%0 Journal Article %1 schaub_combining_2012 %A Schaub, M. %A Kéry, M. %D 2012 %J Animal Conservation %K effects, hierarchical model, random review, sample shrinkage, size small %N 2 %P 125--126 %R 10.1111/j.1469-1795.2012.00531.x %T Combining information in hierarchical models improves inferences in population ecology and demographic population analyses %U http://onlinelibrary.wiley.com/doi/10.1111/j.1469-1795.2012.00531.x/abstract %V 15 %X Statistical models that include random effects are becoming more common in population ecology all the time. Random effects are two or more effects of some grouping factor that belong together, in the sense that we can imagine they were generated by a common stochastic process. Thus, they are similar, but not identical, and therefore assumed to be exchangeable. Models with random effects contain as a description of this common stochastic process so-called prior distributions, with estimable hyperparameters, for instance the mean and the variance for normally distributed random effects. Models with random effects have intrinsically more than one level; therefore, they are often called hierarchical models (Royle & Dorazio, 2008) or multilevel models (Gelman & Hill, 2007). Interest in hierarchical models often focuses on the hyperparameters, but the realizations from the process described by the prior distributions, that is, the random effects, can also be estimated. The main difference to treating a set of effects as fixed is that in a random effects model, the parameters of a grouping factor are no longer estimated independently. Rather, the assumption that they come from a common prior distribution induces a dependence, which means that the estimate of each is somewhat influenced by the estimate of all other effects comprising that factor. This is often called borrowing strength from the ensemble. One consequence of treating a factor as random is that its effect estimates are pulled in towards the overall mean, which is called shrinkage in the literature. If the assumption of a common stochastic process is reasonable, borrowing strength and shrinkage typically leads to better estimates compared with their fixed effects counterparts (Gelman, 2005; chapter 4 in Kéry & Schaub, 2012). Hierarchical models are not at all intrinsically Bayesian; rather, they can be analysed using likelihood or Bayesian methods (Royle & Dorazio, 2008), though Bayesian analysis is often easier, especially for ecologists using MCMC engines like WinBUGS or JAGS. One particularly interesting use of hierarchical model is as a formal way of combining information, for instance, coming from different studies.

@article{schaub_combining_2012, abstract = {Statistical models that include random effects are becoming more common in population ecology all the time. Random effects are two or more effects of some grouping factor that belong together, in the sense that we can imagine they were generated by a common stochastic process. Thus, they are similar, but not identical, and therefore assumed to be exchangeable. Models with random effects contain as a description of this common stochastic process so-called prior distributions, with estimable hyperparameters, for instance the mean and the variance for normally distributed random effects. Models with random effects have intrinsically more than one level; therefore, they are often called hierarchical models (Royle \& Dorazio, 2008) or multilevel models (Gelman \& Hill, 2007). Interest in hierarchical models often focuses on the hyperparameters, but the realizations from the process described by the prior distributions, that is, the random effects, can also be estimated. The main difference to treating a set of effects as fixed is that in a random effects model, the parameters of a grouping factor are no longer estimated independently. Rather, the assumption that they come from a common prior distribution induces a dependence, which means that the estimate of each is somewhat influenced by the estimate of all other effects comprising that factor. This is often called borrowing strength from the ensemble. One consequence of treating a factor as random is that its effect estimates are pulled in towards the overall mean, which is called shrinkage in the literature. If the assumption of a common stochastic process is reasonable, borrowing strength and shrinkage typically leads to better estimates compared with their fixed effects counterparts (Gelman, 2005; chapter 4 in Kéry \& Schaub, 2012). Hierarchical models are not at all intrinsically Bayesian; rather, they can be analysed using likelihood or Bayesian methods (Royle \& Dorazio, 2008), though Bayesian analysis is often easier, especially for ecologists using MCMC engines like WinBUGS or JAGS. One particularly interesting use of hierarchical model is as a formal way of combining information, for instance, coming from different studies.}, added-at = {2017-01-09T13:57:26.000+0100}, author = {Schaub, M. and Kéry, M.}, biburl = {https://www.bibsonomy.org/bibtex/2acfae6f2eee880b671638a93eaccb0a3/yourwelcome}, copyright = {© 2012 The Authors. Animal Conservation © 2012 The Zoological Society of London}, doi = {10.1111/j.1469-1795.2012.00531.x}, interhash = {5527db67b95fe1ed9c21c7cb69533c59}, intrahash = {acfae6f2eee880b671638a93eaccb0a3}, issn = {1469-1795}, journal = {Animal Conservation}, keywords = {effects, hierarchical model, random review, sample shrinkage, size small}, language = {en}, month = mar, number = 2, pages = {125--126}, timestamp = {2017-01-09T14:01:11.000+0100}, title = {Combining information in hierarchical models improves inferences in population ecology and demographic population analyses}, url = {http://onlinelibrary.wiley.com/doi/10.1111/j.1469-1795.2012.00531.x/abstract}, urldate = {2012-05-12}, volume = 15, year = 2012 }