Gamma Regression Model Research Articles

Temporal Incidence and Prevalence Trends of Multiple Sclerosis in Markazi Province, Iran

BackgroundThe epidemiology of multiple sclerosis (MS) exhibits significant variability all over the world. Additionally, the incidence and prevalence of the disease are geographically diverse in the different provinces of Iran. ObjectivesDue to the lack of a research about the epidemiology of MS in the Markazi province of Iran, the present study aimed to estimate its prevalence and incidence in this province. MethodsThis cross-sectional register study was conducted according to the data related to the MS Society of Markazi province. The inclusion criteria were definite MS during 2010–2019, residence in Markazi province, and membership in the MS society of Markazi province. The annual incidence and prevalence of MS (per 100,000 person-years) were computed by sex and age groups. Further, age-standardized prevalence and incidence rates were calculated based on the Iranian population. A gamma regression model with log link was utilized for comparing the rates over time statistically. The prevalence and incidence rates were computed by using Excel, and R 4.0.5 was applied to fit the gamma model. ResultsIn the study, the total number of MS cases was 1,391, among whom 1,098 (78.9%) and 293 (21.1%) were females and males, respectively. The onset of MS occurred at the mean (S.D) age of 31.76 (8.98) years with a female/male ratio of 3.75. During the study period (2010–2019), the incidence rate of the disease was on the decline, while the prevalence rate elevated, by indicating a rising trend in MS prevalence in both sexes. ConclusionThe results represented the decreasing and increasing trend of the incidence and prevalence of MS in Markazi province over the recent years. The province is one of the regions with a high prevalence and incidence rate of MS compared to the national and global statistical data.

On the performance of some biased estimators in the gamma regression model: simulation and applications

The gamma regression model is widely applied when the response variable is continuous and positively skewed. In the multicollinearity problem, the usual maximum likelihood estimator is inadequate due to its inflated variance. To reduce this effect, well-known ridge and Liu estimators are generally used. In this study, we propose some shrinkage parameters for the new estimator and compared with some best ridge parameters indicated by Amin et al. [Performance of some ridge estimators for the gamma regression model. Stat Pap. 2020;61:997–1026] and two proposed ridge parameters for the GRM specified by Lukman et al. [A new ridge-type estimator for the gamma regression model. Scientifica. 2021;2021:5545356]. A Monte Carlo simulation study and an empirical application are conducted to assess the effectiveness of the proposed and other estimators. Based on the findings of simulation results and applications, we found that one of our proposed estimators performed the best for small dispersion levels.

Maximum isometric torque at individually-adjusted joint angles exceeds eccentric and concentric torque in lower extremity joint actions

BackgroundPrevious research indicates the high relevance of optimal joint angles for individual isometric strength assessment. The objective was to compare lower limb peak isometric muscle strength abilities at the strongest joint angles with those of dynamic contractions in healthy young adults.MethodsEighteen young male adults performed maximum concentric, isometric, and eccentric contractions of the ankle, knee, and hip flexors and extensors, and hip adductors and abductors in a randomized sequence on an isokinetic dynamometer (ISOMED 2000). Angular velocity was set at 60°/s. The peak of concentric contraction torque curves was used to define optimal joint angles best suited to generate maximum torque during isometric contractions. Maximum voluntary contraction torque of all contraction conditions was adjusted for limb weight and analyzed via a generalized linear mixed gamma regression model (GLMM).ResultsThe gamma GLMM revealed strongly significant effects for all three categorical covariates (contraction types, muscle group, and test order) (p < 2 times 10^{ - 16}). Eccentric contraction increases the muscle torque (hat{beta }_{k} = 0.147) compared to concentric contraction, and isometric contraction even more (hat{beta }_{k} = 0.258). A moderate individual-specific variation was found (random effects standard deviation sigma_{b} = 0.093).ConclusionThe results support the importance of optimal joint angles for isometric maximum strength assessment. When such conditions are given, isometric contractions can produce higher muscle torques than eccentric contractions in the lower body.

Cost-effectiveness of an 8-week supervised education and exercise therapy programme for knee and hip osteoarthritis: a pre–post analysis of 16 255 patients participating in Good Life with osteoArthritis in Denmark (GLA:D)

ObjectivesTo evaluate 1-year cost-effectiveness of an 8-week supervised education and exercise programme delivered in primary care to patients with symptomatic knee or hip osteoarthritis (OA).DesignA registry-based pre–post study linking patient-level...

Influence measures in gamma modified ridge type estimator

Multicollinearity and unusual observations pose threats to the performance of maximum likelihood estimator in the gamma regression model. Literature has shown that both problems can exist simultaneously in a model. Researchers have paid little attention to the detection of influential observation in the gamma regression model with multicollinearity. This study aims to develop statistics for the detection of unusual observation in a multicollinear gamma regression model using gamma modified ridge-type estimator. The performance of the statistics was examined through a Monte Carlo simulation study and two real applications. The results show that gamma modified ridge-type estimator copes with unusual observations by reducing their influence.

A restricted gamma ridge regression estimator combining the gamma ridge regression and the restricted maximum likelihood methods of estimation

In this article, we propose a restricted gamma ridge regression estimator (RGRRE) by combining the gamma ridge regression (GRR) and restricted maximum likelihood estimator (RMLE) to combat multicollinearity problem for estimating the parameter in the gamma regression model. The properties of the new estimator are discussed, and its superiority over the GRR, RMLE and traditional maximum likelihood estimator is theoretically analysed under different conditions. We also suggest some estimating methods to find the optimal value of the shrinkage parameter. A Monte Carlo simulation study is conducted to judge the performance of the proposed estimator. Finally, an empirical application is analysed to show the benefit of RGRRE over the existing estimators.

Parameter estimation and hypothesis testing of geographically and temporally weighted bivariate Gamma regression model

Geographically Weighted Regression (GWR) study potential relationships in regression models that distinguish geographic spaces using non-stationary parameters to overcome spatial effects. The use of gamma regression, namely regression with the dependent variable with a gamma distribution, can be an alternative if the data do not follow a normal distribution. Gamma distribution is a continuous set of non-negative values, generally skewed to the right or positive skewness. Gamma regression is developed to be Bivariate Gamma Regression (BGR) when there are two dependent variables with gamma distribution. If the observation units are location points, spatial effects may occur. The Geographically Weighted Bivariate Gamma Regression (GWBGR) model can be a solution for spatial heterogeneity. However, during its development, many cases require information from panel data. Using panel data can provide complete information because it covers several periods, but it allows for temporal effects. This study developed a Geographically and Temporally Weighted Bivariate Gamma Regression (GTWBGR) model to handle spatial and temporal heterogeneity simultaneously. The estimation of the GTWBGR model parameters uses the Maximum Likelihood Estimation (MLE) method that followed by the numerical iteration of Berndt Hall Hall Hausman (BHHH). The simultaneous testing uses the Maximum Likelihood Ratio Test (MLRT) method to get a test statistic. With a large sample size, the distribution of the test statistic approaches chi-square. Meanwhile, partial testing uses the Z test statistic.

Almost unbiased Liu-type estimators in gamma regression model

The Liu-type estimator has been consistently demonstrated to be an attractive shrinkage method to reduce the effect of multicollinearity problem. It is known that multicollinearity affects the variance of the maximum likelihood estimator negatively in gamma regression model. Therefore, an almost unbiased Liu-type estimator together with a modified version of it is proposed to overcome the multicollinearity problem. The performance of the new estimators is investigated both theoretically and numerically via a Monte Carlo simulation experiment and a real data illustration. Based on the results, it is observed that the proposed estimators can bring significant improvement relative to other competitor estimators.

A new biased estimator for the gamma regression model: Some applications in medical sciences

The Gamma Regression Model (GRM) has a variety of applications in medical sciences and other disciplines. The results of the GRM may be misleading in the presence of multicollinearity. In this article, a new biased estimator called James-Stein estimator is proposed to reduce the impact of correlated regressors for the GRM. The mean squared error (MSE) properties of the proposed estimator are derived and compared with the existing estimators. We conducted a simulation study and employed the MSE and bias evaluation criterion to judge the proposed estimator’s performance. Finally, two medical dataset are considered to show the benefit of the proposed estimator over existing estimators.

Identification of Associated Factors and Prediction for the Level of Intimate Partner Violence against Women in Sri Lanka

Intimate partner violence (IPV) can be defined as a serious social problem rapidly increasing in Sri Lanka as same as in other countries in the world. The Sri Lanka Demographic and Health Survey (SLDHS) 2016 revealed that 17% of married women age 15-49 in Sri Lanka have become victims of IPV. The objectives of this study were to determine the factors associated with IPV against women in Sri Lanka and to develop an appropriate regression model and feedforward neural network (FNN) to predict the Violence Index which describes the level of IPV against women in the country. The data records of 2494 ever-married women that have experienced IPV were considered from Sri Lanka Demographic and Health Survey 2016. The Violence Index was estimated using Multiple Correspondence Analysis. Gamma regression analysis revealed that religion, education level of the woman, husband’s occupation, woman’s married time, the age difference between husband and wife, Empowerment Indicator, enough money for daily household expenses, and household alcohol consumption were significantly associated with IPV against women. The optimum FNN consists of one hidden layer with 3 neurons provided a better prediction on the Violence Index with the minimum mean squared error for the testing set. Based on the prediction accuracy, the FNN was found to be better than the gamma regression model. The findings of this study would support an effort to develop the current policies and implement prevention programs against IPV in Sri Lanka.

The influence of sensory attributes on overall liking by a gamma regression model: an analysis of Cerrado mixed fruits jams

Factors that influence the acceptability and preferences of consumers have been perceived as sensory attributes, such as color, appearance, flavor, and texture. Understanding which attributes are most important for overall liking would be helpful to establish meaningful criteria for product grading. Thus, in addition to the overall chemical and sensory qualities, it is important to appreciate which sensory attributes make a product pleasant or unpleasant to a consumer. In this context, the aim of this study was to evaluate the sensory attribute that contributes most to the overall liking by a gamma regression model using different formulations of mixed fruit jams made with Brazilian Cerrado fruits. Based on the proposed model, we concluded that appearance was the most important predictor of the overall liking of the assessors.

Decreased human respiratory syncytial virus activity during the COVID-19 pandemic in Japan: an ecological time-series analysis

BackgroundNon-pharmaceutical interventions (NPIs), such as sanitary measures and travel restrictions, aimed at controlling the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), may affect the transmission dynamics of human respiratory syncytial virus (HRSV). We aimed to quantify the contribution of the sales of hand hygiene products and the number of international and domestic airline passenger arrivals on HRSV epidemic in Japan.MethodsThe monthly number of HRSV cases per sentinel site (HRSV activity) in 2020 was compared with the average of the corresponding period in the previous 6 years (from January 2014 to December 2020) using a monthly paired t-test. A generalized linear gamma regression model was used to regress the time-series of the monthly HRSV activity against NPI indicators, including sale of hand hygiene products and the number of domestic and international airline passengers, while controlling for meteorological conditions (monthly average temperature and relative humidity) and seasonal variations between years (2014–2020).ResultsThe average number of monthly HRSV case notifications in 2020 decreased by approximately 85% (p < 0.001) compared to those in the preceding 6 years (2014–2019). For every average ¥1 billion (approximately £680,000/$9,000,000) spent on hand hygiene products during the current month and 1 month before there was a 0.29% (p = 0.003) decrease in HRSV infections. An increase of average 1000 domestic and international airline passenger arrivals during the previous 1–2 months was associated with a 3.8 × 10− 4% (p < 0.001) and 1.2 × 10− 3% (p < 0.001) increase in the monthly number of HRSV infections, respectively.ConclusionsThis study suggests that there is an association between the decrease in the monthly number of HRSV cases and improved hygiene and sanitary measures and travel restrictions for COVID-19 in Japan, indicating that these public health interventions can contribute to the suppression of HRSV activity. These findings may help in public health policy and decision making.

The Log-Kumaraswamy Generalized Gamma Regression Model with Application to Chemical Dependency Data

The five parameter Kumaraswamy generalized gamma model (Pas coa et al., 2011) includes some important distributions as special cases and it is very useful for modeling lifetime data. We propose an extended version of this distribution by assuming that a shape parameter can take negative values. The new distribution can accommodate increasing, decreasing, bath tub and unimodal shaped hazard functions. A second advantage is that it also includes as special models reciprocal distributions such as the recipro cal gamma and reciprocal Weibull distributions. A third advantage is that it can represent the error distribution for the log-Kumaraswamy general ized gamma regression model. We provide a mathematical treatment of the new distribution including explicit expressions for moments, generating function, mean deviations and order statistics. We obtain the moments of the log-transformed distribution. The new regression model can be used more effectively in the analysis of survival data since it includes as sub models several widely-known regression models. The method of maximum likelihood and a Bayesian procedure are used for estimating the model pa rameters for censored data. Overall, the new regression model is very useful to the analysis of real data.

On the generalized biased estimators for the gamma regression model: methods and applications

The gamma regression model (GRM) is commonly used if the response variable is continuous and positively skewed. In the existence of multicollinearity problem, maximum likelihood estimator (MLE) is inadequate for estimating the GRM coefficients. To avoid this issue, well-known estimators such as, ridge and Liu are generally used. In this study, we propose the generalized class of biased estimators, namely generalized ridge, and generalized Liu estimators for the GRM with correlated explanatory variables. The standard properties of the proposed estimators are derived and illustrated using Monte Carlo simulation study and two real applications where mean squared error is considered as an assessment criterion. Based on the findings of simulation and empirical applications, we found that the performance of the generalized gamma ridge regression estimator is better as compared to MLE, and generalized gamma Liu estimator.

A New Ridge-Type Estimator for the Gamma Regression Model.

The known linear regression model (LRM) is used mostly for modelling the QSAR relationship between the response variable (biological activity) and one or more physiochemical or structural properties which serve as the explanatory variables mainly when the distribution of the response variable is normal. The gamma regression model is employed often for a skewed dependent variable. The parameters in both models are estimated using the maximum likelihood estimator (MLE). However, the MLE becomes unstable in the presence of multicollinearity for both models. In this study, we propose a new estimator and suggest some biasing parameters to estimate the regression parameter for the gamma regression model when there is multicollinearity. A simulation study and a real-life application were performed for evaluating the estimators' performance via the mean squared error criterion. The results from simulation and the real-life application revealed that the proposed gamma estimator produced lower MSE values than other considered estimators.

Variable selection in gamma regression model using chaotic firefly algorithm with application in chemometrics

Variable selection is a very helpful procedure for improving computational speed and prediction accuracy by identifying the most important variables that related to the response variable. Regression modeling has received much attention in several science fields. Firefly algorithm is one of the recently efficient proposed nature-inspired algorithms that can efficiently be employed for variable selection. In this work, chaotic firefly algorithm is proposed to perform variable selection for gamma regression model. A real data application related to the chemometrics is conducted to evaluate the performance of the proposed method in terms of prediction accuracy and variable selection criteria. Further, its performance is compared with other methods. The results proved the efficiency of our proposed methods and it outperforms other popular methods.

Associations of atmospheric teleconnections with wintertime extratropical cyclones over East Asia and Northwest Pacific

Extratropical cyclones (ETCs) over East Asia and Northwest Pacific are identified and tracked by applying an objective algorithm to the 850-hPa relative vorticity fields from the ERA-Interim reanalysis. A total of 2866 ETCs originating at the western side of the date line have been identified in the extended November–March winters from 1979 to 2018. The ETC tracks are counted and visualized using a hexagonal tessellation rather than the regular longitude–latitude grids. Two generalized linear models (GLMs), Poisson regression model and Gamma regression model, are firstly applied to investigate the associations of wintertime ETCs with three atmospheric teleconnection patterns. The West Pacific (WP) pattern and the Pacific/North American (PNA) pattern are more responsible for the meridional variability of ETC activities in the North Pacific, while the influence of the Polar/Eurasia pattern on ETC activities is negligible. Results of composite analysis are qualitatively consistent with that of regression analysis. Composite maps of differences of jet stream, thermal gradient and mid-tropospheric baroclinicity in the positive and negative phases of teleconnection patterns also support the close associations of ETC activities with WP and PNA teleconnection patterns.

The Log-Kumaraswamy Generalized Gamma Regression Model with Application to Chemical Dependency Data

The Log-Kumaraswamy Generalized Gamma Regression Model with Application to Chemical Dependency Data

A New Class of Survival Regression Models with Cure Fraction

In this paper, we propose a flexible cure rate survival model by assuming that the number of competing causes of the event of interest follows the negative binomial distribution and the time to event follows a generalized gamma distribution. We define the negative binomial-generalized gamma distribution, which can be used to model survival data. The new model includes as special cases some of the well-known cure rate models discussed in the literature. We consider a frequentist analysis and nonparametric bootstrap for parameter estimation of a negative binomial-generalized gamma regression model with cure rate. Then, we derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes and present some ways to perform global influence analysis. Finally, we analyze a real data set from the medical area.

Residual and local influence analyses for unit gamma regressions

AbstractWe obtain local influence measures and residuals for the unit gamma regression model. In particular, we introduce four residuals that are based on Fisher's iterative scoring parameter estimation algorithm and develop local influence analysis based on several different perturbation schemes: cases weighting, response additive perturbation, and covariate(s) additive perturbation. An empirical application in which variables related to education and investment in research and development are used to explain the proportion of nonpoor people in a set of countries is presented and discussed. Residual and local influence analyses show that the unit gamma regression model yields a good fit to the data, even outperforming the beta regression model. The diagnostic analysis singles out countries whose data are worthy of further investigation. Our results reveal that lower poverty levels are associated with higher shares of investment in high technology. The statistical significance of such a relationship is not sensitive to atypical data points.