Inverse Gaussian Regression Model Research Articles

Variable selection in Inverse Gaussian regression model using modified crow search algorithm

Variable selection in Inverse Gaussian regression model using modified crow search algorithm

Variable selection in Inverse Gaussian regression model using modified crow search algorithm

Variable selection in Inverse Gaussian regression model using modified crow search algorithm

Data-Driven Reachability and Support Estimation With Christoffel Functions

We present algorithms for estimating the forward reachable set of a dynamical system using only a finite collection of independent and identically distributed samples. The produced estimate is the sublevel set of a function called an empirical inverse Christoffel function: empirical inverse Christoffel functions are known to provide good approximations to the support of probability distributions. In addition to reachability analysis, the same approach can be applied to general problems of estimating the support of a random variable, which has applications in data science towards detection of novelties and outliers in data sets. In applications where safety is a concern, having a guarantee of accuracy that holds on finite data sets is critical. In this paper, we prove such bounds for our algorithms under the Probably Approximately Correct (PAC) framework. In addition to applying classical Vapnik- Chervonenkis (VC) dimension bound arguments, we apply the PAC-Bayes theorem by leveraging a formal connection between kernelized empirical inverse Christoffel functions and Gaussian process regression models.

Investigating surrogate safety measures at midblock pedestrian crossings using multivariate models with roadside camera data

This study aims to evaluate and compare Surrogate Safety Measures (SSMs) at five midblock Rectangular Rapid Flashing Beacons (RRFB) and two midblock Pedestrian Hybrid Beacons (PHB) sites in Florida using extensive video data collected over the study period of July to November 2021. Computer vision and data processing resulted in four pedestrian SSMs, namely spatial gap, temporal gap, relative time to collision (RTTC) and Post Encroachment Time (PET). An initial investigation of the SSMs using Mann-Whitney-Wilcoxon tests revealed significant differences in the SSM values across different treatment types and hours of the day. Additionally, univariate regression of spatial gap, and multivariate regression of temporal gap, RTTC and PET revealed significant differences of SSMs across RRFB and PHB sites. The study considered both linear and non-linear (gamma, inverse Gaussian and lognormal) regression models. After considering various traffic and operational parameters, the data were aggregated for each pedestrian-vehicle interaction on each lane to create a total of 395 observations. The SSMs included average spatial gap, temporal gap, RTTC and PET for each interaction of pedestrian and vehicle on each lane. The results indicated that non-linear models performed better than the linear models. Moreover, the presence of the PHB, weekday, signal activation, lane count, pedestrian speed, vehicle speed, land use mix, morning period and pedestrian starting position from the sidewalk have been found to be significant determinants of the SSMs. Results also suggest temporal SSMs increase at the PHB sites compared to the RRFB sites, indicating an improvement of traffic safety at PHB sites. However, the spatial gap decreased for PHB sites compared to the RRFB sites, which suggests that pedestrians tend to start to cross the RRFB sites when they perceive vehicles to be further away than at the PHB sites.

On the performance of some new ridge parameter estimators in the Poisson-inverse Gaussian ridge regression

The Poisson Inverse Gaussian Regression model (PIGRM) is used for modeling the count datasets to deal with the issue of over-dispersion. Generally, the maximum likelihood estimator (MLE) is used to estimate the PIGRM estimates. In the PIGRM, when the explanatory variables are correlated, the MLE does not provide efficient results. To overcome this problem, we propose a ridge estimator for the PIGRM. The matrix mean square error (MSE) and the scalar MSE properties are derived and then compared with the MLE. In the ridge estimator, ridge parameter play a significant role, so, this study also proposes different ridge parameter estimators for the PIGRM. The performance of the proposed estimator is evaluated with the help of a simulation study and a real-life application using MSE as a performance evaluation criterion. The simulation study and the real-life application results show the superiority of the proposed parameter estimators as compared to the MLE.

INVERSE GAUSSIAN REGRESSION MODELING AND ITS APPLICATION IN NEONATAL MORTALITY CASES IN INDONESIA

Inverse Gaussian Regression (IGR) is a suitable model for modeling positively skewed response data, which follows the inverse Gaussian distribution. The IGR model was formed from the Generalized Linear Models (GLM). This study aims to model the IGR with applied to model the factors influencing the infant mortality cases of provinces in Indonesia. Estimation of the IGR model parameters was employed by the Maximum Likelihood Estimation (MLE) and Fisher scoring methods. The Likelihood Ratio Test (LRT) and Wald test were used for hypothesis testing of significance parameters. The IGR model was applied to the infant mortality cases of provinces in Indonesia in 2020. The data for modeling infant mortality cases using IGR were obtained from the Ministry of Health of the Republic of Indonesia and the Central Bureau of Statistics. The result shows that the factors influencing the infant mortality cases of provinces in Indonesia based on the IGR model were: the percentage of pregnant women who received blood-boosting tablets, the percentage of low birth weight, the percentage of complete neonatal visits (KN3), the percentage of toddlers who received early initiation of breastfeeding, the percentage of toddlers who are exclusively breastfeeding, the percentage of toddlers who received complete primary immunization, the percentage of households with access to adequate drinking water, and the percentage of households with access to appropriate sanitation.

A Bayesian-Weighted Inverse Gaussian Regression Model with Application to Seismological Data

Developing an efficient model for analyzing right-skewed positive observations has a long history, and many authors have attempt in this direction. This is because the common analytic modeling procedures such as linear regression are often inappropriate for such data and leads to inadequate results. In this article, we proposed a new model for regression analysis of the right-skewed data by assuming the weighted inverse Gaussian, as a great flexible distribution, for response observations. In the proposed model, the complementary reciprocal of the location parameter of response variable is considered to be a linear function of the explanatory variables. We developed a fully Bayesian framework to infer about the model parameters based on a general noninformative prior structure and employed a Gibbs sampler to derive the posterior inferences by using the Markov chain Monte Carlo methods. A comparative simulation study is worked out to assess and compare the proposed model with other usual competitor models, and it is observed that efficiency is quite satisfactory. A real seismological data set is also analyzed to explain the applicability of the proposed Bayesian model and to access its performance. The results indicate to the more accuracy of proposed regression model in estimation of model parameters and prediction of future observations in comparison to its usual competitors in literature. Particularly, the relative prediction efficiency of the proposed regression model to the inverse Gaussian and log-normal regression models has been obtained to be 1.16 and 64, respectively, for the real-world example discussed in this paper.

The multivariate Poisson‐Generalized Inverse Gaussian claim count regression model with varying dispersion and shape parameters

AbstractWe introduce a multivariate Poisson‐Generalized Inverse Gaussian regression model with varying dispersion and shape for modeling different types of claims and their associated counts in nonlife insurance. The multivariate Poisson‐Generalized Inverse Gaussian regression model is a general class of models which, under the approach adopted herein, allows us to account for overdispersion and positive correlation between the claim count responses in a flexible manner. For expository purposes, we consider the bivariate Poisson‐Generalized Inverse Gaussian with regression structures on the mean, dispersion, and shape parameters. The model's implementation is demonstrated by using bodily injury and property damage claim count data from a European motor insurer. The parameters of the model are estimated via the Expectation‐Maximization algorithm which is computationally tractable and is shown to have a satisfactory performance.

Effect of Socio-Economic Status on Perioperative Outcomes After Robotic-Assisted Pulmonary Lobectomy

Background: Lower socioeconomic status (SES) has been correlated with poor survival rates and surgical outcomes following lung cancer resection. This study sought to determine whether this disparity exists perioperatively in lung cancer patients following robotic-assisted video-thoracoscopic pulmonary lobectomy. Methods: We retrospectively reviewed 447 consecutive patients who underwent robotic-assisted pulmonary lobectomy by one surgeon for known or suspected lung cancer. Ten patients were excluded due to incomplete data. We used median income by residential ZIP code as a surrogate for SES status and grouped patients based on whether ZIP-based median income was less than (Group 1) or greater than (Group 2) 300% of the federal poverty income level. The effects of SES status groups on incidence of postoperative complications, chest tube duration, hospital length of stay (LOS), and in-hospital mortality were evaluated by the logistic regression model and Inverse Gaussian regression model, respectively.Results: Without adjustment, Group 1 tended to have a higher rate of postoperative complications, with 54% of patients experiencing complications compared to 34% of patients in Group 2 (p=0.007). Median chest tube duration and hospital LOS were also significantly longer in Group 1 than in Group 2 (p=0.034). In multivariable logistical regression analysis, while controlling for covariates and considering effect modifications, lower SES was significantly and positively associated with postoperative complications (odds ratio (OR)=1.98, p=0.039). Preoperative chronic obstructive pulmonary disease (COPD) was also a positive and significant predictor of postoperative complications (OR=1.89, p=0.017), chest tube duration (p=0.020), and LOS (p=0.010).Conclusions: Lower median income is associated with a greater number of postoperative complications following pulmonary resection for lung cancer when controlling for covariates.

The 2021 Western North American heat dome increased climate change anxiety among British Columbians: Results from a natural experiment

Extreme weather events caused by climate change pose a risk to mental health. Illustrating this reality, this study estimates the impact of the 2021 Western North American heat dome (June 25th, 2021 – July 1st, 2021) on climate change anxiety among British Columbians. We conducted an online survey of British Columbians, aged ≥ 16. Participants were recruited using paid advertisements on social media. Data were collected pre- and post- heat dome between May 12th, 2021 – June 21st, 2021 (n = 439), and July 15th, 2021 – July 18th, 2021 (n = 420), respectively. A multivariable inverse Gaussian regression model tested differences in Climate Change Anxiety Scale (CCAS) scores pre- and post- heat dome. Potential confounders measured included age, gender, ethnicity, education, income, and political orientation. CCAS reliability was assessed using Cronbach's alpha. Most participants indicated that they were much (40.1%) or somewhat (18.4%) more worried about climate change due to the heat dome. Mean CCAS scores increased from 1.66 (standard deviation [SD]= 0.80) to 1.87 (SD = 0.87) pre- and post- heat dome, respectively. In multivariable modeling, this effect was significant after controlling for potential confounders (Estimate = 0.057, standard error = 0.148, p < 0.001). The CCAS reliability was high (Cronbach's alpha = 0.94). Our results found that British Columbians had significantly higher climate change anxiety following the 2021 Western North American heat dome. Ongoing monitoring of climate change anxiety is needed to understand the impact of individual and compounding climate change-related weather events over time.

The Geographically Weighted Multivariate Poisson Inverse Gaussian Regression Model and Its Applications

This study aims to develop a method for multivariate spatial overdispersion count data with mixed Poisson distribution, namely the Geographically Weighted Multivariate Poisson Inverse Gaussian Regression (GWMPIGR) model. The parameters of the GWMPIGR model are estimated locally using the maximum likelihood estimation (MLE) method by considering spatial effects. Therefore, the significance of the regression parameter differs for each location. In this study, four GWMPIGR models are evaluated based on the exposure variable and the spatial weighting function. We compare the performance of those four models in real-world application using data on the number of infant, under-5 and maternal deaths in East Java in 2019 using five predictor variables. In this study, the GWMPIGR model uses one exposure variable and three exposure variables. Compared to the fixed kernel Gaussian weighting function, the GWMPIGR model with the fixed kernel bisquare weighting function and one exposure variable has a better fit based on the AICc value. Furthermore, according to the best GWMPIGR model, there are several regional groups formed based on predictors that significantly affected each event in East Java in 2019.

A new improved Liu estimator for the QSAR model with inverse Gaussian response

The regression model is one of the important quantitative structure-activity relationship (QSAR) model tools that is used chiefly in chemometrics studies. In chemometrics, when the response variable is continuous, positively skewed, and well fitted to the inverse Gaussian distribution, then the inverse Gaussian regression model (IGRM) is a better choice QSAR model. Multicollinearity in the IGRM affects the IGRM estimation and inferences. To overcome the effect of multicollinearity, biased estimators such as ridge and Liu are discussed in the literature. However, the disadvantage of using the traditional Liu estimator is that the shrinkage parameter, d, returns a negative value that severely affects the estimator's performance. To mitigate this problem, we propose a new improved Liu estimator for the IGRM. The new estimator's performance is compared with the maximum likelihood estimator (MLE) and the other biased estimators. A Monte Carlo simulation study is conducted to assess the newly proposed estimator's performance under different parametric conditions. A QSAR chemometric application is also considered to see the clear picture of the proposed estimator. The simulation and QSAR application findings demonstrate that the newly proposed estimator consistently dominates the other competitive estimators in all the evaluated conditions.

A Comparison of Bivariate Zero-Inflated Poisson Inverse Gaussian Regression Models with and without Exposure Variables

In this paper, we focus on the comparison of the bivariate zero-inflated Poisson inverse Gaussian regression (BZIPIGR) type II model in two cases: with and without exposure variables. The BZIPIGR type II model is applied to analyze the occurrence of maternal and early neonatal mortality in South Sulawesi Province, Indonesia using 2019 data, which contain many zero values and have the issue of overdispersion in the response variable. Furthermore, to analyze the number of deaths in various areas, the exposure variable is considered. The maximum likelihood estimation (MLE) is used in parameter estimation, which involves numerical iteration and application of the Berndt–Hall–Hall–Hausman (BHHH) algorithm. Sum square error (SSE) serves as the criterion of model selection when exposure variables are included. The existence of exposure variables strongly affects the model’s accuracy, especially using the BZIPIGR type II model. According to the SSE and RMSE values, the BZIPIGR type II model with exposure variables performs better than the model without exposure variables in estimating parameter values. All predictors with exposure variables in this study had a significant influence on the number of maternal and early neonatal mortalities.

Principal component ridge type estimator for the inverse Gaussian regression model

The inverse Gaussian regression model (IGRM) is applied when the response variable is continuous, positively skewed and well fitted to the inverse Gaussian distribution. In the presence of multicollinearity, the maximum likelihood estimation (MLE) is not a right choice. Therefore, we proposed a new estimator called the principal component ridge estimator for the IGRM which combines the principal component estimator and the ridge estimator. We also consider a two-parameter estimator (TPE) and other biased estimators to see a clear image of our proposed estimator. A Monte Carlo simulation study is also presented to examine the performance of the proposed estimators. Furthermore, we analysed a dataset to assess the superiority of the proposed estimator. Based on the simulation and application results, it is evident that the proposed estimator dominates the classical MLE, and other considered biased estimation methods.

Bivariate Zero-Inflated Poisson Inverse Gaussian Regression Model and Its Application

Bivariate Zero-Inflated Poisson Inverse Gaussian Regression Model and Its Application

Parameter estimation and hypothesis testing of geographically and temporally weighted bivariate Poisson inverse Gaussian regression model

One of the appropriate methods used to model count data response and its corresponding predictors is Poisson regression. Poisson regression strictly assumes that the mean and variance of response variables should be equal (equidispersion). Nonetheless, some cases of the count data unsatisfied this assumption because variance can be larger than mean (over-dispersion). If overdispersion is violated, causing the underestimate standard error. Furthermore, this will lead to incorrect conclusions in the statistical test. Thus, a suitable method for modelling this kind of data needs to develop. One alternative model to outcome the overdispersion issue in bivariate response variable is the Bivariate Poisson Inverse Gaussian Regression (BPIGR) model. The BPIGR model can produce a global model for all locations. On the other hand, each location and time have different geographic conditions, social, cultural, and economical so that Geographically and Temporally Bivariate Poisson Inverse Gaussian Regression (GTWBPIGR)) is needed. The weighting function spatial-temporal in GTWBPIGR generates a different local model for each period. GTWBPIGR model solves the overdispersion case and generates global models for each period and location. The parameter estimation of the GTWBPIGR model uses the Maximum Likelihood Estimation (MLE) method, followed by Newton Raphson iteration. Meanwhile, the test statistics on the hypothesis testing is simultaneously testing of the GTWBPIGR model is obtained with the Maximum Likelihood Ratio Test (MLRT) approach, using n large samples of the statistical test is chi-square distribution. Moreover, the test statistics for partially testing used the Z-test statistic.

Inverse Gaussian Liu-type estimator

The inverse Gaussian regression (IGR) model parameters are generally estimated using the maximum likelihood (ML) estimation method. Since the multicollinearity problem exists among the explanatory variables, the ML estimation method becomes inflated. When the multicollinearity problem occurs, biased estimators can be used to estimate the parameters of the model. One of the most widely used biased estimators is the Liu-type estimator. In this study, we extend the Liu-type estimator for the IGR model. The proposed estimator is compared with the Ridge and Liu estimators defined for the IGR model in terms of the mean squared error (MSE) criterion. Also, a real data example is presented to illustrate the superiority of the proposed estimator. Experimental results show that the Liu-type estimator outperforms the Ridge and Liu estimators when multicollinearity exists.

Modified ridge-type estimator for the inverse Gaussian regression model

This paper considers the parameter estimation for the inverse Gaussian regression model (IGRM) in the presence of multicollinearity. The inverse Gaussian modified ridge-type estimator (IGMRTE) is developed for efficient parameter estimation and compared with other estimation methods such as the maximum likelihood estimator (MLE), ridge and Liu estimator. We derived the properties of the proposed estimator and conducted a theoretical comparison with some of the existing estimators using the matrix mean squared error and mean squared error criterions. Furthermore, the statistical properties of these estimators are systematically scrutinized via a Monte Carlo simulation study under different conditions. The findings of the simulation study demonstrate that the proposed IGMRTE showed a much more robust behavior in the presence of severe multicollinearity. A real life example is also analyzed to evaluate the effectiveness of the estimators under study. Both the simulation and the application results confirm the use of IGMRTE for the estimation of unknown regression coefficients of the IGRM when the explanatory variables are highly correlated.

Two parameter Ridge estimator in the inverse Gaussian regression model

It is well known that multicollinearity, which occurs among the explanatory variables, has adverse effects on the maximum likelihood estimator in the inverse Gaussian regression model. Biased estimators are proposed to cope with the multicollinearity problem in the inverse Gaussian regression model. The main interest of this article is to introduce a new biased estimator. Also, we compare newly proposed estimator with the other estimators given in the literature. We conduct a Monte Carlo simulation and provide a real data example to illustrate the performance of the proposed estimator over the maximum likelihood and Ridge estimators. As a result of the simulation study and real data example, the newly proposed estimator is superior to the other estimators used in this study.

Influence diagnostics in the inverse Gaussian ridge regression model: Applications in chemometrics

AbstractThe influential observation affects the regression model inferences. Literature has shown that the problems of multicollinearity and influential observations can jointly exist in a model. The ridge regression estimator has been developed to handle the challenge of multicollinearity. The detection of influential observations with multicollinearity and its impact on the ridge estimates is necessary for better decision making. In this article, we proposed some influence diagnostics for the inverse Gaussian ridge regression model (IGRRM). The proposed diagnostics are evaluated with the help of a simulation study and two chemometric‐related data sets. We found that the covariance ratio (CVR) method is better than other methods for the detection of influential observations under smaller dispersion. While for larger dispersion, all the IGRRM diagnostics perform equally well for the identification of influential observations.