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Hierarchical models in ecology: confidence intervals, hypothesis testing, and model selection using data cloning
Author(s) -
Ponciano José Miguel,
Taper Mark L.,
Dennis Brian,
Lele Subhash R.
Publication year - 2009
Publication title -
ecology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.144
H-Index - 294
eISSN - 1939-9170
pISSN - 0012-9658
DOI - 10.1890/08-0967.1
Subject(s) - model selection , statistics , markov chain monte carlo , likelihood ratio test , hierarchical database model , frequentist inference , selection (genetic algorithm) , statistical hypothesis testing , likelihood function , statistical inference , context (archaeology) , computer science , mathematics , bayesian inference , bayesian probability , ecology , estimation theory , data mining , biology , machine learning , paleontology
Hierarchical statistical models are increasingly being used to describe complex ecological processes. The data cloning (DC) method is a new general technique that uses Markov chain Monte Carlo (MCMC) algorithms to compute maximum likelihood (ML) estimates along with their asymptotic variance estimates for hierarchical models. Despite its generality, the method has two inferential limitations. First, it only provides Wald‐type confidence intervals, known to be inaccurate in small samples. Second, it only yields ML parameter estimates, but not the maximized likelihood values used for profile likelihood intervals, likelihood ratio hypothesis tests, and information‐theoretic model selection. Here we describe how to overcome these inferential limitations with a computationally efficient method for calculating likelihood ratios via data cloning. The ability to calculate likelihood ratios allows one to do hypothesis tests, construct accurate confidence intervals and undertake information‐based model selection with hierarchical models in a frequentist context. To demonstrate the use of these tools with complex ecological models, we reanalyze part of Gause's classic Paramecium data with state–space population models containing both environmental noise and sampling error. The analysis results include improved confidence intervals for parameters, a hypothesis test of laboratory replication, and a comparison of the Beverton‐Holt and the Ricker growth forms based on a model selection index.