Optimal ridge estimation in the restricted logistic semiparametric regression models using generalized cross-validation

Understanding the distribution and propagation of train delay is crucial for railway management. This paper combines the interpretability of logistic regression models with the robustness and accuracy of Random Forest models to create a combined model which was applied to predict punctuality. The data consists of relative timetable deviation of train movement for all stations, as well as punctuality observations at destination stations. The data was recorded for both passenger and freight trains in Sweden between year 2017 and 2018.The data consists of many policy and categorical variables such as train operator which are known to indirectly effect delay risk, but are labeled as insignificant in classical regression making their coefficients unstable and difficult to interpret. For this reason, the study has applied logistic regression model with the variables of interest such as train type as well as first registered delay (relative deviation compared with timetable) along with "bagging" of Random Forest capturing indirect or/and sensitive predictors. This semi-parametric logistic regression model was trained using 2017 data and was accurate and robust when tested using the 2018 data. It has shown to be capable of handling the delays caused by unforeseen disruptions such as abnormal weather in the test year. In this paper we show that the semi-parametric model has significantly better prediction performance than linear models, Weibull distributions, Binomial logistic regression and Random Forest alone. Furthermore, the semiparametric model maintains its interpretability whilst producing accurate predictions with new data.

Multicollinearity in logistic semiparametric regression models inflates the variance of maximum likelihood estimators, leading to unreliable parameter estimates. While these models offer flexibility by combining parametric and nonparametric components, they are sensitive to multicollinearity. To address this, we propose a restricted ridge estimator for logistic semiparametric regression models with exact linear restrictions, extending the method introduced by Asar (2017) for standard logistic regression. This approach effectively reduces variance and provides more stable estimates. Additionally, we use generalized cross-validation (GCV) to select the optimal ridge penalty and kernel bandwidth, ensuring a balanced bias-variance tradeoff for both components. We validate the proposed method through simulation and real-data applications. The simulation results show that the restricted ridge estimator outperforms traditional maximum likelihood estimation (MLE) in terms of stability and accuracy under multicollinearity. The real-data application demonstrates its practical advantages in producing reliable and interpretable estimates.

In this article, a biased estimator is proposed to combat multi-collinearity in the logistic regression model. The proposed estimator is a general estimator which includes other biased estimators, such as the ridge estimator and the Liu estimator as special cases. Necessary and sufficient conditions for the superiority of the new biased estimator over the maximum likelihood estimator, the ridge estimator are obtained and some properties in the mean squared error sense are discussed. Furthermore, a Monte Carlo simulation study is given to illustrate some of the theoretical results.

In a short period, a variety of technically different digital radiography chest systems have become available for clinical use. Our purpose was to assess the diagnostic performance of eight different digital radiography chest systems for detection of simulated chest disease under clinical conditions. Assessed were four different flat-panel detector systems, two different charge-coupled device systems, one selenium-coated drum, and one storage phosphor system. For each system, 10 chest images of an anthropomorphic chest phantom were obtained. Each image contained one to 12 simulated chest lesions. Eight radiologists performed soft-copy interpretations. Entrance dose was measured and effective dose calculated. A semi-parametric logistic regression model was used for statistical analysis. Statistically significant differences were found in the diagnostic performance of the eight digital chest systems (p = 0.01). Best performance was observed with the charge-coupled device system with slot-scan technology, yielding a sensitivity of 46% (132 of 288) lesions detected. The performance of three flat-panel detectors and the selenium-drum system was not significantly different from the slot-scan charge-coupled device system. Fewer lesions were detected with the storage phosphor system than with all other digital technologies, with a sensitivity of 34% (99 of 288) lesions detected, slot-scan charge-coupled device system versus storage phosphor system, p < 0.001. The effective dose varied among the digital systems. We found differences in diagnostic performance among the eight different digital chest systems. Differences in detection rates are predominantly explained by detector design.

In the May 15, 1997, issue of Transplantation (1997; 63[9]: 1257), Dr. Shield and co-workers (1) reported on an analysis of the United Network for Organ Sharing to compare results in renal transplant recipients treated with and without antilymphocyte products. We agree that the use of this very large database offers an important opportunity to elucidate the critical issues in this controversial area. However, after carefully reviewing this article, we are left with a number of important questions about the data. Are we correct in assuming that only patients whose data was validated (84% of the total) were used in this study? There is a comment regarding validation of data with respect to the antilymphocyte product and the duration of its administration. Was there any attempt to validate data relating to rejection episodes, graft survival, and the other data that were used in the study? We believe (without having seen data) that most U.S. centers will have definite policies regarding the use of antilymphocyte products. We would appreciate comments by the authors on this issue. A potential beneficial effect of antilymphocyte products is to reduce the rejection rate. Table 3 gives rejection episodes up to the time of discharge from hospital, but no information is given on rejection episodes that recurred after this time. Is this data available? A listing of the variables that were entered into the Cox regimen analysis would be helpful. For example, in the entire group of patients, was delayed graft function an independent risk factor or was it a dependent variable interacting with the presence or absence of an antilymphocyte product? Furthermore, was the complete absence of the use of an antilymphocyte product associated with an increase in relative risk (data not given in Table 6)? Additional information on the panel-reactive antibody as a dependent or independent risk factor for delayed graft function and graft outcome would be helpful to interpret the results. Since one of the main findings of the study seems to be that if graft loss during the first week is excluded, there is no difference in outcomes among the three groups, we believe that an analysis of the causes of graft loss in the three groups, including an analysis of the causes of graft loss within the first week separately, would be useful. Finally, we are confused by Table 8, in that data are shown for patients not receiving an antilymphocyte product based on the number of days of induction. Is this also used to indicate the day after transplant on which the events occurred in this group? Jolanta Karpinski Carl Cardella Edward Cole1 Renal Transplant Program; University of Toronto; Toronto, Ontario, Canada

A cost-minimizing diagnostic methodology for discrimination between neoplastic and non-neoplastic brain lesions: utilizing a genetic algorithm 1 scientific reports

Semiparametric regression is a regression model consisting of two components, namely the parametric and the nonparametric component. The parametric component is a component with curves are known and the nonparametric component is a component with unknown shape of the curve. Bi-response semiparametric regression is regression analysis which has two response variables with the combination of parametric and nonparametric curves. The purpose of this research is to compare the bi-response semiparametric regression model using spline truncated with component parametric linear and quadratic. In this research, the method that used for the estimation parameter is WLS (Weighted Least Square) and the selection of optimal knot points is done by looking at the minimum GCV (Generalized Cross-Validation) value. WLS is minimizing partial derivative based on a parameter in the model. Each the linear bi-responsese semiparametric regression and quadratic bi-responsese semiparametric regression using spline truncated has two parameters that are parameter for parametric and nonparametric components. The difference between the two models contained in the parametric component of the predictor variable and parameter matrix of parametric component is estimator linear bi-response semiparametric regression model and is estimator quadratic bi-response semiparametric regression model using spline truncated.

USING A MULTIVARIABLE MODEL FOR PREDICTION AND DIAGNOSIS

Uncertainties in spatially aggregated predictions from a logistic regression model

This study proposed a method for constructing confidence intervals for parameters in a semiparametric regression model using a truncated spline estimator, tailored for multiresponse and multipredictor longitudinal data. The semiparametric model integrated parametric and nonparametric components, facilitating the analysis of complex relationships. Confidence intervals were estimated using a pivotal quantity method.The approach was applied to COVID-19 data from Indonesia, exploring the associations between Time, Temperature, and Sunlight Intensity with the Case Increase Rate (CIR) and Case Fatality Rate (CFR). Data spanning April to November 2020 were sourced from 10 provinces with the highest CIR and CFR, obtained from http://kawalcovid.com/ and https://power.larc.nasa.gov/.The analysis identified an optimal Generalized Cross-Validation (GCV) value of 220, with one knot at 24.35°C for Temperature and two knots at 11.33 and 13 units for Sunlight Intensity. Confidence interval estimation demonstrated that all parametric components associated with Time were statistically significant, reflecting a consistent decline in CIR and CFR over time. For the nonparametric components, four parameters significantly influenced CIR, while three parameters significantly affected CFR, contingent on the knot points.The findings underscored the role of environmental factors in shaping COVID-19 dynamics and provided a robust analytical framework for future pandemic modeling. This study highlighted the utility of semiparametric regression with truncated splines in addressing complex epidemiological data, offering valuable insights for policymakers to design evidence-based mitigation strategies

Logistic regression models used to predict tree mortality are critical to post-fire management, planning prescribed burns and understanding disturbance ecology. We review literature concerning post-fire mortality prediction using logistic regression models for coniferous tree species in the western USA. We include synthesis and review of: methods to develop, evaluate and interpret logistic regression models; explanatory variables in logistic regression models; factors influencing scope of inference and model limitations; model validation; and management applications. Logistic regression is currently the most widely used and available technique for predicting post-fire tree mortality. Over 100 logistic regression models have been developed to predict post-fire tree mortality for 19 coniferous species following wild and prescribed fires. The most widely used explanatory variables in post-fire tree mortality logistic regression models have been measurements of crown (e.g. crown scorch) and stem (e.g. bole char) injury. Prediction of post-fire tree mortality improves when crown and stem variables are used collectively. Logistic regression models that predict post-fire tree mortality are the basis of simple field tools and contribute to larger fire-effects models. Future post-fire tree mortality prediction models should include consistent definition of model variables, model validation and direct incorporation of physiological responses that link to process modelling efforts.

Multiple linear regression model is a widely used statistical technique in social and life sciences.Ordinary Least Squares (OLS) estimator is the Best Linear Unbiased Estimator (BLUE) for the unknown population parameters of this model.Unfortunately, sometimes two or more of the regressors may be moderately or highly correlated causing multicollinearity problem.Various biased estimators are proposed to refine the ill-conditioning of X'X matrix and shrink the variance under the multicollinearity.The most popular of them is Ridge estimator.But it may worsen the fit when solving the ill-conditioning problem.Two-Parameter Ridge (2PR) and Liu Type (LT) estimators are proposed to overcome the fitting degeneration of Ridge estimator by using a tuning parameter.In this study, holding the parameter refining the ill-conditioning of X'X matrix fixed, the success of the tuning parameters of these estimators is investigated.Minimizers of Predicted Sum of Squares (PRESS) and Generalized Cross Validation (GCV) statistics are used as estimates of tuning parameters.Optimum parameter estimates are compared via their Scalar Mean Squared Errors (SMSE).It is observed that the SMSEs of estimates obtained by LT and 2PR estimators decreases when estimates of parameter refining the ill-conditioning of X'X matrix increases, and in all cases estimates obtained by the 2PR estimator are much more efficient than estimates obtained by LT and OLS estimators.

Detection of outliers and other diagnostics based on residuals have gained widespread use in linear regression. Logistic regression has been both blessed and hindered by this development. Certainly logistic regression requires procedures to detect global and local model weaknesses. Thus the wealth of work done in linear regression provides guides and suggestions that may, with care and ingenuity, be applied to logistic regression. Several innovative attempts in this direction have been made by authors such as Tsiatis (1980), Pregibon (1979, 1981), Landwehr, Pregibon, and Shoemaker (1984), and Cook and Weisberg (1982). Unfortunately the similarities that allow such techniques to adapt to logistic regression seem, in addition, to hide many of the differences. Two such differences are discussed here. The first examines the effect of events of small probability on estimation in logistic regression. The simple conclusion is that to estimate the probability of success p in an area in which p is small, one must observe events of small probability. This suggests that the motives for outlier detection should be carefully considered. The second difference examined deals with the distribution of residuals. Let y be the response variable and let x be a p×1 vector of explanatory variable. In linear regression with normal errors, Y — E (Y | x) is normally distributed with mean 0 and variance σ2. Thus the distribution of this residual from the true model does not depend on the explanatory variables x. This is not true in logistic regression with binary data. There Y has a Bernoulli distribution with probability of success p(x) = Pr(Y = 1 | x). Thus any reasonable definition of a residual from the true model, for example, Y — p(x), has a two-point distribution that depends on x through p(x). That is, each residual has a unique distribution. In this setting claims that “standardized residuals” exist that are asymptotically normal or chi squared are not appropriate. The argument based on difference in likelihoods to support such claims as made by Pregibon (1981) and alluded to by Beckman and Cook (1983) relies on asymptotic conditions that are not obtained in strictly binary data. Diagnostics must consider the effects of differing residual distributions. For example, the local mean deviance plot suggested by Landwehr et al. (1984) is seriously affected by the underlying p(x i ). A modification, however, that replaces the deviance residual by (y — p)2 appears to be useful. The general intent of this article is to point out that direct application of linear regression techniques to logistic regression does not necessarily produce useful diagnostic tools. Thus careful consideration of each diagnostic technique is necessary. In addition, logistic regression might benefit from views and methods different from those applied to problems with continuous errors due to the 0–1 nature of the data.

&lt;abstract&gt;&lt;p&gt;This paper is concerned with proposing a generalized Liu-type estimator (GLTE) to address the multicollinearity problem of explanatory variable of the linear part in the logistic partially linear regression model. Using the profile likelihood method, we propose the GLTE as a general class of Liu-type estimator, which includes the profile likelihood estimator, the ridge estimator, the Liu estimator and the Liu-type estimator as special cases. The conditional superiority of the proposed GLTE over the other estimators is derived under the asymptotic mean square error matrix (MSEM) criterion. Moreover, the optimal choices of biasing parameters and function of biasing parameter are given. Numerical simulations demonstrate that the proposed GLTE performs better than the existing estimators. An application on a set of real data arising from the study of Indian Liver Patient is shown for illustrating our theoretical results.&lt;/p&gt;&lt;/abstract&gt;

The binary logistic regression model (LRM) is practical in situations when the response variable (RV) is dichotomous. The maximum likelihood estimator (MLE) is generally considered to estimate the LRM parameters. However, in the presence of multicollinearity (MC), the MLE is not the correct choice due to its inflated standard deviation (SD) and standard errors (SE) of the estimates. To combat MC, commonly used biased estimators, i.e., the Ridge estimators (RE) and Liu estimators (LEs), are preferred. However, most of the time, the traditional LE attains a negative value for its Liu parameter (LP), which is considered to be a major drawback. Therefore, to overcome this issue, we proposed a new adjusted LE for the binary LRM. Owing to numerical evaluation purposes, Monte Carlo simulation (MCS) study is performed under different conditions where bias and mean squared error are the performance criteria. Findings showed the superiority of our proposed estimator in comparison with the other estimation methods due to the existence of high but imperfect multicollinearity, which clearly means that it is consistent when the regressors are multicollinear. Furthermore, the findings demonstrated that whenever there is MC, the MLE is not the best choice. Finally, a real application is being considered to be evidence for the advantage of the intended estimator. The MCS and the application findings pointed out that the considered adjusted LE for the binary logistic regression model is a more efficient estimation method whenever the regressors are highly multicollinear.