Gamma Regression Model Research Articles

Analysis of the Railway Accident-Related Damages in South Korea

Railway accidents are critical issues characterized by a large number of injuries and fatalities per accident due to massive public transport systems. This study proposes a new approach for evaluating the damages resulting from railway accidents using the two-part models (TPMs) such as the zero-inflated Poisson regression model (ZIP model) and the zero-inflated negative-binomial regression model (ZINB model) for the non-negative count measurements and the zero-inflated gamma regression model (ZIG model) and the zero-inflated log-normal regression model (ZILN model) for the semi-continuous measurements. The models are employed for the evaluation of the railway accidents on Korea Railroad, considering the accident damages, such as the train delay time, the number of trains delayed and the cost of considering the accident count responses, for the period 2008 to 2016. From the results obtained, we found that the human-related factors, the high-speed railway system or the Korea Train Express (KTX) and the number of casualties, are the main cost-escalating factors. The number of trains delayed and the amount of delay time tend to increase both the probability of incurring costs and the amount of cost. For better evaluation, the railway accident data should contain accurate information with less recurrence of zeros.

The Lomax regression model with residual analysis: an application to insurance data

ABSTRACT In this paper, we introduce a new regression model, called Lomax regression model, as an alternative to the gamma regression model. The maximum-likelihood method is used to estimate the unknown parameters of the proposed model, and the finite sample performance of the maximum-likelihood estimation method is evaluated by means of the Monte-Carlo simulation study. The randomized quantile residuals are used to check the adequacy of the fitted model. The insurance data are analyzed to demonstrate the usefulness of the proposed regression model against the gamma regression model.

EM Estimation for the Poisson-Inverse Gamma Regression Model with Varying Dispersion: An Application to Insurance Ratemaking

This article presents the Poisson-Inverse Gamma regression model with varying dispersion for approximating heavy-tailed and overdispersed claim counts. Our main contribution is that we develop an Expectation-Maximization (EM) type algorithm for maximum likelihood (ML) estimation of the Poisson-Inverse Gamma regression model with varying dispersion. The empirical analysis examines a portfolio of motor insurance data in order to investigate the efficiency of the proposed algorithm. Finally, both the a priori and a posteriori, or Bonus-Malus, premium rates that are determined by the Poisson-Inverse Gamma model are compared to those that result from the classic Negative Binomial Type I and the Poisson-Inverse Gaussian distributions with regression structures for their mean and dispersion parameters.

A test of Generalized Bayesian dating: A new linguistic dating method.

In current practice, when dating the root of a Bayesian language phylogeny the researcher is required to supply some of the information beforehand, including a distribution of root ages and dates for some nodes serving as calibration points. In addition to the potential subjectivity that this leaves room for, the problem arises that for many of the language families of the world there are no available internal calibration points. Here we address the following questions: Can a new Bayesian framework which overcomes these problems be introduced and how well does it perform? The new framework that we present is generalized in the sense that no family-specific priors or calibration points are needed. We moreover introduce a way to overcome another potential source of subjectivity in Bayesian tree inference as commonly practiced, namely that of manual cognate identification; instead, we apply an automated approach. Dates are obtained by fitting a Gamma regression model to tree lengths and known time depths for 30 phylogenetically independent calibration points. This model is used to predict the time depths of both the root and the internal nodes for 116 language families, producing a total of 1,287 dates for families and subgroups. It turns out that results are similar to those of published Bayesian studies of individual language families. The performance of the method is compared to automated glottochronology, which is an update of the classical method of Swadesh drawing upon automated cognate recognition and a new formula for deriving a time depth from percentages of shared cognates. It is also compared to a third dating method, that of the Automated Similarity Judgment Program (ASJP). In terms of errors and correlations with known dates, ASJP works better than the new method and both work better than automated glottochronology.

Application of Statistical Models: Parameters Estimation of Road Accident in Bangladesh

Road traffic accident is the most unwanted situation and one of the significant reasons for death and injuries of people of all ages worldwide. Statistical analysis of highway-related accidents is of utmost importance to evaluate the severity of the problem and speed up taking decision toward its attenuation. In this research, three statistical models, namely negative binomial, gamma regression and Poisson regression model, were developed by using the statistical software IBM SPSS 25.0 to determine the various contributing factors which were significantly responsible for road accidents occurring in Bangladesh. The parameters selected to develop each of the models are collision type, junction type, vehicle type, weather conditions, and driver behaviors. The goodness of fit test of the Poisson regression model indicates that there was an overdispersion problem in the accident data. The value of deviance and Pearson Chi-square of negative binomial regression analysis were found to be approximately 1.00. This determination declines that the negative binomial regression model was the best fit for the data. The gamma regression analysis was selected due to the handle under dispersion data. The significant contributing factors for road traffic accident occurring in this city based on the appropriate model were head-on and sideswipe as a collision type; T junction and cross junction as a junction type; bus and truck as a vehicle type; high speed and loss of control as a driver behavior. The weather condition is the only factor that has no significant contribution to road traffic accident occurrence.

A comparison of preliminary test, Stein-type and penalty estimators in gamma regression model

Owing to the broad applicability of gamma regression, we propose some improved estimators based on the preliminary test and Stein-type strategies to estimate the unknown parameters in a gamma regression model. These estimators are considered when it is suspected that the parameters may be restricted to a subspace of the parameter space. Two penalty estimators such as LASSO and ridge regression are also presented. An asymptotic theory for the preliminary test and Stein-type estimators is developed, and asymptotic distributional bias and asymptotic quadratic risk of the proposed estimators are obtained. Comprehensive Monte-Carlo simulation experiments are conducted. Comparisons are then made based on simulated relative efficiency to clarify the performance of the proposed estimators. Practitioners are recommended to use the positive-part Stein-type estimator since its performance is robust irrespective of the reliability of the subspace information. A real data on prostate cancer is considered to illustrate the performance of the proposed estimators.

Ethnic Variation in Immigrants' Diets and Food Acculturation – United States 1999–2012

AbstractImmigration has changed the United States from having a predominantly white to a more ethnically diverse population. People who move to the U.S. may initially have diets unlike native-born Americans but gradually adopt eating patterns more like them. Using NHANES data and a censored gamma regression model, this study estimated the daily consumption of major food products among groups of immigrants and the corresponding groups born in the U.S. Results show that immigrants had lower consumption of meat and higher consumption of fruits and vegetables, and immigrants’ consumption converged towards a less healthy American diet after five years in the U.S.

Variable selection in Gamma regression model using binary gray Wolf optimization algorithm

In the real life applications, large amounts of variables have been accumulated quickly. Selection of variables is a very useful tool for improving the prediction accuracy by identifying the most relative variables that related to the study. Gamma regression model is one of the most models that applied in several science fields. Gray Wolf optimization algorithm (GWO) is one of the proposed nature-inspired algorithms that can efficiently be employed for variable selection. In this paper, chaotic GWO is proposed to perform variable selection for gamma regression model. The simulation studies and a real data application are used to evaluate the performance of our proposed procedure in terms of prediction accuracy and variable selection criteria. The obtained results demonstrated the efficiency of our proposed methods comparing with other popular methods.

Three-parameter bivariate gamma regression model for analyzing under-five mortality rate and maternal mortality rate

Gamma regression is often used to model continuous, right-skewed and strictly positive data. This paper discusses three-parameter gamma regression, namely scale, shape, and location parameter, with two correlated response variables. The purpose of this study is to determine the estimator parameters, perform the testing for the parameters using Maximum Likelihood Ratio Test (MLRT) and its application in the cases of the Under-five Mortality Rate (U5MR) and the Maternal Mortality Rate (MMR) in North Sulawesi, Gorontalo, Central Sulawesi Provinces in 2016. The parameter estimation in this global model obtained through MLE. Nevertheless, the results showed an unsolvable equation in closed-form, then we used numerical optimization. In this study, we were using the Berndt-Hall-Hall-Hausman optimization method. After the estimation results are obtained, the estimation parameters need to be tested with a simultaneous test with the MLRT,while for test partially, we used the Z test. Moreover, the factors that influence U5MR and MMR are the poor population, the obstetric complications handled, the mothers received Fe3 during pregnancy, the teenage pregnancy,the children under-five received vitamin A and the households with clean and healthy life behavior.

Modified ridge-type estimator for the gamma regression model

The modified ridge-type estimator has been shown to cushion the effects of multicollinearity in the linear regression model. Recent studies have shown the adverse effects of multicollinearity in the gamma regression model (GRM). We proposed a gamma modified ridge-type estimator to tackle this problem. We derived the properties of this estimator and conducted a theoretical comparison with some of the existing estimators. A real-life example and simulation study show that the proposed estimator gains an advantage over other estimators in terms of the mean square error.

Almost unbiased ridge estimator in the gamma regression model

This article introduces the almost unbiased gamma ridge regression estimator (AUGRRE) estimator based on the gamma ridge regression estimator (GRRE). Furthermore, some shrinkage parameters are proposed for the AUGRRE. The performance of the AUGRRE by using different shrinkage parameters is compared with the existing GRRE and maximum likelihood estimator. A Monte Carlo simulation is carried out to assess the performance of the estimators where the bias and mean squared error performance criteria are used. We also used a real-life dataset to demonstrate the benefit of the proposed estimators. The simulation and real-life example results show the superiority of AUGRRE over the GRRE and the maximum likelihood estimator for the gamma regression model with collinear explanatory variables.

Effects of a multifactorial intervention for improving frailty on risk of long-term care insurance certification, death, and long-term care cost among community-dwelling older adults: A quasi-experimental study using propensity score matching

Objectives To examine the effects of a multifactorial intervention for improving frailty-comprising resistance exercise and nutritional and psychosocial programs-on the risk of long-term care insurance (LTCI) certification, death, and long-term care (LTC) cost among community-dwelling older adults.Methods Seventy-seven individuals (47 in 2011 and 30 in 2013) from the Hatoyama Cohort Study (742 individuals) participated in a multifactorial intervention. Non-participants were from the same cohort (including people who were invited to participate in the multifactorial intervention but declined). We performed propensity score matching with a ratio of 1 : 2 (intervention group vs. non-participant group). Afterward, 70 individuals undergoing the multifactorial intervention and 140 non-participants were selected. The risk of LTCI certification and/or death and the mean LTC cost during the follow-up period (32 months) were compared using the Cox proportional hazards model and generalized linear model (gamma regression model).Results The incidence of new LTCI certification (per 1,000 person-years) tended to be lower in the intervention group than in the non-participant group (1.8 vs. 3.6), but this was not statistically significant as per the Cox proportional hazards model (hazard ratio=0.51, 95% confidence interval [CI]=0.17-1.54). Although the incidence of LTC cost was not significant, the mean cumulative LTC cost during the 32 months and the mean LTC cost per unit during the follow-up period (1 month) were 375,308 JPY and 11,906 JPY/month, respectively, in the intervention group and 1,040,727 JPY and 33,460 JPY/month, respectively, in the non-participant group. Cost tended to be lower in the intervention group than in the non-participant group as per the gamma regression model (cumulative LTC cost: cost ratio=0.36, 95%CI=0.11-1.21, P=0.099; LTC cost per unit follow-up period: cost ratio=0.36, 95%CI=0.11-1.12, P=0.076).Conclusions These results suggest that a multifactorial intervention comprising resistance exercise, nutritional, and psychosocial programs is effective in lowering the incidence of LTCI certification, consequently saving LTC cost, although the results were not statistically significant. Further research with a stricter study design is needed.

The extended gamma distribution with regression model and applications

<abstract> <p>This paper introduces a new extension of the gamma distribution, named as a <italic>new extended gamma</italic> distribution, via mixture representation of xgamma and gamma distributions. The statistical properties of the proposed distribution are derived such as moment generating and characteristic functions, variance, skewness, and kurtosis measures, Lorenz curve, and mean residual life function. The maximum likelihood, parametric bootstrap, method of moments, least squares, and weighted least squares estimation methods are considered to obtain the unknown model parameters. The finite sample performance of estimation methods is discussed via a simulation study. Using the proposed distribution, we propose a new regression model for the right-skewed response variable as an alternative to the gamma regression model. Two real data sets are analyzed to convince the readers for the usefulness of the proposed model.</p> </abstract>

Adaptive Estimation Strategies in Gamma Regression Model

In this study, we considered parameter estimation and inference in the gamma regression model when there exist many covariates, some of which may be treated as a nuisance. We proposed novel estimators based on the pretest and shrinkage strategies and used these to improve the efficiency of estimation. Their asymptotic properties were established. The performance of the proposed estimators was compared with that of the classical estimator through Monte Carlo simulations and application to a real dataset. The pretest and shrinkage estimation strategies were shown to perform well in terms of both parameter estimation and predictive power.

Weighted-exponential regression model: An alternative to the gamma regression model

In this study, weighted-exponential regression model is proposed for modeling the right-skewed response variable as an alternative to the gamma regression model. The maximum likelihood, method of moments, least-squares and weighted least-squares estimation methods are used to estimate unknown parameters of re-parametrized weighted-exponential distribution. The simulation study is conducted to compare the efficiencies of parameter estimation methods. An application on coalition duration dataset is given to demonstrate the usefulness of proposed regression model against the gamma regression model. The residual analysis is performed to evaluate the accuracy of the fitted model. Empirical findings show that the weighted-exponential regression model provides better fits than the gamma regression model and could be a good choice for modeling the right-skewed response variable.

Modified likelihood ratio tests for unit gamma regressions

Regression analyses are commonly performed with doubly limited continuous dependent variables; for instance, when modeling the behavior of rates, proportions and income concentration indices. Several models are available in the literature for use with such variables, one of them being the unit gamma regression model. In all such models, parameter estimation is typically performed using the maximum likelihood method and testing inferences on the model's parameters are usually based on the likelihood ratio test. Such a test can, however, deliver quite imprecise inferences when the sample size is small. In this paper, we propose two modified likelihood ratio test statistics for use with the unit gamma regressions that deliver much more accurate inferences when the number of data points in small. Numerical (i.e. simulation) evidence is presented for both fixed dispersion and varying dispersion models, and also for tests that involve nonnested models. We also present and discuss two empirical applications.

Estimation of lacunarity using gamma regression model

In this study we evaluate estimated lacunarity in three different databases using the power (standard) and gamma model. Results showed that estimates of lacunarity using gamma regression model was superior to those with the power regression model. The gamma regression model had a higher coefficient of model determination than the power regression model for all three used databases and, additionally, had smaller sums of residuals squared. The Gamma model was chosen the most appropriate model for lacunarity estimates.

Performance of Asar and Genç and Huang and Yang’s Two-Parameter Estimation Methods for the Gamma Regression Model

This study assesses the performance of two-parameter estimation methods to combat multicollinearity in the Gamma regression model. We derived optimal values for two-parameter estimation methods in the Gamma regression model. Furthermore, we proposed some estimation methods to estimate the shrinkage parameters and these methods improve the efficiency of the two-parameter estimator. We compare the performance of these estimators by means of Monte Carlo simulation study where the mean squared error (MSE) is considered as a performance criterion. Finally, consider a reaction rate data to evaluate the performance of the estimators. The simulation and numerical example results showed that the two-parameter biased estimators have smaller MSE than the maximum likelihood estimator under certain conditions.

Hierarchical Bayesian models for continuous and positively skewed data from small areas

There are numerous types of continuous and positively skewed data. We develop a hierarchical Bayesian generalized gamma regression model for continuous and positively skewed data. For skewed data, the log-transformation is one of the widely used transformation to meet the normality assumption. However, log-transformation could be problematic, so we use a generalized gamma distribution instead. Because the posterior distribution corresponding to this model is complex, we have used a second order Taylor’s series to obtain approximate multivariate normal distributions, which provide proposal densities for Metropolis samplers. We have applied our models to consumption data from a national household survey and chose the best-fitted model among the generalized gamma distribution and two special cases, the gamma and the exponential distributions. It is then linked to census data to provide small area estimates for poverty indicators. A simulation study shows that our methodology is reasonable.

Stein-type shrinkage estimators in gamma regression model with application to prostate cancer data.

Gamma regression is applied in several areas such as life testing, forecasting cancer incidences, genomics, rainfall prediction, experimental designs, and quality control. Gamma regression models allow for a monotone and no constant hazard in survival models. Owing to the broad applicability of gamma regression, we propose some novel and improved methods to estimate the coefficients of gamma regression model. We combine the unrestricted maximum likelihood (ML) estimators and the estimators that are restricted by linear hypothesis, and we present Stein-type shrinkage estimators (SEs). We then develop an asymptotic theory for SEs and obtain their asymptotic quadratic risks. In addition, we conduct Monte Carlo simulations to study the performance of the estimators in terms of their simulated relative efficiencies. It is evident from our studies that the proposed SEs outperform the usual ML estimators. Furthermore, some tabular and graphical representations are given as proofs of our assertions. This study is finally ended by appraising the performance of our estimators for a real prostate cancer data.