Similar constraints exist for hierarchical or mixed effects models, but calculating degrees of freedom becomes more complex ( Spiegelhalter et al., 2002 Bolker et al., 2009). Furthermore, as p approaches n, the ability to estimate parameter uncertainty also diminishes. For example, in basic linear regression analyses, the number of estimated parameters p cannot exceed the sample size n, because the degrees of freedom ( n − p) is constrained to be greater than 0 ( Zar, 1999). These types of statistical analyses are often constrained by the “small n, large p” problem ( West, 2003). Results from this analysis indicate that regularization improves predictive performance of the VAR model, while still identifying important inter-specific interactions.Īcross a wide range of statistical tools-ranging from simple linear regression to complicated spatiotemporal models-a fundamental question in ecology, fisheries, and related fields is identifying a subset of important predictor variables from a larger set of potential explanatory variables. We then apply the Bayesian VAR model with regularized priors to a output from a large marine food web model (37 species) from the west coast of the USA. Results from these simulations show that for sparse matrices, the regularized horseshoe prior minimizes the bias and variance across all inter-specific interactions. We first perform a large-scale simulation study, examining the performance of alternative priors across various levels of observation error. To address this issue, we use Bayesian methods to explore the potential benefits of using regularized priors, such as Laplace and regularized horseshoe, on estimating interspecific interactions with VAR and VARSS models. However, as the number of species or functional groups increases, the length of the time series must also increase to provide enough degrees of freedom with which to estimate the pairwise interactions. To date, most studies have used these approaches on relatively small food webs where the total number of interactions to be estimated is relatively small. Using multi-species time series data has long been of interest for estimating inter-specific interactions with vector autoregressive models (VAR) and state space VAR models (VARSS) these methods are also described in the ecological literature as multivariate autoregressive models (MAR, MARSS).
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |