperformthe Tweedie regressionmodel learned independently by a single party.

Statistical Analysis of Fuzzy Linear Regression Model Based on Centroid Method

This paper transforms fuzzy number into clear number using the centroid method, thus we can research the traditional linear regression model which is transformed from the fuzzy linear regression model. The model’s input and output are fuzzy numbers, and the regression coefficients are clear numbers. This paper considers the parameter estimation and impact analysis based on data deletion. Through the study of example and comparison with other models, it can be concluded that the model in this paper is applied easily and better.

A fault recognition method based on clustering linear regression

Aiming at the problems of low accuracy,long time consumption,and failure to obtain quantita-tive fault identification results of existing automatic fault identification technic,a fault recognition method based on clustering linear regression is proposed.Firstly,Hough transform is used to detect the line segment of the enhanced image obtained by the coherence cube algorithm.Secondly,the endpoint of the line segment detected by Hough transform is taken as the key point,and the adaptive clustering linear regression algorithm is used to cluster the key points adaptively according to the lin-ear relationship between them.Finally,a fault is generated from each category of key points based on least squares curve fitting method to realize fault identification.To verify the feasibility and pro-gressiveness of the proposed method,it is compared with the traditional method and the latest meth-od on the actual seismic data through experiments,and the effectiveness of the proposed method is verified by the experimental results on the actual seismic data.