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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, summarize general findings on the choice of the working correlation matrix, and show the existence of a dilemma for the optimal choice of the working correlation matrix for dichotomous dependent variables. Results: Biological and statistical arguments for choosing a specific working correlation matrix are given. Three approaches are described for overcoming the range restriction of the correlation coefficient. Conclusions: The three approaches described in this article for overcoming the range restrictions for dichotomous dependent variables in GEE models provide a simple and practical way for use in applications.

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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 (January 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 (November 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 (November 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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Breitung, J., N. R. Chaganty, R. M. Daniel, M. G. Kenward, M. Lechner, P. Martus, R. T. Sabo, Y. G. Wang, and C. Zorn. "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 aspects in data analysis. Conclusions: In general, careful modeling correlation is encouraged when considering estimation efficiency and other implications, and a comparison of choosing instruments in GMM and generalized estimating equations (GEE) would be worthwhile. Some theoretical drawbacks of GEE need to be further addressed and require careful analysis of data. This particularly applies to the situation when data are missing at random.

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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 (August 25, 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 Study (HRS) (HRS, 2019)

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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 (July 5, 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 (May 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 (June 2009): 590–99. http://dx.doi.org/10.1111/j.1365-2664.2009.01642.x.

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Nikita, Efthymia. "The use of generalized linear models and generalized estimating equations in bioarchaeological studies." American Journal of Physical Anthropology 153, no. 3 (December 13, 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 (November 1, 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 (September 17, 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 models. The small sample performance of this approach is improved by a bias adjustment to the estimate of the joint covariance matrix of the regression coefficients from multiple models. As a further small sample improvement a multivariate t-distribution with appropriate degrees of freedom is specified as reference distribution. In addition, a generalized score test based on the stacked estimating equations is derived. Simulation results show strong control of the family-wise type I error rate for these methods even with small sample sizes and increased power compared to a Bonferroni-Holm multiplicity adjustment. Thus, the proposed methods are suitable to efficiently use the information from repeated observations of multiple endpoints in small-sample studies.

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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 (July 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 (August 13, 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 the application of generalized additive models (GAMs) to estimate erosivity utilizing daily rainfall records. As a case study, pluviograph data with a time step of 30 min from the Water District of Thrace in Greece were used. By applying GAMs, it became possible to model the nonlinear relation between daily rainfall, seasonal periodicity, and rainfall erosivity more effectively, in terms of accuracy, than the application of two well-known nonlinear empirical equations, both on a daily and an annual basis.

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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 (March 2002): 271–83. http://dx.doi.org/10.1198/016214502753479400.

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16

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 (November 2004): 295–310. http://dx.doi.org/10.1348/0007110042307177.

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17

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 (February 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 (July 13, 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 estimates for a series of reduced models from the different studies. The specification of the equations requires a reference dataset for estimating the joint distribution of the covariates. We propose to solve these equations using the generalized method of moments approach, with the optimal weighting of the equations taking into account uncertainty associated with estimates of the parameters of the reduced models. We describe extensions of the iterated reweighted least-squares algorithm for fitting generalized linear regression models using the proposed framework. Based on the same moment equations, we also develop a diagnostic test for detecting violations of underlying model assumptions, such as those arising from heterogeneity in the underlying study populations. The proposed methods are illustrated with extensive simulation studies and a real-data example involving the development of a breast cancer risk prediction model using disparate risk factor information from multiple studies.

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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 (June 6, 2008): 268–88. http://dx.doi.org/10.1080/00273170802034877.

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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 (August 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 (January 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 (November 15, 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 linear mixed-effects models with pseudo-likelihood estimation are advocated for valid and robust inference. We also propose a controlled multiple imputation method as a sensitivity analysis of the missing data assumption. Lastly, we implement the proposed models and the sensitivity analysis in two real data examples with binary data.

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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 (October 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 (January 29, 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 marginal model. The proposed method explicitly models the correlation structure within clusters or correlated variables by using a prespecified working correlation matrix. The asymptotic properties of the estimators from the penalized generalized estimating equations are established and the number of candidate covariates is allowed to increase in the same order as the number of clusters does. We evaluate the performance of the proposed method through a simulation study and analyze two real datasets for the application.

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Morley, Clive L. "A Comparison of Three Methods for Estimating Tourism Demand Models." Tourism Economics 2, no. 3 (September 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 (November 17, 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 the utility of an alternative approach, generalized profiling, which provides robustness to violations of a deterministic model without needing to specify a complete probabilistic model. We introduce novel means for estimating the robustness parameters and for statistical inference in this framework. The methods are applied to a model for pre-vaccination measles incidence in Ontario, and we demonstrate the statistical validity of our inference through extensive simulation. The results confirm that school term versus summer drives seasonality of transmission, but we find no effects of short school breaks and the estimated basic reproductive ratio ℛ 0 greatly exceeds previous estimates. The approach applies naturally to any system for which candidate differential equations are available, and avoids many challenges that have limited Monte Carlo inference for state–space models.

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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 (August 16, 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 parameters using data extracted from a smaller sample. Here, we established two additive biomass model systems using the independent diameter and the combined variable that comprises diameter and tree height. The logarithmic Nonlinear Seemingly Uncorrelated (logarithmic NSUR) method and the Generalized Method of Moments (GMM) method were applied to estimate the parameters of these models. By comparing four distinct approaches, the following key results were obtained: (1) Both the GMM and logarithmic NSUR methods can yield satisfactory goodness of fit and estimation precision for the additive biomass equations, with the root mean square error (RMSE) were significantly low, and coefficients of determination (R2) were mostly higher than 0.9. (2) Comparatively, examining the fitted curves of predicted values, the GMM method provided better fitting than the NSUR method. The GMM method with the combined variable is the most suggested approach for the calculation and research of single-tree biomass models with a small sample size.

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Jentsch, Carsten, and Lena Reichmann. "Generalized Binary Time Series Models." Econometrics 7, no. 4 (December 14, 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 any negative serial correlation. For the special case of binary data, we propose an extension of the NDARMA model class that allows for negative model parameters, and, hence, autocorrelations leading to the considerably larger and more flexible model class of generalized binary ARMA (gbARMA) processes. We provide stationary conditions, give the stationary solution, and derive stochastic properties of gbARMA processes. For the purely autoregressive case, classical Yule–Walker equations hold that facilitate parameter estimation of gbAR models. Yule–Walker type equations are also derived for gbARMA processes.

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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 (October 8, 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 order to help guide the design of future cluster randomized trials. Therefore, numerous methods have been proposed to accurately estimate the intra-cluster correlation coefficient, with much attention given to binary outcomes. As marginal models are often of interest, we focus on intra-cluster correlation coefficient estimation in the context of fitting such a model with binary outcomes using generalized estimating equations. Traditionally, intra-cluster correlation coefficient estimation with generalized estimating equations has been based on the method of moments, although such estimators can be negatively biased. Furthermore, alternative estimators that work well, such as the analysis of variance estimator, are not as readily applicable in the context of practical data analyses with generalized estimating equations. Therefore, in this article we assess, in terms of bias, the readily available residual pseudo-likelihood approach to intra-cluster correlation coefficient estimation with the GLIMMIX procedure of SAS (SAS Institute, Cary, NC). Furthermore, we study a possible corresponding approach to confidence interval construction for the intra-cluster correlation coefficient. Methods We utilize a simulation study and application example to assess bias in intra-cluster correlation coefficient estimates obtained from GLIMMIX using residual pseudo-likelihood. This estimator is contrasted with method of moments and analysis of variance estimators which are standards of comparison. The approach to confidence interval construction is assessed by examining coverage probabilities. Results Overall, the residual pseudo-likelihood estimator performs very well. It has considerably less bias than moment estimators, which are its competitor for general generalized estimating equation–based analyses, and therefore, it is a major improvement in practice. Furthermore, it works almost as well as analysis of variance estimators when they are applicable. Confidence intervals have near-nominal coverage when the intra-cluster correlation coefficient estimate has negligible bias. Conclusion Our results show that the residual pseudo-likelihood estimator is a good option for intra-cluster correlation coefficient estimation when conducting a generalized estimating equation–based analysis of binary outcome data arising from cluster randomized trials. The estimator is practical in that it is simply a result from fitting a marginal model with GLIMMIX, and a confidence interval can be easily obtained. An additional advantage is that, unlike most other options for performing generalized estimating equation–based analyses, GLIMMIX provides analysts the option to utilize small-sample adjustments that ensure valid inference.

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30

Zhang, Zhigang. "Linear transformation models for interval-censored data." Statistical Modelling 9, no. 4 (December 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 probability prediction via generalized estimating equations. We also consider a graphical model checking technique and a model selection tool. Some theoretical properties are established and the performance of our procedures is evaluated and illustrated by numerical studies including a real-life data analysis.

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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 (January 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 are used in the safety analysis of a site. With many years of data, however, it is necessary to account for the year-to-year variation, or trend, in accident counts because of the influence of factors that change every year. To capture this variation, the count for each year is treated as a separate observation. Unfortunately, the disaggregation of the data in this manner creates a temporal correlation that presents difficulties for traditional model calibration procedures. An application is presented of a generalized estimating equations (GEE) procedure to develop an APM that incorporates trend in accident data. Data for the application pertain to a sample of four-legged signalized intersections in Toronto, Canada, for the years 1990 through 1995. The GEE model incorporating the time trend is shown to be superior to models that do not accommodate trend and/or the temporal correlation in accident data.

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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 (April 2013): 172–89. http://dx.doi.org/10.3102/1076998611432175.

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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 (August 12, 2015): 1203–34. http://dx.doi.org/10.1007/s00180-015-0612-8.

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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 (August 7, 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 (February 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 context are also covered.

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36

Bravo, Francesco. "Robust estimation and inference for general varying coefficient models with missing observations." TEST 29, no. 4 (November 27, 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 are consistent as the drifts diverge. The results of the paper are illustrated with three examples: robust local generalized estimating equations, robust local quasi-likelihood and robust local nonlinear least squares estimation. A simulation study shows that the proposed estimators and test statistics have competitive finite sample properties, whereas two empirical examples illustrate the applicability of the proposed estimation and testing methods.

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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 (March 8, 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, must be used with either GLMMs or GEEs when developing RSFs. There are several important differences between these approaches; in particular, GLMMs are best for producing parameter estimates that predict how management might influence individuals, while GEEs are best for predicting how management might influence populations. As the interpretation, value, and statistical significance of both types of parameter estimates differ, it is important that users select the appropriate analytical method. We also outline the use of k-fold cross validation to assess fit of these models. Both GLMMs and GEEs hold promise for developing RSFs as long as they are used appropriately.

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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 (February 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 degradation (hence the supply of microbial protein to the duodenum) to be evaluated, thus linking the gas production technique to animal production.

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

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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 (November 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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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 not as general as required for designing clinical trials. Methods: We extended the previously developed SAS macro GEESIZE to overcome this restriction. Specifically, we have added the option of an independence working correlation matrix required for the IEE. Additionally, we have reformulated the hypotheses to allow for coding that includes an intercept term instead of the previously used analysis of variance coding. Results: To demonstrate the validity of GEESIZE we investigate the calculated sample sizes for specific models where closed formulae are available. For illustration, we utilize GEESIZE for planning a new trial on the treatment of hypertension and thereby exemplify its flexibility. Conclusions: We show that our freely available macro is a very general and useful tool for sample size calculation purposes in clinical trials with correlated data.

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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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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 regression model. The coefficients of this model are different for different components. An estimator is proposed for these regression coefficients estimation based on the least squares and generalized estimating equations. Consistency of this estimator is demonstrated under general assumptions. A mixture of logistic regression models with continuous response is considered as an example. It is shown that the general consistency conditions are satisfied for this model under very mild assumptions. Performance of the estimator is assessed by simulations.

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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 (September 29, 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 assumptions on latent variable distributions and avoid parametric assumptions about error distributions, therefore, providing more robust evidence on treatment effects. However, cluster randomized trials typically have a small number of clusters, rendering the standard generalized estimating equation sandwich variance estimator biased and highly variable and hence yielding incorrect inferences. We study the usual asymptotic generalized estimating equation inferences (i.e., using sandwich variance estimators and asymptotic normality) and four small-sample corrections to generalized estimating equation for stepped wedge cluster randomized trials and for parallel cluster randomized trials as a comparison. We show by simulation that the small-sample corrections provide improvement, with one correction appearing to provide at least nominal coverage even with only 10 clusters per group. These results demonstrate the viability of the marginal mean approach for both stepped wedge and parallel cluster randomized trials. We also study the comparative performance of the corrected methods for stepped wedge and parallel designs, and describe how the methods can accommodate interval censoring of individual failure times and incorporate semiparametric efficient estimators.

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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 (October 26, 2015): 1235. http://dx.doi.org/10.1007/s00180-015-0626-2.

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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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ELENES PLATONA, Iulia. "THE ECONOMIC FREEDOM, COUNTRY RISK AND FOREIGN DIRECT INVESTMENTS." Annals of the University of Oradea. Economic Sciences 31, me 31 (December 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 employed for between within models, growth curve models, contextual models, generalized estimating equations models (GEE), and asymmetric effects models. Interesting is the different significance of the five indicators in different models. For the first three models within -between model, the growth curve model and the contextual model- statistical significance have trade openness, freedom from corruption, and investment freedom. For the Generalized equations model (GEE) the only indicator that has statistical significance is Investment freedom. For the asymmetric effects model that shows the effect of asymmetric increase and decrease of each indicator, there is no statistical significance for the analyzed indicators. The within – between models combine the robustness of the fix effects models with the flexibility of the random-effects models.

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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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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 models that require estimation of the “number of trials” parameter along with the “probability” component is derived. Some questions pertaining to estimation of this class of models are raised for future discussion.

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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 the trade-off analysis of the so-called Pareto front. In this context, the multiobjective PSO algorithm, based on the Pareto dominance principle, is used in this work for estimating the parameters of the generalized cubic equation of state, by fitting its results to synthetic experimental data of vapor pressure and saturated liquid volume. The performance of the new estimated parameters of the three temperature functions is investigated through the calculation of thermodynamic properties of interest in industry and academia. In addition, comparisons against real experimental data available in the literature are performed.

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