Overdispersed and Spatio-temporal Bayesian Count Data Models Proposals
December 4th, 2024, 9:00 – 10:30
Seminar held by
Vicente Núñez-Antón
Full Professor of Statistics,
Department of Quantitative Methods,
University of the Basque Country, Bilbao, Spain
Where
University of Milano-Bicocca
Department of Statistics and Quantitative Methods
Computer Lab 716, U7, Via Bicocca degli Arcimboldi 8, Milan
The seminars will be also available on WebEx at the following links:
https://unimib.webex.com/unimib-it/j.php?MTID=m31a9db9e45d21e0d251c1a8bd147c088
Meeting ID: 2743 019 5508
Password: gHAj8nJx6V3 (from mobile phones: 44258659)
Abstract
When working with count data, it is common to use generalized linear models (GLMs). However, regression models for count data often present overdispersion, a phenomenon that arises when the real variance of the data is larger than the one specified in the theoretical distributional model. Additionally, in the presence of geographically referenced (spatial) data, any spatial dependence among the different locations must be also accounted for to produce reliable inference processes from the estimations. In this work, we introduce and review the spatial conditional overdispersion models for fitting spatial count data. In these models, the possible existing spatial correlation in the data is taken into account by incorporating a spatial term in the regression structure by means of a parameter that directly estimates the intensity of the spatial association. Overdispersion is handled through the inclusion of overdispersion parameters in the model. We illustrate their performance for Poisson distributed responses by fitting them to the study of infant mortality rates in Colombia. Moreover, we also include their comparison with the widely used Besag-York-Mollié (BYM) and BYM2 models. For fitting spatio-temporal count data, where temporal correlation may also be present, we propose a direct spatio-temporal extension of the spatial conditional overdispersion models. This extension includes the spatial lag of the response variable for each time unit in the linear predictor. Moreover, we propose the temporally varying spatial lag coefficient models, which allow the coefficient for the spatial term to vary over time. In order to illustrate their behavior and usefulness, we apply our proposals, for Poisson distributed responses, to the respiratory hospital admissions in Glasgow data, where we compare their performance with the widely used Knorr-Held models. Our proposals fall within the context of Bayesian approaches and the software package R-INLA has been used for fitting purposes.
About the Speaker
Full Professor of Statistics at The University of the Basque Country UPV/EHU in Bilbao, Spain. He was awarded an undergraduate degree in Electronic Engineering (1987) at ESPOL in Guayaquil, Ecuador, a Master in Theoretical Statistics (1989) and a Ph.D. in Statistics (1993) from The University of Iowa, USA. He has published more than 100 scientific articles in the areas of longitudinal data analysis, survival data, nonparametric estimation methods, goodness-of-fit testing and health related quality of life methods. He was Associate Editor for Applied Statistics (2004-2007), for Statistical Modelling (2005-2017) and for METHODOLOGY: European Journal of Research Methods for the Behavioral and Social Sciences. Since 2017 he is the Coordinating Editor of Statistical Modelling. He was member of the International Programme (IPC) for the International Biometric Conferences in Montreal, Canada (IBC2006), Dublin, Ireland (IBC2008), and the Chair of the International Programme Committee (IPC) for the International Biometric Conference in Florianopolis, Brazil (IBC2010). He was a member of the International Programme (IPC) for the International Biometric Conference in Kobe, Japan (IBC2012) and of the IBS Council representing the Spanish Region. He was a member of the organizing and scientific committees for the V Meeting of the International Biometric Society Network for Central America, The Caribbean, Mexico, Colombia and Venezuela (Xalapa, Veracruz, Mexico, 1997), and Chair of the Scientific Committee for the 15th International Workshop on Statistical Modelling (Bilbao, Spain, 2000), and organized, with Goeran Kauermann, the workshop Survival of the Fittest. Time to Event Analysis in Biostatistics, Economics and Related Fields (Bielefeld, Germany, 2004). He is one of the founders and was one of the main researchers of the BIOSTATNET Network in Biostatistics. Jointly with Dale Zimmerman, Philippe Vieu and Frederic Ferraty, he authored books on longitudinal data and nonparametric regression methods. He was one of the founders of the Statistical Modelling Society, member of its Board of Trustees (1999-2002), member of its Executive Committee (2002-2006) and its Secretary (2002-2006). He was also Chair of the Subcommittee of the American Statistical Association's Committee on Nominations for International Representative to the American Statistical Association (ASA) Board of Directors. He has served as member and Chair of the Conference Advisory Committee, and as elected member of the Executive Board for the International Biometric Society. He has recently served as Secretary and Treasurer of the International Biometric Society. He has given invited talks at different Universities in Belgium, Germany, France, Italy, USA, Mexico, Colombia, Chile, Cuba, Ecuador, Belgium, The Netherlands, and in Spain, as well at different meetings in the area of Statistics.