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.

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.

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.

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.

Composition Analysis and Identification of Ancient Glass Products Based on L1 Regularization Logistic Regression

In view of the composition analysis and identification of ancient glass products, L1 regularization, K-Means cluster analysis, elbow rule and other methods were comprehensively used to build logical regression, cluster analysis, hyper-parameter test and other models, and SPSS, Python and other tools were used to obtain the classification rules of glass products under different fluxes, sub classification under different chemical compositions, hyper-parameter K value test and rationality analysis. Research can provide theoretical support for the protection and restoration of ancient glass relics.

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.

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.

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.

Modeling Cyber Loss Severity Using a Spliced Regression Distribution with Mixture Components

Cyber losses in terms of number of records breached under cyber incidents commonly feature a significant portion of zeros, specific characteristics of mid-range losses and large losses, which make it hard to model the whole range of the losses using a standard loss distribution. We tackle this modeling problem by proposing a three-component spliced regression model that can simultaneously model zeros, moderate and large losses and consider heterogeneous effects in mixture components. To apply our proposed model to Privacy Right Clearinghouse (PRC) data breach chronology, we segment geographical groups using unsupervised cluster analysis, and utilize a covariate-dependent probability to model zero losses, finite mixture distributions for moderate body and an extreme value distribution for large losses capturing the heavy-tailed nature of the loss data. Parameters and coefficients are estimated using the Expectation-Maximization (EM) algorithm. Combining with our frequency model (generalized linear mixed model) for data breaches, aggregate loss distributions are investigated and applications on cyber insurance pricing and risk management are discussed.

Time Series Analysis and Prediction of COVID-19 Pandemic Using Dynamic Harmonic Regression Models

Rapidly spreading COVID-19 virus and its variants, especially in metropolitan areas around the world, became a major health public concern. The tendency of COVID-19 pandemic and statistical modelling represents an urgent challenge in the United States for which there are few solutions. In this paper, we demonstrate combining Fourier terms for capturing seasonality with ARIMA errors and other dynamics in the data. Therefore, we have analyzed 156 weeks COVID-19 dataset on national level using Dynamic Harmonic Regression model, including simulation analysis and accuracy improvement from 2020 to 2023. Most importantly, we provide new advanced pathways which may serve as targets for developing new solutions and approaches.

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.

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.

Predictive Modeling for Analysis of Coronavirus Symptoms Using Logistic Regression

This paper presents a case study on the IPUMS NHIS database,which provides data from censuses and surveys on the health of the U.S.population,including data related to COVID-19.By addressing gaps in previous studies,we propose a machine learning approach to train predictive models for identifying and measuring factors that affect the severity of COVID-19 symptoms.Our experiments focus on four groups of factors:demographic,socio-economic,health condition,and related to COVID-19 vaccination.By analysing the sensitivity of the variables used to train the models and the VEC(variable effect characteristics)analysis on the variable values,we identify and measure importance of various factors that influence the severity of COVID-19 symptoms.

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.

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.

Small-time scale network traffic prediction based on a local support vector machine regression model

In this paper we apply the nonlinear time series analysis method to small-time scale traffic measurement data. The prediction-based method is used to determine the embedding dimension of the traffic data. Based on the reconstructed phase space, the local support vector machine prediction method is used to predict the traffic measurement data, and the BIC-based neighbouring point selection method is used to choose the number of the nearest neighbouring points for the local support vector machine regression model. The experimental results show that the local support vector machine prediction method whose neighbouring points are optimized can effectively predict the small-time scale traffic measurement data and can reproduce the statistical features of real traffic measurements.

WAVELET ESTIMATION FOR JUMPS IN A HETEROSCEDASTIC REGRESSION MODEL

Wavelets are applied to detect the jumps in a heteroscedastic regression model. It is shown that the wavelet coefficients of the data have significantly large absolute values across fine scale levels near the jump points. Then a procedure is developed to estimate the jumps and jump heights. All estimators are proved to be consistent.

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.

Evaluation of Inference Adequacy in Cumulative Logistic Regression Models:An Empirical Validation of ISW-Ridge Relationships

Internal solitary wave propagation over a submarine ridge results in energy dissipation, in which the hydrodynamic interaction between a wave and ridge affects marine environment. This study analyzes the effects of ridge height and potential energy during wave-ridge interaction with a binary and cumulative logistic regression model. In testing the Global Null Hypothesis, all values are p 〈0.001, with three statistical methods, such as Likelihood Ratio, Score, and Wald. While comparing with two kinds of models, tests values obtained by cumulative logistic regression models are better than those by binary logistic regression models. Although this study employed cumulative logistic regression model, three probability functions p^1, p^2 and p^3, are utilized for investigating the weighted influence of factors on wave reflection. Deviance and Pearson tests are applied to cheek the goodness-of-fit of the proposed model. The analytical results demonstrated that both ridge height （X1 ） and potential energy （X2 ） significantly impact （p 〈 0. 0001 ） the amplitude-based refleeted rate; the P-values for the deviance and Pearson are all 〉 0.05 （0.2839, 0.3438, respectively）. That is, the goodness-of-fit between ridge height （ X1 ） and potential energy （X2） can further predict parameters under the scenario of the best parsimonious model. Investigation of 6 predictive powers （ R2, Max-rescaled R^2, Sorners＇ D, Gamma, Tau-a, and c, respectively） indicate that these predictive estimates of the proposed model have better predictive ability than ridge height alone, and are very similar to the interaction of ridge height and potential energy. It can be concluded that the goodness-of-fit and prediction ability of the cumulative logistic regression model are better than that of the binary logistic regression model.

EFFICIENT ESTIMATION OF FUNCTIONAL-COEFFICIENT REGRESSION MODELS WITH DIFFERENT SMOOTHING VARIABLES

In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the local linear technique and the averaged method,the initial estimates of the coefficient functions are given.Second step,based on the initial estimates,the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure.The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions.Two simulated examples show that the procedure is effective.