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Collinearity in generalized linear models

Murray J. Mackinnon, Martin L. Puterman
1989 Communications in Statistics - Theory and Methods  
Poisson, binomial proportion and negative binomial) collinearity in the standard linear model implies collinearity in the generalized linear model.  ...  The fifth chapter briefly illustrates the ideas of the previous chapters with a restricted Monte Carlo simulation of a gamma model.  ...  Simulation Results and Conclusions The results of the simulations are displayed in Tables 5.1 and 5.2 and Figure 5 .1.  ... 
doi:10.1080/03610928908830102 fatcat:64udvc4355cgvjarlvznc3bmbe

Simultaneous Transformation and Rounding (STAR) Models for Integer-Valued Data [article]

Daniel R. Kowal, Antonio Canale
2019 arXiv   pre-print
The STAR additive model is applied to study the recent decline in Amazon river dolphins.  ...  The data-generating process is defined by Simultaneously Transforming and Rounding (STAR) a continuous-valued process, which produces a flexible family of integer-valued distributions capable of modeling  ...  We emphasize that in all cases, the simulated datasets are not generated under the proposed star model: they are simulated from negative-binomial and (approximate) Poisson distributions.  ... 
arXiv:1906.11653v2 fatcat:r7ls7exppraulcfsrwzlt43yqq

Regression Models for Multivariate Count Data

Yiwen Zhang, Hua Zhou, Jin Zhou, Wei Sun
2017 Journal of Computational And Graphical Statistics  
We study the estimation, testing, and variable selection for these models in a unifying framework. The regression models are compared on both synthetic and real RNA-seq data.  ...  In this article, we study some generalized linear models that incorporate various correlation structures among the counts.  ...  Acknowledgments The work is partially supported by National Science Foundation (NSF) grant DMS-1310319 and National Institutes of Health (NIH) grants HG006139, GM105785, and GM53275.  ... 
doi:10.1080/10618600.2016.1154063 pmid:28348500 pmcid:PMC5365157 fatcat:tejlueo6ivbylnkdff7jfe7ssq

Bayesian Generalized Additive Models for Location, Scale, and Shape for Zero-Inflated and Overdispersed Count Data

Nadja Klein, Thomas Kneib, Stefan Lang
2015 Journal of the American Statistical Association  
The proposed approach is evaluated in simulation studies and applied to count data arising from patent citations and claim frequencies in car insurances.  ...  We develop Bayesian inference based on Markov chain Monte Carlo simulation techniques where suitable proposal densities are constructed based on iteratively weighted least squares approximations to the  ...  Monte Carlo (MCMC) simulations [Brezger and Lang, 2006 , Jullion and Lambert, 2007 , Lang et al., 2013 .  ... 
doi:10.1080/01621459.2014.912955 fatcat:lidyuptuufc6jco45dje4hyj4u

Modelling sparse generalized longitudinal observations with latent Gaussian processes

Peter Hall, Hans-Georg Mller, Fang Yao
2008 Journal of The Royal Statistical Society Series B-statistical Methodology  
We illustrate these non-parametric methods with longitudinal data on primary biliary cirrhosis and show in simulations that they are competitive in comparisons with generalized estimating equations and  ...  generalized linear mixed models.  ...  This research was supported in part by National Science Foundation grants DMS03-54448 and DMS05-05537.  ... 
doi:10.1111/j.1467-9868.2008.00656.x fatcat:6u2sqpjvcjdang2wbzyzwauzfe

Propriety of posteriors in structured additive regression models: Theory and empirical evidence

Ludwig Fahrmeir, Thomas Kneib
2009 Journal of Statistical Planning and Inference  
Hence, propriety of the joint posterior is a crucial issue for full Bayesian inference in particular if based on Markov chain Monte Carlo simulations.  ...  We establish theoretical results providing sufficient (and sometimes necessary) conditions for propriety and provide empirical evidence through several accompanying simulation studies.  ...  When considering Binomial and Poisson distributed results, the findings of the simulation study where qualitatively of the same type as for Bernoulli distributed response.  ... 
doi:10.1016/j.jspi.2008.05.036 fatcat:64hfid4uunhs7hpuxzohl6dfr4

Power-Expected-Posterior Priors for Generalized Linear Models [article]

Dimitris Fouskakis, Ioannis Ntzoufras, Konstantinos Perrakis
2017 arXiv   pre-print
In this work we generalize the applicability of the PEP methodology, focusing on the framework of generalized linear models (GLMs), by introducing two new PEP definitions which are in effect applicable  ...  Several simulation scenarios and one real life example are considered in order to evaluate the performance of the proposed methods compared to other commonly used approaches based on mixtures of g-priors  ...  Acknowledgement This research has been co-financed in part by the European Union (European Social Fund-ESF) and by Greek national funds through the Operational Program "Education and Lifelong Learning"  ... 
arXiv:1508.00793v4 fatcat:2idx3dsh6rdipl3rlpaowrvfmq

An Information Matrix Prior for Bayesian Analysis in Generalized Linear Models with High Dimensional Data

Mayetri Gupta, Joseph G Ibrahim
2009 Statistica sinica  
The IM and IMR priors are based on a broad generalization of Zellner's g-prior for Gaussian linear models.  ...  In this article, we develop a novel specification for a general class of prior distributions, called Information Matrix (IM) priors, for high-dimensional generalized linear models.  ...  Acknowledgements We would like to thank two anonymous referees whose valuable insights and suggestions led to major improvements in the overall clarity and presentation of this paper, and to thank Jason  ... 
pmid:20664718 pmcid:PMC2909687 fatcat:bpnq7j6em5gfpi334iev3xttoq

Penalized likelihood regression for generalized linear models with non-quadratic penalties

Anestis Antoniadis, Irène Gijbels, Mila Nikolova
2009 Annals of the Institute of Statistical Mathematics  
We report on a simulation study including comparisons between our method and some existing ones.  ...  Most of the smoothing methods employ quadratic penalties, leading to linear estimates, and are in general incapable of recovering discontinuities or other important attributes in the regression function  ...  Acknowledgments The authors are grateful to an Associate Editor and a reviewer for valuable comments that led to an improved presentation. Support from the IAP research network no.  ... 
doi:10.1007/s10463-009-0242-4 fatcat:53s7eednjzfehkrtudgonavofy

Power-Expected-Posterior Priors for Generalized Linear Models

Dimitris Fouskakis, Ioannis Ntzoufras, Konstantinos Perrakis
2018 Bayesian Analysis  
Acknowledgments The authors thank the Editor-in-Chief, the Associate Editor and the Referee for their comments on a previous version of our work that greatly strengthened the current article.  ...  For further details and results, we defer to Section 7.2 where we illustrate, for several simulated scenarios with binomial and Poisson response models, that the posterior probability of the true model  ...  For the remainder of this paper, without loss of generality we restrict the scale parameter φ to be known, which is the case for the binomial, Poisson and normal with known error variance regression models  ... 
doi:10.1214/17-ba1066 fatcat:52hxuv4rp5a6jmb4ig355grpmq

Generalised additive and index models with shape constraints [article]

Yining Chen, Richard J. Samworth
2014 arXiv   pre-print
We study generalised additive models, with shape restrictions (e.g. monotonicity, convexity, concavity) imposed on each component of the additive prediction function.  ...  More generally, our methodology can be applied to generalised additive index models.  ...  Simulation study To analyse the empirical performance of SCMLE and SCAIE, we ran a simulation study focusing on the running time and the predictive performance.  ... 
arXiv:1404.2957v1 fatcat:3e3cshq4sfdpze5lbxq655m4f4

Modeling Understory Vegetation and Its Response to Fire [chapter]

Donald McKenzie, Crystal L. Raymond, Samuel A. Cushman
2009 Models for Planning Wildlife Conservation in Large Landscapes  
Process-based models, which simulate understory development, usually within a mechanistic ecosystem-modeling paradigm that focuses on photosynthesis, element cycling, mortality, and decomposition; and  ...  A leading edge of research in this area studies hierarchical models that incorporate multiple contingencies; 2.  ...  Chain Monte Carlo procedures.  ... 
doi:10.1016/b978-0-12-373631-4.00015-0 fatcat:wvijdn7rrvhgpbvyjrkuzzhnea

Student-t Stochastic Volatility Model With Composite Likelihood EM-Algorithm [article]

Raanju R. Sundararajan, Wagner Barreto-Souza
2021 arXiv   pre-print
The finite-sample performance of our composite likelihood methods is assessed through Monte Carlo simulations. The methodology is motivated by an empirical application in the financial market.  ...  We analyze the relationship, across multiple time periods, between various US sector Exchange-Traded Funds returns and individual companies' stock price returns based on our novel Student-t model.  ...  Monte Carlo simulations to study and compare the CL and CLEM approaches are presented in Section 4.  ... 
arXiv:2105.13081v1 fatcat:b3g2staba5c3tetqpdfpxijony

Variable selection for inhomogeneous spatial point process models

Yu Ryan Yue, Ji Meng Loh
2015 Canadian journal of statistics  
the generalized linear model framework for fitting these point models.  ...  We perform simulation studies to explore the effectiveness of using each of the three regularization methods in our procedure.  ...  Acknowledgment We thank associate editor and two referees for their great comments on our manuscript, which has significantly improved its quality.  ... 
doi:10.1002/cjs.11244 fatcat:3yqkbgerabcjtie6ymmr74slw4

Species Distribution Modeling: Comparison of Fixed and Mixed Effects Models Using INLA

Lara Dutra Silva, Eduardo Brito de Azevedo, Rui Bento Elias, Luís Silva
2017 ISPRS International Journal of Geo-Information  
A binomial Generalized Linear Model uses presence-absence records to model the distribution of the species based on a relationship (i.e., link function) between the mean of the response variable and the  ...  In fitting these models, INLA calculates accurate, deterministic approximations to posterior marginal distributions in place of long Markov Chain Monte Carlo (MCMC) simulations, gaining in time [52].  ...  Prediction of the Response Grid We predicted the response jointly with the estimation process by computation of the posterior distributions, also called posterior mean of linear predictor.  ... 
doi:10.3390/ijgi6120391 fatcat:44acftaquvfx3ig7cmg5hofmoe
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