Bayesian predictive model selection in circular random effects models with applications in ecological and environmental
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Bayesian predictive model selection in circular random effects models with applications in ecological and environmental studies Onur Camli1 · Zeynep Kalaylioglu1 Received: 24 November 2019 / Revised: 21 September 2020 / Accepted: 30 September 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In this paper we present a detailed comparison of the prediction error based model selection criteria in circular random effects models. The study is primarily motivated by the need for an understanding of their performance in real life ecological and environmental applications. Prediction errors are based on posterior predictive distributions and the model selection methods are adjusted for the circular manifold. Plug-in estimators of the circular distance parameters are also considered. A Monte Carlo experiment scheme taking the account of various realistic ecological and biological scenarios is designed. We introduced a coefficient that is based on conditional expectations to examine how the deviation from von Mises (vM) distribution, the standard choice in applications, effects the performances. Our results show that the performances of widely used circular predictive model selection criteria mostly depend on the sample size as well as within-sample-correlation. The approaches and selection strategies are then applied to investigate orientational behaviour of Talitrus saltator under the risk of dehydration and direction of wind with respect to associated atmoshperic variables. Keywords Directional statistics · Model comparison · Sandhoppers · von Mises distribution · Wind direction
Handling Editor: Pierre Dutilleul.
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Zeynep Kalaylioglu [email protected] Onur Camli [email protected]
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Department of Statistics, Middle East Technical University, Ankara, Turkey
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Environmental and Ecological Statistics
1 Introduction Circular random effects models are used in various different environmental and ecological studies in which response data are angular or directional and observed for each subject multiple times (D’Elia 2001; Hall and Shen 2015; Maruotti 2016; Maruotti et al. 2016; McMillan et al. 2013; Nunez-Antonio and Gutierrez-Pena 2014). For instance, as seen in our Sect. 5.1, Talitrus saltator, a beach amphipod, are observed in many ecological studies to investigate their orientation with respect to important environmental and ecological factors (Scapini 1997). In these studies, the response data consist of directional recordings of their consecutive jumps whereas covariate data consist of several environmental factors including wind direction and sun azimuth. As in such experiments on animal orientations, the aim is to understand the orientation of a particular species under given and advancing ecological conditions as well as to determine the environmental factors that play significant role in their orientation. In this regard, the focus is on determining the most significant factors that should take place in a model with good predictive abilities. This can be accomplished by us
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