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Journal articles on the topic 'Models of generalized estimating equations'

Author: Grafiati

Published: 25 May 2024

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1

Vens, M., and A. Ziegler. "Generalized Estimating Equations." Methods of Information in Medicine 49, no. 05 (2010): 421–25. http://dx.doi.org/10.3414/me10-01-0026.

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Summary Background: Generalized estimating equations (GEE) are an extension of generalized linear models (GLM) in that they allow adjusting for correlations between observations. A major strength of GEE is that they do not require the correct specification of the multivariate distribution but only of the mean structure. Objectives: Several concerns have been raised about the validity of GEE when applied to dichotomous dependent variables. In this contribution, we summarize the theoretical findings concerning efficiency and validity of GEE. Methods: We introduce the GEE in a formal way, summari

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2

Feddag, Mohand-Larbi, Ion Grama, and Mounir Mesbah. "Generalized Estimating Equations (GEE) for Mixed Logistic Models." Communications in Statistics - Theory and Methods 32, no. 4 (2003): 851–74. http://dx.doi.org/10.1081/sta-120018833.

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Lo, Chi Ho, Wing Kam Fung, and Zhong Yi Zhu. "Structural Parameter Estimation Using Generalized Estimating Equations for Regression Credibility Models." ASTIN Bulletin 37, no. 02 (2007): 323–43. http://dx.doi.org/10.2143/ast.37.2.2024070.

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A generalized estimating equations (GEE) approach is developed to estimate structural parameters of a regression credibility model with independent or moving average errors. A comprehensive account is given to illustrate how GEE estimators are worked out within an extended Hachemeister (1975) framework. Evidenced by results of simulation studies, the proposed GEE estimators appear to outperform those given by Hachemeister, and have led to a remarkable improvement in accuracy of the credibility estimators so constructed.

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Lo, Chi Ho, Wing Kam Fung, and Zhong Yi Zhu. "Structural Parameter Estimation Using Generalized Estimating Equations for Regression Credibility Models." ASTIN Bulletin 37, no. 2 (2007): 323–43. http://dx.doi.org/10.1017/s0515036100014896.

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A generalized estimating equations (GEE) approach is developed to estimate structural parameters of a regression credibility model with independent or moving average errors. A comprehensive account is given to illustrate how GEE estimators are worked out within an extended Hachemeister (1975) framework. Evidenced by results of simulation studies, the proposed GEE estimators appear to outperform those given by Hachemeister, and have led to a remarkable improvement in accuracy of the credibility estimators so constructed.

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5

Breitung, J., N. R. Chaganty, R. M. Daniel, et al. "Discussion of “Generalized Estimating Equations: Notes on the Choice of the Working Correlation Matrix”." Methods of Information in Medicine 49, no. 05 (2010): 426–32. http://dx.doi.org/10.1055/s-0038-1625133.

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Summary Objective: To discuss generalized estimating equations as an extension of generalized linear models by commenting on the paper of Ziegler and Vens “Generalized Estimating Equations: Notes on the Choice of the Working Correlation Matrix”. Methods: Inviting an international group of experts to comment on this paper. Results: Several perspectives have been taken by the discussants. Econometricians have established parallels to the generalized method of moments (GMM). Statisticians discussed model assumptions and the aspect of missing data. Applied statisticians commented on practical aspe

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Zubair, Seema, and Sanjoy K. Sinha. "Marginal models for longitudinal count data with dropouts." Journal of Statistical Research 54, no. 1 (2020): 27–42. http://dx.doi.org/10.47302/jsr.2020540102.

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In this article, we investigate marginal models for analyzing incomplete longitudinal count data with dropouts. Specifically, we explore commonly used generalized estimating equations and weighted generalized estimating equations for fitting log-linear models to count data in the presence of monotone missing responses. A series of simulations were carried out to examine the finite-sample properties of the estimators in the presence of both correctly specified and misspecified dropout mechanisms. An application is provided using actual longitudinal survey data from the Health and Retirement Stu

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Ma, Yanyuan, and Marc G. Genton. "Explicit estimating equations for semiparametric generalized linear latent variable models." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 72, no. 4 (2010): 475–95. http://dx.doi.org/10.1111/j.1467-9868.2010.00741.x.

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Corrente, JosÉ Eduardo, and Maria Del Pilar DÍAz. "Ordinal models and generalized estimating equations to evaluate disease severity." Journal of Applied Statistics 30, no. 4 (2003): 425–39. http://dx.doi.org/10.1080/0266476032000035458.

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Koper, Nicola, and Micheline Manseau. "Generalized estimating equations and generalized linear mixed-effects models for modelling resource selection." Journal of Applied Ecology 46, no. 3 (2009): 590–99. http://dx.doi.org/10.1111/j.1365-2664.2009.01642.x.

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10

Nikita, Efthymia. "The use of generalized linear models and generalized estimating equations in bioarchaeological studies." American Journal of Physical Anthropology 153, no. 3 (2013): 473–83. http://dx.doi.org/10.1002/ajpa.22448.

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11

Danlami, Nasiru, Madzlan Napiah, Ahmad Farhan M. Sadullah, and Nura Bala. "Estimating Annual Road Deaths: Comparison Between Temporal Causal Models and Generalized Estimating Equations." Advanced Science Letters 24, no. 11 (2018): 8679–82. http://dx.doi.org/10.1166/asl.2018.12323.

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12

Ristl, Robin, Ludwig Hothorn, Christian Ritz, and Martin Posch. "Simultaneous inference for multiple marginal generalized estimating equation models." Statistical Methods in Medical Research 29, no. 6 (2019): 1746–62. http://dx.doi.org/10.1177/0962280219873005.

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Motivated by small-sample studies in ophthalmology and dermatology, we study the problem of simultaneous inference for multiple endpoints in the presence of repeated observations. We propose a framework in which a generalized estimating equation model is fit for each endpoint marginally, taking into account dependencies within the same subject. The asymptotic joint normality of the stacked vector of marginal estimating equations is used to derive Wald-type simultaneous confidence intervals and hypothesis tests for multiple linear contrasts of regression coefficients of the multiple marginal mo

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Hwang, Heungsun, and Yoshio Takane. "Estimation of Growth Curve Models with Structured Error Covariances by Generalized Estimating Equations." Behaviormetrika 32, no. 2 (2005): 155–63. http://dx.doi.org/10.2333/bhmk.32.155.

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14

Vantas, Konstantinos, Epaminondas Sidiropoulos, and Chris Evangelides. "Estimating Rainfall Erosivity from Daily Precipitation Using Generalized Additive Models." Environmental Sciences Proceedings 2, no. 1 (2020): 21. http://dx.doi.org/10.3390/environsciproc2020002021.

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One of the most important natural processes responsible for soil loss is rainfall-induced erosion. The calculation of rainfall erosivity, as defined in the Universal Soil Loss Equation, requires the availability of rainfall data, either continuous breakpoint, or pluviograph, with sampling intervals on the order of minutes. Due to the limited temporal coverage and spatial scarcity of such data, worldwide, alternative equations have been developed that utilize coarser rainfall records, in an effort to estimate erosivity equivalently to that calculated using pluviograph data. This paper presents

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15

Vonesh, Edward F., Hao Wang, Lei Nie, and Dibyen Majumdar. "Conditional Second-Order Generalized Estimating Equations for Generalized Linear and Nonlinear Mixed-Effects Models." Journal of the American Statistical Association 97, no. 457 (2002): 271–83. http://dx.doi.org/10.1198/016214502753479400.

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Johnson, Timothy R., and Jee-Seon Kim. "A generalized estimating equations approach to mixed-effects ordinal probit models." British Journal of Mathematical and Statistical Psychology 57, no. 2 (2004): 295–310. http://dx.doi.org/10.1348/0007110042307177.

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Akanda, Md Abdus Salam, and Russell Alpizar-Jara. "A generalized estimating equations approach for capture–recapture closed population models." Environmental and Ecological Statistics 21, no. 4 (2014): 667–88. http://dx.doi.org/10.1007/s10651-014-0274-7.

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18

Kundu, Prosenjit, Runlong Tang, and Nilanjan Chatterjee. "Generalized meta-analysis for multiple regression models across studies with disparate covariate information." Biometrika 106, no. 3 (2019): 567–85. http://dx.doi.org/10.1093/biomet/asz030.

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Summary Meta-analysis is widely popular for synthesizing information on common parameters of interest across multiple studies because of its logistical convenience and statistical efficiency. We develop a generalized meta-analysis approach to combining information on multivariate regression parameters across multiple studies that have varying levels of covariate information. Using algebraic relationships among regression parameters in different dimensions, we specify a set of moment equations for estimating parameters of a maximal model through information available from sets of parameter esti

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19

Schluchter, Mark D. "Flexible Approaches to Computing Mediated Effects in Generalized Linear Models: Generalized Estimating Equations and Bootstrapping." Multivariate Behavioral Research 43, no. 2 (2008): 268–88. http://dx.doi.org/10.1080/00273170802034877.

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20

Lo, Chi Ho, Wing Kam Fung, and Zhong Yi Zhu. "Generalized estimating equations for variance and covariance parameters in regression credibility models." Insurance: Mathematics and Economics 39, no. 1 (2006): 99–113. http://dx.doi.org/10.1016/j.insmatheco.2006.01.006.

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21

Sherman, Michael, and Saskia le Cessie. "A comparison between bootstrap methods and generalized estimating equations for correlated outcomes in generalized linear models." Communications in Statistics - Simulation and Computation 26, no. 3 (1997): 901–25. http://dx.doi.org/10.1080/03610919708813417.

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22

Wang, Xi, and Vernon M. Chinchilli. "Analysis of crossover designs for longitudinal binary data with ignorable and nonignorable dropout." Statistical Methods in Medical Research 31, no. 1 (2021): 119–38. http://dx.doi.org/10.1177/09622802211047177.

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Longitudinal binary data in crossover designs with missing data due to ignorable and nonignorable dropout is common. This paper evaluates available conditional and marginal models and establishes the relationship between the conditional and marginal parameters with the primary objective of comparing the treatment mean effects. We perform extensive simulation studies to investigate these models under complete data and the selection models under missing data with different parametric distributions and missingness patterns and mechanisms. The generalized estimating equations and the generalized l

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23

Lange, Christoph, John C. Whittaker, and Alex J. Macgregor. "Generalized estimating equations: A hybrid approach for mean parameters in multivariate regression models." Statistical Modelling: An International Journal 2, no. 3 (2002): 163–81. http://dx.doi.org/10.1191/1471082x02st031oa.

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Niu, Yi, Xiaoguang Wang, Hui Cao, and Yingwei Peng. "Variable selection via penalized generalized estimating equations for a marginal survival model." Statistical Methods in Medical Research 29, no. 9 (2020): 2493–506. http://dx.doi.org/10.1177/0962280220901728.

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Clustered and multivariate survival times, such as times to recurrent events, commonly arise in biomedical and health research, and marginal survival models are often used to model such data. When a large number of predictors are available, variable selection is always an important issue when modeling such data with a survival model. We consider a Cox’s proportional hazards model for a marginal survival model. Under the sparsity assumption, we propose a penalized generalized estimating equation approach to select important variables and to estimate regression coefficients simultaneously in the

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25

Morley, Clive L. "A Comparison of Three Methods for Estimating Tourism Demand Models." Tourism Economics 2, no. 3 (1996): 223–34. http://dx.doi.org/10.1177/135481669600200302.

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Estimation of tourism demand models involves a set of related equations with errors which may not satisfy the common assumptions of regression modelling. Results from a simulation exercise show that, for the error types and small samples considered, the Generalized Method of Moments is less accurate on average than the Ordinary Least Squares and Seemingly Unrelated Regression methods, which had very similar accuracies. Overall, the Ordinary Least Squares technique performs well and the results give little reason to use the more complex estimation techniques.

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Hooker, Giles, Stephen P. Ellner, Laura De Vargas Roditi, and David J. D. Earn. "Parameterizing state–space models for infectious disease dynamics by generalized profiling: measles in Ontario." Journal of The Royal Society Interface 8, no. 60 (2010): 961–74. http://dx.doi.org/10.1098/rsif.2010.0412.

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Parameter estimation for infectious disease models is important for basic understanding (e.g. to identify major transmission pathways), for forecasting emerging epidemics, and for designing control measures. Differential equation models are often used, but statistical inference for differential equations suffers from numerical challenges and poor agreement between observational data and deterministic models. Accounting for these departures via stochastic model terms requires full specification of the probabilistic dynamics, and computationally demanding estimation methods. Here, we demonstrate

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27

Xiong, Nina, Yue Qiao, Huiru Ren, Li Zhang, Rihui Chen, and Jia Wang. "Comparison of Parameter Estimation Methods Based on Two Additive Biomass Models with Small Samples." Forests 14, no. 8 (2023): 1655. http://dx.doi.org/10.3390/f14081655.

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Accurately estimating tree biomass is crucial for monitoring and managing forest resources, and understanding regional climate change and material cycles. The additive model system has proven reliable for biomass estimation in Chinese forestry since it considers the inherent correlation among variables based on allometric equations. However, due to the increasing difficulty of obtaining a substantial amount of sample data, estimating parameters for the additive model equations becomes a formidable challenge when working with limited sample sizes. This study primarily focuses on analyzing these

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28

Jentsch, Carsten, and Lena Reichmann. "Generalized Binary Time Series Models." Econometrics 7, no. 4 (2019): 47. http://dx.doi.org/10.3390/econometrics7040047.

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The serial dependence of categorical data is commonly described using Markovian models. Such models are very flexible, but they can suffer from a huge number of parameters if the state space or the model order becomes large. To address the problem of a large number of model parameters, the class of (new) discrete autoregressive moving-average (NDARMA) models has been proposed as a parsimonious alternative to Markov models. However, NDARMA models do not allow any negative model parameters, which might be a severe drawback in practical applications. In particular, this model class cannot capture

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29

Westgate, Philip M. "A readily available improvement over method of moments for intra-cluster correlation estimation in the context of cluster randomized trials and fitting a GEE–type marginal model for binary outcomes." Clinical Trials 16, no. 1 (2018): 41–51. http://dx.doi.org/10.1177/1740774518803635.

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Background/aims Cluster randomized trials are popular in health-related research due to the need or desire to randomize clusters of subjects to different trial arms as opposed to randomizing each subject individually. As outcomes from subjects within the same cluster tend to be more alike than outcomes from subjects within other clusters, an exchangeable correlation arises that is measured via the intra-cluster correlation coefficient. Intra-cluster correlation coefficient estimation is especially important due to the increasing awareness of the need to publish such values from studies in orde

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30

Zhang, Zhigang. "Linear transformation models for interval-censored data." Statistical Modelling 9, no. 4 (2009): 321–43. http://dx.doi.org/10.1177/1471082x0900900404.

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In statistical analysis, when the value of a random variable is only known to be between two bounds, we say that this random variable is interval censored. This complicated censoring pattern is a common problem in research fields such as clinical trials or actuarial studies and raises challenges for statistical analysis. In this paper, we focus on regression analysis of case 2 interval-censored data. We first briefly review existing regression methods and an estimation approach under the class of linear transformation models developed by Zhang et al. We then propose a method for survival proba

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Lord, Dominique, and Bhagwant N. Persaud. "Accident Prediction Models With and Without Trend: Application of the Generalized Estimating Equations Procedure." Transportation Research Record: Journal of the Transportation Research Board 1717, no. 1 (2000): 102–8. http://dx.doi.org/10.3141/1717-13.

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Accident prediction models (APMs) are useful tools for estimating the expected number of accidents on entities such as intersections and road sections. These estimates typically are used in the identification of sites for possible safety treatment and in the evaluation of such treatments. An APM is, in essence, a mathematical equation that expresses the average accident frequency of a site as a function of traffic flow and other site characteristics. The reliability of an APM estimate is enhanced if the APM is based on data for as many years as possible, especially if data for those same years

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32

Yan, Jun, Robert H. Aseltine, and Ofer Harel. "Comparing Regression Coefficients Between Nested Linear Models for Clustered Data With Generalized Estimating Equations." Journal of Educational and Behavioral Statistics 38, no. 2 (2013): 172–89. http://dx.doi.org/10.3102/1076998611432175.

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33

Lv, Jing, Hu Yang, and Chaohui Guo. "Smoothing combined generalized estimating equations in quantile partially linear additive models with longitudinal data." Computational Statistics 31, no. 3 (2015): 1203–34. http://dx.doi.org/10.1007/s00180-015-0612-8.

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34

M, Amany, Mousa, Ahmed A, El sheikh, Fatma El Zahraa S. Salama, and Ahmed M. Gad. "Reviewing of Different Methods for Handling Longitudinal Count data." Journal of University of Shanghai for Science and Technology 23, no. 08 (2021): 195–206. http://dx.doi.org/10.51201/jusst/21/08349.

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In this paper, we will review the methods that used to handle longitudinal data in the case of marginal models when inferences about the population average are the primary focus [1] or when future applications of the results require the expectation of the response as a function of the current covariates [7]. We will review the generalized estimating equations method (GEE), quadratic inference functions (QIF), generalized quasi likelihood (GQL) and the generalized method of moments (GMM). These methods will be reviewed by discussing its advantages and disadvantages in more details.

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35

Engle, Robert F., and Kenneth F. Kroner. "Multivariate Simultaneous Generalized ARCH." Econometric Theory 11, no. 1 (1995): 122–50. http://dx.doi.org/10.1017/s0266466600009063.

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This paper presents theoretical results on the formulation and estimation of multivariate generalized ARCH models within simultaneous equations systems. A new parameterization of the multivariate ARCH process is proposed, and equivalence relations are discussed for the various ARCH parameterizations. Constraints sufficient to guarantee the positive definiteness of the conditional covariance matrices are developed, and necessary and sufficient conditions for covariance stationarity are presented. Identification and maximum likelihood estimation of the parameters in the simultaneous equations co

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36

Bravo, Francesco. "Robust estimation and inference for general varying coefficient models with missing observations." TEST 29, no. 4 (2019): 966–88. http://dx.doi.org/10.1007/s11749-019-00692-0.

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AbstractThis paper considers estimation and inference for a class of varying coefficient models in which some of the responses and some of the covariates are missing at random and outliers are present. The paper proposes two general estimators—and a computationally attractive and asymptotically equivalent one-step version of them—that combine inverse probability weighting and robust local linear estimation. The paper also considers inference for the unknown infinite-dimensional parameter and proposes two Wald statistics that are shown to have power under a sequence of local Pitman drifts and a

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37

Koper, Nicola, and Micheline Manseau. "A guide to developing resource selection functions from telemetry data using generalized estimating equations and generalized linear mixed models." Rangifer 32, no. 2 (2012): 195. http://dx.doi.org/10.7557/2.32.2.2269.

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Resource selection functions (RSF) are often developed using satellite (ARGOS) or Global Positioning System (GPS) telemetry datasets, which provide a large amount of highly correlated data. We discuss and compare the use of generalized linear mixed-effects models (GLMM) and generalized estimating equations (GEE) for using this type of data to develop RSFs. GLMMs directly model differences among caribou, while GEEs depend on an adjustment of the standard error to compensate for correlation of data points within individuals. Empirical standard errors, rather than model-based standard errors, mus

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38

France, J., J. Dijkstra, M. S. Dhanoa, S. Lopez, and A. Bannink. "Estimating the extent of degradation of ruminant feeds from a description of their gas production profiles observed in vitro:derivation of models and other mathematical considerations." British Journal of Nutrition 83, no. 2 (2000): 143–50. http://dx.doi.org/10.1017/s0007114500000180.

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Equations to describe gas production profiles, obtained using manual or automated systems for in vitro fermentation of ruminant feeds, were derived from first principles by considering a simple three-pool scheme. The pools represented were the potentially degradable and undegradable feed fractions, and accumulated gases. The equations derived and investigated mathematically were the generalized Mitscherlich, generalized Michaelis–Menten, Gompertz, and logistic. They were obtained by allowing the fractional rate of degradation to vary with time. The equations permit the extent of ruminal degrad

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39

Ma, Shujie. "Two-step spline estimating equations for generalized additive partially linear models with large cluster sizes." Annals of Statistics 40, no. 6 (2012): 2943–72. http://dx.doi.org/10.1214/12-aos1056.

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40

Bartlett, Roy F., and Brajendra C. Sutradhar. "On estimating equations for parameters in generalized linear mixed models with application to binary data." Environmetrics 10, no. 6 (1999): 769–84. http://dx.doi.org/10.1002/(sici)1099-095x(199911/12)10:6<769::aid-env389>3.0.co;2-z.

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41

Rochon, J., I. R. König, A. Ziegler, and G. Dahmen. "Sample Size Calculations for Controlled Clinical Trials Using Generalized Estimating Equations (GEE)." Methods of Information in Medicine 43, no. 05 (2004): 451–56. http://dx.doi.org/10.1055/s-0038-1633896.

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Summary Objectives: Clinical trials with correlated response data based on generalized estimating equations (GEE) have become increasingly popular as they require smaller samples than classical methods that ignore the clustered nature of the data. We have recently derived the recommendation to use the independence estimating equations (IEE) as primary analysis in most controlled clinical trials instead of GEE with estimated correlations [1]. Although several approaches for sample size and power calculation have been proposed, we have shown that most of these procedures are very specific and no

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42

Vujačić, Ivan, Seyed Mahdi Mahmoudi, and Ernst Wit. "Generalized Tikhonov regularization in estimation of ordinary differential equations models." Stat 5, no. 1 (2016): 132–43. http://dx.doi.org/10.1002/sta4.111.

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43

Miroshnychenko, V. "Generalized least squares estimates for mixture of nonlinear regressions." Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, no. 3 (2018): 25–29. http://dx.doi.org/10.17721/1812-5409.2018/3.3.

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We consider data in which each observed subject belongs to one of different subpopulations (components). The true number of component which a subject belongs to is unknown, but the researcher knows the probabilities that a subject belongs to a given component (concentration of the component in the mixture). The concentrations are different for different observations. So the distribution of the observed data is a mixture of components’ distributions with varying concentrations. A set of variables is observed for each subject. Dependence between these variables is described by a nonlinear regres

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Scott, JoAnna M., Allan deCamp, Michal Juraska, Michael P. Fay, and Peter B. Gilbert. "Finite-sample corrected generalized estimating equation of population average treatment effects in stepped wedge cluster randomized trials." Statistical Methods in Medical Research 26, no. 2 (2014): 583–97. http://dx.doi.org/10.1177/0962280214552092.

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Stepped wedge designs are increasingly commonplace and advantageous for cluster randomized trials when it is both unethical to assign placebo, and it is logistically difficult to allocate an intervention simultaneously to many clusters. We study marginal mean models fit with generalized estimating equations for assessing treatment effectiveness in stepped wedge cluster randomized trials. This approach has advantages over the more commonly used mixed models that (1) the population-average parameters have an important interpretation for public health applications and (2) they avoid untestable as

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Lv, Jing, Hu Yang, and Chaohui Guo. "Erratum to: Smoothing combined generalized estimating equations in quantile partially linear additive models with longitudinal data." Computational Statistics 31, no. 3 (2015): 1235. http://dx.doi.org/10.1007/s00180-015-0626-2.

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46

Lee, Hang, Daniel O. Stram, and Duncan C. Thomas. "A generalized estimating equations approach to fitting major gene models in segregation analysis of continuous phenotypes." Genetic Epidemiology 10, no. 1 (1993): 61–74. http://dx.doi.org/10.1002/gepi.1370100107.

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47

ELENES PLATONA, Iulia. "THE ECONOMIC FREEDOM, COUNTRY RISK AND FOREIGN DIRECT INVESTMENTS." Annals of the University of Oradea. Economic Sciences 31, me 31 (2022): 206–12. http://dx.doi.org/10.47535/1991auoes31(2)020.

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The interlinkages between country risk and foreign direct investments are the subject of research interest. The article tests the intuitive hypothesis that economic freedom is associated with low country risk and is an incentive for foreign direct investments. The research paper employs empirical quantitative within-between models to analyze the relationship between foreign direct investments and five indices: trade openness, freedom from corruption, trade freedom, investment freedom, and economic freedom. The database used is The Global Economy for 44 European Countries resulting a panel data

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48

Spiess, Martin, and Martin Kroh. "A Selection Model for Panel Data: The Prospects of Green Party Support." Political Analysis 18, no. 2 (2010): 172–88. http://dx.doi.org/10.1093/pan/mpp045.

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Although sample selection bias is a frequent problem of applied research, there has been no generalization of sample selection models with binary dependent variables of interest to data with temporal error correlations. We suggest a generalized estimating equation approach to panel data selection models, considering binary responses in both equations. We demonstrate the utility of this model by a simulation study and by analyzing highly unbalanced annual panel data taken from the German Socio-Economic Panel Study covering two decades of Green party support.

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49

Amato, Timothy W. "On Difference Equations, Probability Models and the “Generalized Event Count” Distribution." Political Analysis 6 (1996): 175–212. http://dx.doi.org/10.1093/pan/6.1.175.

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In this article, the mathematical and probabilistic foundations of Gary King's “generalized event count” (GEC) model for dealing with unequally dispersed event count data are explored. It is shown that the GEC model is a probability model that joins together the binomial, negative binomial, and Poisson distributions. Some aspects of the GEC's reparameterization are described and extended and it is shown how different reparameterizations lead to different interpretations of the dispersion parameter. The common mathematical and statistical structure of “unequally dispersed” event count models as

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Torres, Maicon de Paiva, Géssica Ramos da Silva, Tânia Maria Galo, Acir Moreno Soares Junior, and Luiz Nélio Henderson Guedes de Oliveira. "Application of Multiobjective Optimization in the Analysis of the Performance of Different Temperature Functions for a Generalized Cubic Equation of State." Defect and Diffusion Forum 427 (July 14, 2023): 157–66. http://dx.doi.org/10.4028/p-j80lyr.

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Since the emergence of van der Waals equation of state, several equations have been proposed to represent the behavior of pure compounds and mixtures, such as GEOS, which is a new generalized cubic equation of state form that employs a temperature function dependent on two or three adjustable parameters. Recently, multiobjective optimization has started to be applied in equations of state for parameters estimation, due to the conflicting nature of the objective functions. This methodology is attractive because it can be used to compare different models or variants of the same problem, through

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