The BinomialBeta Hierarchical Model for Ecological Inference: Methodological Issues and Fast Implementation via the ECM Algorithm (original) (raw)
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Binomial-beta hierarchical models for ecological inference
1999
Abstract The authors develop binomial-beta hierarchical models for ecological inference using insights from the literature on hierarchical models based on Markov chain Monte Carlo algorithms and King's ecological inference model. The new approach reveals some features of the data that King's approach does not, can be easily generalized to more complicated problems such as general R× C tables, allows the data analyst to adjust for covariates, and provides a formal evaluation of the significance of the covariates.
Bayesian and frequentist inference for ecological inference: The R× C case
2001
In this paper we propose Bayesian and frequentist approaches to ecological inference, based on R 3 C contingency tables, including a covariate. The proposed Bayesian model extends the binomial-beta hierarchical model developed by KING, ROSEN and TANNER (1999) from the 2 3 2 case to the R 3 C case. As in the 2 3 2 case, the inferential procedure employs Markov chain Monte Carlo (MCMC) methods. As such, the resulting MCMC analysis is rich but computationally intensive.
Estimating King’s ecological inference normal model via the EM Algorithm1
2014
Recently, King (1997) introduced a new model for ecological inference (EI), based on a truncated bivariate normal, which he estimates by maximum probability and uses to simulate the predictive densities of the disaggregate data. This paper reviews King's model and its assumption of truncated normality, with the aim to implement maximum probability estimation of his model and disaggregate data prediction in an alternative fashion via the EM Algorithm. In addition, we highlight and discuss important modeling issues related to the chance of non– existence of maximum likelihood estimates, and to the degree that corrections for this non–existence by means of suitably chosen priors are effective. At the end, a Monte Carlo simulation study is run in order to compare the two approaches.
Ecological Applications, 2009
Analyses of ecological data should account for the uncertainty in the process(es) that generated the data. However, accounting for these uncertainties is a difficult task, since ecology is known for its complexity. Measurement and/or process errors are often the only sources of uncertainty modeled when addressing complex ecological problems, yet analyses should also account for uncertainty in sampling design, in model specification, in parameters governing the specified model, and in initial and boundary conditions. Only then can we be confident in the scientific inferences and forecasts made from an analysis. Probability and statistics provide a framework that accounts for multiple sources of uncertainty. Given the complexities of ecological studies, the hierarchical statistical model is an invaluable tool. This approach is not new in ecology, and there are many examples (both Bayesian and non-Bayesian) in the literature illustrating the benefits of this approach. In this article, we provide a baseline for concepts, notation, and methods, from which discussion on hierarchical statistical modeling in ecology can proceed. We have also planted some seeds for discussion and tried to show where the practical difficulties lie. Our thesis is that hierarchical statistical modeling is a powerful way of approaching ecological analysis in the presence of inevitable but quantifiable uncertainties, even if practical issues sometimes require pragmatic compromises.
Estimating King ’ s ecological inference normal model via the EM Algorithm
2001
Recently, King (1997) introduced a new model for ecological inference (EI), based on a truncated bivariate normal, which he estimates by maximum probability and uses to simulate the predictive densities of the disaggregate data. This paper reviews King's model and its assumption of truncated normality, with the aim to implement maximum probability estimation of his model and disaggregate data prediction in an alternative fashion via the EM Algorithm. In addition, we highlight and discuss important modeling issues related to the chance of non– existence of maximum likelihood estimates, and to the degree that corrections for this non–existence by means of suitably chosen priors are effective. At the end, a Monte Carlo simulation study is run in order to compare the two approaches.
A hierarchical bayesian approach to ecological count data: A flexible tool for ecologists
2011
Many ecological studies use the analysis of count data to arrive at biologically meaningful inferences. Here, we introduce a hierarchical Bayesian approach to count data. This approach has the advantage over traditional approaches in that it directly estimates the parameters of interest at both the individual-level and population-level, appropriately models uncertainty, and allows for comparisons among models, including those that exceed the complexity of many traditional approaches, such as ANOVA or non-parametric analogs. As an example, we apply this method to oviposition preference data for butterflies in the genus Lycaeides. Using this method, we estimate the parameters that describe preference for each population, compare the preference hierarchies among populations, and explore various models that group populations that share the same preference hierarchy.
Ecological Modelling, 2019
The spatial prediction of species distributions from survey data is a significant component of spatial planning and the ecosystem-based management approach to marine resources. Statistical analysis of species occurrences and their relationships with associated environmental factors is used to predict how likely a species is to occur in unsampled locations as well as future conditions. However, it is known that environmental factors alone may not be sufficient to account for species distribution. Other ecological processes including species interactions (such as competition and predation), and the impact of human activities, may affect the spatial arrangement of a species. Novel techniques have been developed to take a more holistic approach to estimating species distributions, such as Bayesian Hierarchical Species Distribution model (B-HSD model) and mechanistic food-web models using the new Ecospace Habitat Foraging Capacity model (E-HFC model). Here we used both species distribution and spatial food-web models to predict the distribution of European hake (Merluccius merluccius), anglerfishes (Lophius piscatorius and L. budegassa) and red mullets (Mullus barbatus and M. surmuletus) in an exploited marine ecosystem of the Northwestern Mediterranean Sea. We explored the complementarity of both approaches, comparing results of food-web models previously informed with species distribution modelling results, aside from their applicability as independent techniques. The study shows that both modelling results are positively and significantly correlated with observational data. Predicted spatial patterns of biomasses show positive and significant correlations between modelling approaches and are more similar when using both methodologies in a complementary way: when using the E-HFC model previously informed with the environmental envelopes obtained from the B-HSD model outputs, or directly using niche calculations from B-HSD models to drive the niche priors of E-HFC. We discuss advantages, limitations and future developments of both modelling techniques.
A consensus on second-stage analyses in ecological inference models
2003
Since Herron and Shotts (2003a; hereinafter HS), Adolph and King (2003; hereinafter AK), and Herron and Shotts (2003b; hereinafter HS2), the four of us have iterated many more times, learned a great deal, and arrived at a consensus on this issue. This paper describes our joint recommendations for how to run second-stage ecological regressions, and provides detailed analyses to back up our claims.