Much of animal ecology is devoted to studies of abundance and occurrence of species, based on surveys of spatially referenced sample units. These surveys frequently yield sparse counts that are contaminated by imperfect detection, making direct inference about abundance or occurrence based on observational data infeasible. This article describes a flexible hierarchical modeling framework for estimation and inference about animal abundance and occurrence from survey data that are subject to imperfect detection. Within this framework, we specify models of abundance and detectability of animals at the level of the local populations defined by the sample units. Information at the level of the local population is aggregated by specifying models that describe variation in abundance and detection among sites. We describe likelihood-based and Bayesian methods for estimation and inference under the resulting hierarchical model. We provide two examples of the application of hierarchical models to animal survey data, the first based on removal counts of stream fish and the second based on avian quadrat counts. For both examples, we provide a Bayesian analysis of the models using the software WinBUGS.
Hierarchical Models in Environmental Science.pdf
Abstract:Recent developments in remote sensing (RS) technology have made several sources of auxiliary data available to support forest inventories. Thus, a pertinent question is how different sources of RS data should be combined with field data to make inventories cost-efficient. Hierarchical model-based estimation has been proposed as a promising way of combining: (i) wall-to-wall optical data that are only weakly correlated with forest structure; (ii) a discontinuous sample of active RS data that are more strongly correlated with structure; and (iii) a sparse sample of field data. Model predictions based on the strongly correlated RS data source are used for estimating a model linking the target quantity with weakly correlated wall-to-wall RS data. Basing the inference on the latter model, uncertainties due to both modeling steps must be accounted for to obtain reliable variance estimates of estimated population parameters, such as totals or means. Here, we generalize previously existing estimators for hierarchical model-based estimation to cases with non-homogeneous error variance and cases with correlated errors, for example due to clustered sample data. This is an important generalization to take into account data from practical surveys. We apply the new estimation framework to case studies that mimic the data that will be available from the Global Ecosystem Dynamics Investigation (GEDI) mission and compare the proposed estimation framework with alternative methods. Aboveground biomass was the variable of interest, Landsat data were available wall-to-wall, and sample RS data were obtained from an airborne LiDAR campaign that produced simulated GEDI waveforms. The results show that generalized hierarchical model-based estimation has potential to yield more precise estimates than approaches utilizing only one source of RS data, such as conventional model-based and hybrid inferential approaches.Keywords: carbon monitoring; GEDI; Landsat 7 ETM+; model-based inference; superpopulation models; variance estimation
We searched and found 146 relevant publications on SEM applications in ecological studies. We found that five SEM variants had not commenly been applied in ecology, including the latent growth curve model, Bayesian SEM, partial least square SEM, hierarchical SEM, and variable/model selection. We identified ten common issues in SEM applications including strength of causal assumption, specification of feedback loops, selection of models and variables, identification of models, methods of estimation, explanation of latent variables, selection of fit indices, report of results, estimation of sample size, and the fit of model.
My research interest is in the development and application of quantitative methods for analyzing complex environmental and ecological data. An important feature of ecological study is that we use variables operating at different scales, some representing spatiotemporal scales and some representing conceptual scales. For example, regional annual means of temperature and precipitation represent local and instantaneous conditions; individual species compositions are observed and summarized to derive variables representing changes at a community or ecosystem level. In all cases, we observe data representing a fine spatiotemporal scale or at individual species level and we aggregate these observations to make inference at a larger spatiotemporal scale or at community level. Mathematically, the multiple levels in the data can be represented by the hierarchical structure of a Bayesian hierarchical/multilevel model. However, the full potential of the hierarchical modeling approach has yet to be explored. In the past five years, I have focused on using the Bayesian hierarchical modeling approach in several research areas:
At the graduate level, I teach two required courses: (1) Advanced environmental data management and (2) Advanced biostatistics on an annual basis. I also teach Environmental models and introduction to Bayesian statistics every other year. In addition I offer a number of special topics courses.
In this paper, we discuss an extension to two popular approaches to modeling complex structures in ecological data: the generalized additive model (GAM) and the hierarchical model (HGLM). The hierarchical GAM (HGAM), allows modeling of nonlinear functional relationships between covariates and outcomes where the shape of the function itself varies between different grouping levels. We describe the theoretical connection between HGAMs, HGLMs, and GAMs, explain how to model different assumptions about the degree of intergroup variability in functional response, and show how HGAMs can be readily fitted using existing GAM software, the mgcv package in R. We also discuss computational and statistical issues with fitting these models, and demonstrate how to fit HGAMs on example data. All code and data used to generate this paper are available at: github.com/eric-pedersen/mixed-effect-gams.
Evolutionary analyses of gene sequence data are increasingly reliant on model-based phylogenetic approaches. In recent years, this has been given substantial impetus by the surge in genome-scale data, improvements in computational power, and the application of Bayesian statistical methods to phylogenetics [1]. Statistical models are typically used to describe the substitution process in nucleotide or amino acid sequences [2], diversification and demographic processes [3, 4], and patterns of evolutionary rate variation among lineages [5]. In a Bayesian framework, the various components describing different aspects of the evolutionary process collectively form the hierarchical model.
We extend the cross-validation method proposed by Lartillot et al. [19] for substitution models to other components of the Bayesian hierarchical model: the molecular clock model and the demographic model. We also test whether the performance of the method depends on the length of the sequence alignment, because the probability of identifying the optimal model should improve with the amount of data (i.e., statistical consistency).
Our analyses of simulated and empirical data show that cross-validation provides a useful model-selection method for Bayesian phylogenetics. Although marginal-likelihood methods are more effective in many cases, one potential advantage of cross-validation is that as long as the data are sufficiently informative model choice is not affected by the prior, such that it might be more readily applied than complex hierarchical Bayesian models where selecting appropriate priors for all parameters is difficult. Further research into cross-validation methods has the potential to improve the reliability of model selection in Bayesian phylogenetics.
We present hierarchical models for estimating long-term exposure concentrations and estimating a common exposure-response curve. The exposure concentration model combines temporally sparse, clustered longitudinal observations to estimate household-specific long-term average concentrations. The exposure-response model provides a flexible, semiparametric estimate of the exposure-response relationship while accommodating heterogeneous clustered data from multiple studies. We apply these models to three studies of fine particulate matter (PM2.5) and ALRIs in children in Nepal: a case-control study in Bhaktapur, a stepped-wedge trial in Sarlahi, and a parallel trial in Sarlahi. For each study, we estimate household-level long-term PM2.5 concentrations. We apply the exposure-response model separately to each study and jointly to the pooled data.
Currently, there is no theory that explains how the large-scale organization of the human brain can be related to our environment. This is astonishing because neuroscientists generally assume that the brain represents events in our environment by decoding sensory input. Here, we propose that the brain models the entire environment as a collection of hierarchical, dynamical systems, where slower environmental changes provide the context for faster changes. We suggest that there is a simple mapping between this temporal hierarchy and the anatomical hierarchy of the brain. Our theory provides a framework for explaining a wide range of neuroscientific findings by a single principle.
The novel contribution of this paper is to consider hierarchical models, in which high-level states change more slowly than low-level states, and to relate these models to structure-function relationships in the brain. The basic idea is that temporal hierarchies in the environment are transcribed into anatomical hierarchies in the brain; high-level cortical areas encode slowly changing contextual states of the world, while low-level areas encode fast trajectories. We will present two arguments in support of this hypothesis. First, using simulations, we will demonstrate that hierarchical dependencies among dynamics in the environment can be exploited to recognise the causes of sensory input. The ensuing recognition models have a hierarchical structure that is reminiscent of cortical hierarchies in the brain. Second, we will consider neuroscientific evidence that suggests the cortical organisation recapitulates hierarchical dependencies among environmental dynamics. 2ff7e9595c
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