Academic literature on the topic 'Generalized linear models'

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Journal articles on the topic "Generalized linear models"

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Schuenemeyer, John H., P. McCullagh, and J. A. Nelder. "Generalized Linear Models." Technometrics 34, no. 2 (May 1992): 224. http://dx.doi.org/10.2307/1269238.

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Lachenbruch, P. A., P. McCullagh, and J. A. Nelder. "Generalized Linear Models." Biometrics 46, no. 4 (December 1990): 1231. http://dx.doi.org/10.2307/2532465.

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Hilbe, Joseph M. "Generalized Linear Models." American Statistician 48, no. 3 (August 1994): 255. http://dx.doi.org/10.2307/2684732.

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Hu, X. Joan. "Generalized Linear Models." American Statistician 57, no. 1 (February 2003): 67–68. http://dx.doi.org/10.1198/tas.2003.s212.

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Hilbe, Joseph M. "Generalized Linear Models." American Statistician 48, no. 3 (August 1994): 255–65. http://dx.doi.org/10.1080/00031305.1994.10476073.

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Ziegel, Eric R. "Generalized Linear Models." Technometrics 44, no. 3 (August 2002): 287–88. http://dx.doi.org/10.1198/004017002320256422.

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Thompson, W. A., P. McCullagh, J. A. Nelder, and Annette J. Dobson. "Generalized Linear Models." Journal of the American Statistical Association 80, no. 392 (December 1985): 1066. http://dx.doi.org/10.2307/2288581.

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Burridge, Jim, P. McCullagh, and J. A. Nelder. "Generalized Linear Models." Journal of the Royal Statistical Society. Series A (Statistics in Society) 154, no. 2 (1991): 361. http://dx.doi.org/10.2307/2983054.

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McCulloch, Charles E. "Generalized Linear Models." Journal of the American Statistical Association 95, no. 452 (December 2000): 1320–24. http://dx.doi.org/10.1080/01621459.2000.10474340.

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Pukelsheim, F. "Generalized linear models." Metrika 33, no. 1 (December 1986): 290. http://dx.doi.org/10.1007/bf01894758.

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Dissertations / Theses on the topic "Generalized linear models"

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Mackinnon, Murray J. "Collinearity in generalized linear models." Thesis, University of British Columbia, 1986. http://hdl.handle.net/2429/25711.

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The concept of collinearity for generalized linear models is introduced and compared to that for standard linear models. Two approaches for detecting collinearity are presented and shown to lead to the same diagnostic procedure. These are analysed for the Poisson, gamma, inverse Gaussian, pth order, binomial proportion and negative binomial models. A bound is derived for the degree of collinearity in a generalized linear model in terms of that of the standard linear model. Estimation methods based on ridge, prior likelihood and principal components are proposed, and briefly illustrated with a Monte Carlo simulation of a gamma model.
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Benghiat, Sonia. "Diagnostics for generalized linear models." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/MQ64046.pdf.

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Creagh-Osborne, Jane. "Latent variable generalized linear models." Thesis, University of Plymouth, 1998. http://hdl.handle.net/10026.1/1885.

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Generalized Linear Models (GLMs) (McCullagh and Nelder, 1989) provide a unified framework for fixed effect models where response data arise from exponential family distributions. Much recent research has attempted to extend the framework to include random effects in the linear predictors. Different methodologies have been employed to solve different motivating problems, for example Generalized Linear Mixed Models (Clayton, 1994) and Multilevel Models (Goldstein, 1995). A thorough review and classification of this and related material is presented. In Item Response Theory (IRT) subjects are tested using banks of pre-calibrated test items. A useful model is based on the logistic function with a binary response dependent on the unknown ability of the subject. Item parameters contribute to the probability of a correct response. Within the framework of the GLM, a latent variable, the unknown ability, is introduced as a new component of the linear predictor. This approach affords the opportunity to structure intercept and slope parameters so that item characteristics are represented. A methodology for fitting such GLMs with latent variables, based on the EM algorithm (Dempster, Laird and Rubin, 1977) and using standard Generalized Linear Model fitting software GLIM (Payne, 1987) to perform the expectation step, is developed and applied to a model for binary response data. Accurate numerical integration to evaluate the likelihood functions is a vital part of the computational process. A study of the comparative benefits of two different integration strategies is undertaken and leads to the adoption, unusually, of Gauss-Legendre rules. It is shown how the fitting algorithms are implemented with GLIM programs which incorporate FORTRAN subroutines. Examples from IRT are given. A simulation study is undertaken to investigate the sampling distributions of the estimators and the effect of certain numerical attributes of the computational process. Finally a generalized latent variable model is developed for responses from any exponential family distribution.
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Vasconcelos, Julio Cezar Souza. "Modelo linear parcial generalizado simétrico." Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/11/11134/tde-26072017-105153/.

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Neste trabalho foi proposto o modelo linear parcial generalizado simétrico, com base nos modelos lineares parciais generalizados e nos modelos lineares simétricos, em que a variável resposta segue uma distribuição que pertence à família de distribuições simétricas, considerando um preditor linear que possui uma parte paramétrica e uma não paramétrica. Algumas distribuições que pertencem a essa classe são as distribuições: Normal, t-Student, Exponencial potência, Slash e Hiperbólica, dentre outras. Uma breve revisão dos conceitos utilizados ao longo do trabalho foram apresentados, a saber: análise residual, influência local, parâmetro de suavização, spline, spline cúbico, spline cúbico natural e algoritmo backfitting, dentre outros. Além disso, é apresentada uma breve teoria dos modelos GAMLSS (modelos aditivos generalizados para posição, escala e forma). Os modelos foram ajustados utilizando o pacote gamlss disponível no software livre R. A seleção de modelos foi baseada no critério de Akaike (AIC). Finalmente, uma aplicação é apresentada com base em um conjunto de dados reais da área financeira do Chile.
In this work we propose the symmetric generalized partial linear model, based on the generalized partial linear models and symmetric linear models, that is, the response variable follows a distribution that belongs to the symmetric distribution family, considering a linear predictor that has a parametric and a non-parametric component. Some distributions that belong to this class are distributions: Normal, t-Student, Power Exponential, Slash and Hyperbolic among others. A brief review of the concepts used throughout the work was presented, namely: residual analysis, local influence, smoothing parameter, spline, cubic spline, natural cubic spline and backfitting algorithm, among others. In addition, a brief theory of GAMLSS models is presented (generalized additive models for position, scale and shape). The models were adjusted using the package gamlss available in the free R software. The model selection was based on the Akaike criterion (AIC). Finally, an application is presented based on a set of real data from Chile\'s financial area.
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Stroinski, Krzysztof Jerzy. "Generalized linear models in motor insurance." Thesis, Heriot-Watt University, 1987. http://hdl.handle.net/10399/1044.

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Holmberg, Henrik. "Generalized linear models with clustered data." Doctoral thesis, Umeå universitet, Statistik, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-52902.

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In situations where a large data set is partitioned into many relatively small groups, and where the members within a group have some common unmeasured characteristics, the number of parameters requiring estimation tends to increase with sample size if a fixed effects model is applied. This fact causes the assumptions underlying asymptotic results to be violated. The first paper in this thesis considers two possible solutions to this problem, a random intercepts model and a fixed effects model, where asymptotics are replaced by a simple form of bootstrapping. A profiling approach is introduced in the fixed effects case, which makes it computationally efficient even with a huge number of groups. The grouping effect is mainly seen as a nuisance in this paper. In the second paper the effect of misspecifying the distribution of the random effects in a generalized linear mixed model for binary data is studied. One problem with mixed effects models is that the distributional assumptions about the random effects are not easily checked from real data. Models with Gaussian, logistic and Cauchy distributional assumptions are used for parameter estimation on data simulated using the same three distributions. The eect of these assumptions on parameter estimation is presented. Two criteria for model selection are investigated, the Akaike information criterion and a criterion based on a X2 statistic. The estimators for fixed effects parameters are quite robust against misspecification of the random effects distribution, at least with the distributions used in this paper. Even when the true random effects distribution is Cauchy, models assuming a Gaussian or a logistic distribution regularly produce estimates with less bias. In the third paper the results from the first two papers are applied to infant mortality data. We found that there was significant clustering of infant mortality in the Skellefteå region in the years 1831-1890. An "ad hoc" method for comparing the magnitude of unexplained clustering after a model is applied is also presented. The last paper of this thesis is concerned with the problem of testing for spatial clustering caused by autocorrelation. A test that is robust against heteroscedasticity is proposed. In a simulation study the properties of the proposed statistic, K, are investigated. The power of the test based on K is compared to that of Moran's I in the simulation study. Both tests are then applied to mortality data from Swedish municipalities.
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Gory, Jeffrey J. "Marginally Interpretable Generalized Linear Mixed Models." The Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1497966698387606.

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Jiang, Dingfeng. "Concave selection in generalized linear models." Diss., University of Iowa, 2012. https://ir.uiowa.edu/etd/2902.

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A family of concave penalties, including the smoothly clipped absolute deviation (SCAD) and minimax concave penalties (MCP), has been shown to have attractive properties in variable selection. The computation of concave penalized solutions, however, is a difficult task. We propose a majorization minimization by coordinate descent (MMCD) algorithm to compute the solutions of concave penalized generalized linear models (GLM). In contrast to the existing algorithms that uses local quadratic or local linear approximation of the penalty, the MMCD majorizes the negative log-likelihood by a quadratic loss, but does not use any approximation to the penalty. This strategy avoids the computation of scaling factors in iterative steps, hence improves the efficiency of coordinate descent. Under certain regularity conditions, we establish the theoretical convergence property of the MMCD algorithm. We implement this algorithm in a penalized logistic regression model using the SCAD and MCP penalties. Simulation studies and a data example demonstrate that the MMCD works sufficiently fast for the penalized logistic regression in high-dimensional settings where the number of covariates is much larger than the sample size. Grouping structure among predictors exists in many regression applications. We first propose an l2 grouped concave penalty to incorporate such group information in a regression model. The l2 grouped concave penalty performs group selection and includes group Lasso as a special case. An efficient algorithm is developed and its theoretical convergence property is established under certain regularity conditions. The group selection property of the l2 grouped concave penalty is desirable in some applications; while in other applications selection at both group and individual levels is needed. Hence, we propose an l1 grouped concave penalty for variable selection at both individual and group levels. An efficient algorithm is also developed for the l1 grouped concave penalty. Simulation studies are performed to evaluate the finite-sample performance of the two grouped concave selection methods. The new grouped penalties are also used in analyzing two motivation datasets. The results from both the simulation and real data analyses demonstrate certain benefits of using grouped penalties. Therefore, the proposed concave group penalties are valuable alternatives to the standard concave penalties.
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Sammut, Fiona. "Using generalized linear models to model compositional response data." Thesis, University of Warwick, 2016. http://wrap.warwick.ac.uk/89876/.

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This work proposes a multivariate logit model which models the influence of explanatory variables on continuous compositional response variables. This multivariate logit model generalizes an elegant method that was suggested previously by Wedderburn (1974) for the analysis of leaf blotch data in the special case of J = 2, leading to our naming this new approach as the generalized Wedderburn method. In contrast to the logratio modelling approach devised by Aitchison (1982, J. Roy Stat. Soc. B.), the multivariate logit model used under the generalized Wedderburn approach models the expectation of a compositional response variable directly and is also able to handle zeros in the data. The estimation of the parameters in the new model is carried out using the technique of generalized estimating equations (GEE). This technique relies on the specification of a working variance-covariance structure. A working variance-covariance structure which caters for the specific variability arising in compositional data is derived. The GEE estimator that is used to estimate the parameters of the multivariate logit model is shown to be invariant to the values of the correlation and dispersion parameters in the working variance-covariance structure. Due to this invariance property and the fact that the estimating equations used under the generalized Wedderburn method are linear and unbiased, the GEE estimator achieves full efficiency across a wide class of potential dispersion and correlation matrices for the compositional response variables. As for any other GEE estimator, the estimator used in the generalized Wedderburn method is also asymptotically unbiased and consistent, provided that the marginal mean model specification is correct. The theoretical results derived in this thesis are substantiated by simulation experiments, and properties of the new model are also studied empirically on some classic datasets from the literature.
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Zulj, Valentin. "On The Jackknife Averaging of Generalized Linear Models." Thesis, Uppsala universitet, Statistiska institutionen, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-412831.

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Frequentist model averaging has started to grow in popularity, and it is considered a good alternative to model selection. It has recently been applied favourably to gen- eralized linear models, where it has mainly been purposed to aid the prediction of probabilities. The performance of averaging estimators has largely been compared to that of models selected using AIC or BIC, without much discussion of model screening. In this paper, we study the performance of model averaging in classification problems, and evaluate performances with reference to a single prediction model tuned using cross-validation. We discuss the concept of model screening and suggest two methods of constructing a candidate model set; averaging over the models that make up the LASSO regularization path, and the so called LASSO-GLM hybrid. By means of a Monte Carlo simulation study, we conclude that model averaging does not necessarily offer any improvement in classification rates. In terms of risk, however, we see that both methods of model screening are efficient, and their errors are more stable than those achieved by the cross-validated model of comparison.
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Books on the topic "Generalized linear models"

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Gilchrist, Robert, Brian Francis, and Joe Whittaker, eds. Generalized Linear Models. New York, NY: Springer US, 1985. http://dx.doi.org/10.1007/978-1-4615-7070-7.

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Myers, Raymond H., Douglas C. Montgomery, G. Geoffrey Vining, and Timothy J. Robinson. Generalized Linear Models. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2010. http://dx.doi.org/10.1002/9780470556986.

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McCullagh, P., and J. A. Nelder. Generalized Linear Models. Boston, MA: Springer US, 1989. http://dx.doi.org/10.1007/978-1-4899-3242-6.

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Gill, Jeff. Generalized Linear Models. 2455 Teller Road, Thousand Oaks California 91320 United States of America: SAGE Publications, Inc., 2001. http://dx.doi.org/10.4135/9781412984348.

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A, Nelder John, ed. Generalized linear models. 2nd ed. London: Chapman and Hall, 1989.

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McCulloch, Charles E. Generalized Linear Mixed Models. Beechwood OH and Alexandria VA: Institute of Mathematical Statistics and American Statistical Association, 2003. http://dx.doi.org/10.1214/cbms/1462106059.

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Conference Board of the Mathematical Sciences. and National Science Foundation (U.S.), eds. Generalized linear mixed models. Beachwood, Ohio: Institute of Mathematical Statistics, 2003.

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McCulloch, Charles E. Generalized, linear, and mixed models. New York: John Wiley & Sons, 2001.

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McCulloch, Charles E. Generalized, Linear, and Mixed Models. New York: John Wiley & Sons, Ltd., 2005.

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Hardin, James W. Generalized linear models and extensions. 3rd ed. College Station, Tex: Stata Press, 2012.

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Book chapters on the topic "Generalized linear models"

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Salinas Ruíz, Josafhat, Osval Antonio Montesinos López, Gabriela Hernández Ramírez, and Jose Crossa Hiriart. "Generalized Linear Models." In Generalized Linear Mixed Models with Applications in Agriculture and Biology, 43–84. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-32800-8_2.

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AbstractIn the generalized linear model (GLM) (which is not highly general) y = Xβ + ϵ, the response variables are normally distributed, with constant variance across the values of all the predictor variables, and are linear functions of the predictor variables. Transformations of data are used to try to force the data into a normal linear regression model or to find a non-normal-type response variable transformation (discrete, categorical, positive continuous scale, etc.) that is linearly related to the predictor variables; however, this is no longer necessary. Instead of using a normal distribution, a positively skewed distribution with values that are positive real numbers can be selected. Generalized linear models (GLMs) go beyond linear mixed models, taking into account that the response variables are not of continuous scale (not normally distributed), GLMs are heteroscedastic, and there is a linear relationship between the mean of the response variable and the predictor or explanatory variables.
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Bapat, R. B. "Generalized Inverses." In Linear Algebra and Linear Models, 31–36. London: Springer London, 2012. http://dx.doi.org/10.1007/978-1-4471-2739-0_4.

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McCullagh, P., and J. A. Nelder. "Log-linear models." In Generalized Linear Models, 193–244. Boston, MA: Springer US, 1989. http://dx.doi.org/10.1007/978-1-4899-3242-6_6.

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Ziegler, Andreas. "Generalized linear models." In Generalized Estimating Equations, 21–28. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4614-0499-6_3.

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McCullagh, P., and J. A. Nelder. "Introduction." In Generalized Linear Models, 1–20. Boston, MA: Springer US, 1989. http://dx.doi.org/10.1007/978-1-4899-3242-6_1.

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McCullagh, P., and J. A. Nelder. "Joint modelling of mean and dispersion." In Generalized Linear Models, 357–71. Boston, MA: Springer US, 1989. http://dx.doi.org/10.1007/978-1-4899-3242-6_10.

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McCullagh, P., and J. A. Nelder. "Models with additional non-linear parameters." In Generalized Linear Models, 372–90. Boston, MA: Springer US, 1989. http://dx.doi.org/10.1007/978-1-4899-3242-6_11.

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McCullagh, P., and J. A. Nelder. "Model checking." In Generalized Linear Models, 391–418. Boston, MA: Springer US, 1989. http://dx.doi.org/10.1007/978-1-4899-3242-6_12.

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McCullagh, P., and J. A. Nelder. "Models for survival data." In Generalized Linear Models, 419–31. Boston, MA: Springer US, 1989. http://dx.doi.org/10.1007/978-1-4899-3242-6_13.

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McCullagh, P., and J. A. Nelder. "Components of dispersion." In Generalized Linear Models, 432–54. Boston, MA: Springer US, 1989. http://dx.doi.org/10.1007/978-1-4899-3242-6_14.

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Conference papers on the topic "Generalized linear models"

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Zhou, Yuhong, Xuewei Li, and Wanqiu Xie. "Association analysis of ordinal traits in generalized partial linear cumulative logistic models." In 2024 Fourth International Conference on Biomedicine and Bioinformatics Engineering (ICBBE 2024), edited by Pier Paolo Piccaluga, Ahmed El-Hashash, and Xiangqian Guo, 9. SPIE, 2024. http://dx.doi.org/10.1117/12.3044097.

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Jambulapati, Arun, James R. Lee, Yang P. Liu, and Aaron Sidford. "Sparsifying Generalized Linear Models." In STOC '24: 56th Annual ACM Symposium on Theory of Computing. New York, NY, USA: ACM, 2024. http://dx.doi.org/10.1145/3618260.3649684.

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Lee, Kuan-Yun, and Thomas A. Courtade. "Linear Models are Most Favorable among Generalized Linear Models." In 2020 IEEE International Symposium on Information Theory (ISIT). IEEE, 2020. http://dx.doi.org/10.1109/isit44484.2020.9174124.

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Bo-June (Paul) Hsu. "Generalized linear interpolation of language models." In 2007 IEEE Workshop on Automatic Speech Recognition & Understanding (ASRU). IEEE, 2007. http://dx.doi.org/10.1109/asru.2007.4430098.

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Bosowski, Nicholas, Vinay Ingle, and Dimitris Manolakis. "Generalized Linear Models for count time series." In 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2017. http://dx.doi.org/10.1109/icassp.2017.7952962.

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Roth, Volker, and Bernd Fischer. "The Group-Lasso for generalized linear models." In the 25th international conference. New York, New York, USA: ACM Press, 2008. http://dx.doi.org/10.1145/1390156.1390263.

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Hansen, M. H., and Bin Yu. "Mdl selection criteria for generalized linear models." In IEEE International Symposium on Information Theory, 2003. Proceedings. IEEE, 2003. http://dx.doi.org/10.1109/isit.2003.1228302.

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Kumar, Arun, Jeffrey Naughton, and Jignesh M. Patel. "Learning Generalized Linear Models Over Normalized Data." In SIGMOD/PODS'15: International Conference on Management of Data. New York, NY, USA: ACM, 2015. http://dx.doi.org/10.1145/2723372.2723713.

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Yang, Shuhua, Hui Yuan, Xiaoying Zhang, Mengdi Wang, Hong Zhang, and Huazheng Wang. "Conversational Dueling Bandits in Generalized Linear Models." In KDD '24: The 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, 3806–17. New York, NY, USA: ACM, 2024. http://dx.doi.org/10.1145/3637528.3671892.

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Hakimdavoodi, Hamidreza, and Maryam Amirmazlghani. "Maximum likelihood estimation of generalized linear models with generalized Gaussian residuals." In 2016 2nd International Conference of Signal Processing and Intelligent Systems (ICSPIS). IEEE, 2016. http://dx.doi.org/10.1109/icspis.2016.7869893.

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Reports on the topic "Generalized linear models"

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Moral, Rafael. Introduction to Generalized Linear Models. Instats Inc., 2024. http://dx.doi.org/10.61700/vteee3zjf6fsm1478.

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This seminar provides a comprehensive introduction to Generalized Linear Models (GLMs), covering binary, binomial, categorical logistic regression, Poisson regression, and advanced topics like overdispersion and zero-inflated models. Participants will gain theoretical knowledge and practical skills in applying GLMs using R, enhancing their ability to perform rigorous statistical analyses in various research scenarios.
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Yee, Thomas. Vector Generalized Linear and Additive Models. Instats Inc., 2024. http://dx.doi.org/10.61700/dw398w3pmbj5f1724.

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This workshop provides a comprehensive introduction to Vector Generalized Linear and Additive Models (VGLMs and VGAMs), equipping researchers with advanced skills for analyzing complex data structures often encountered in the social, health, and natural sciences. Participants will gain practical experience using the VGAM package in R for data analysis, enhancing their ability to apply sophisticated yet easy-to-use methods for their own research projects.
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Juricek, Ben C. Generalized Linear Mixed-Effects Models in R. Fort Belvoir, VA: Defense Technical Information Center, February 2003. http://dx.doi.org/10.21236/ada413561.

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Carroll, Raymond J. Covariance Analysis in Generalized Linear Measurement Error Models. Fort Belvoir, VA: Defense Technical Information Center, August 1988. http://dx.doi.org/10.21236/ada197661.

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Armstrong, Dave. Generalized Linear Models for Social and Health Sciences. Instats Inc., 2023. http://dx.doi.org/10.61700/dpngncc99f4pr469.

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This 12-week workshop provides a comprehensive understanding of GLMs and their application in various social and health science disciplines. With a lecture overview and hands-on lab component for each week, participants will gain practical experience in using R for implementing GLMs, evaluating model fit and presenting model results. An official Instats certificate of completion and 3 ECTS Equivalent points are provided at the conclusion of the seminar.
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Bianchi, Francesco, and Giovanni Nicolò. A Generalized Approach to Indeterminacy in Linear Rational Expectations Models. Cambridge, MA: National Bureau of Economic Research, June 2017. http://dx.doi.org/10.3386/w23521.

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Zhong, Xiaojing. Aggregation Effects in Generalized Linear Models: A Biochemical Engineering Application. Ames (Iowa): Iowa State University, January 2019. http://dx.doi.org/10.31274/cc-20240624-126.

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Stefanski, Leonard A., and Raymond J. Carroll. Conditional Scores and Optimal Scores for Generalized Linear Measurement-Error Models. Fort Belvoir, VA: Defense Technical Information Center, October 1985. http://dx.doi.org/10.21236/ada168533.

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Kunsch, H. R., L. A. Stefanski, and R. J. Carroll. Conditionally Unbiased Bounded Influence Robust Regression with Applications to Generalized Linear Models. Fort Belvoir, VA: Defense Technical Information Center, March 1987. http://dx.doi.org/10.21236/ada186319.

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10

Armstrong, Dave. Interactions and Non-Linearities in Regression Models. Instats Inc., 2023. http://dx.doi.org/10.61700/lnujxkrxa8jtk469.

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Abstract:
Many theories in the social sciences and beyond suggest non-linear or conditional relationships. Even if relationships of interest are assumed to be linear, it is important to test whether those assumptions are tenable. In this course, we consider how to diagnose un-modeled non-linearity in generalized linear models, how to estimate models with non-linear and/or conditional relationships and how to best present the results of those models to people who may engage with your work. An official Instats certificate of completion is provided at the conclusion of the seminar. The seminar offers 2 ECTS Equivalent points for European PhD students.
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