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Regression and model-building in conservation biology, biogeography and ecology: The distinction between – and reconciliation of – ‘predictive’ and ‘explanatory’ models
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In this article, it is suggested that if the two approaches do not agree upon which of the independent variables are likely to be'significant' then the deductions must be subject to doubt.Abstract:
In many large-scale conservation or ecological problems where experiments are intractable or unethical, regression methods are used to attempt to gauge the impact of a set of nominally independent variables (X) upon a dependent variable (Y). Workers often want to assert that a given X has a major influence on Y, and so, by using this indirection to infer a probable causal relationship. There are two difficulties apart from the demonstrability issue itself: (1) multiple regression is plagued by collinear relationships in X; and (2) any regression is designed to produce a function that in some way minimizes the overall difference between the observed and ‘predicted’ Ys, which does not necessarily equate to determining probable influence in a multivariate setting. Problem (1) may be explored by comparing two avenues, one in which a single ‘best’ regression model is sought and the other where all possible regression models are considered contemporaneously. It is suggested that if the two approaches do not agree upon which of the independent variables are likely to be ‘significant’, then the deductions must be subject to doubt.read more
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Experimental Design and Data Analysis for Biologists
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TL;DR: An essential textbook for any student or researcher in biology needing to design experiments, sample programs or analyse the resulting data is as discussed by the authors, covering both classical and Bayesian philosophies, before advancing to the analysis of linear and generalized linear models Topics covered include linear and logistic regression, simple and complex ANOVA models (for factorial, nested, block, split-plot and repeated measures and covariance designs), and log-linear models Multivariate techniques, including classification and ordination, are then introduced.
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References
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Estimating the Dimension of a Model
TL;DR: In this paper, the problem of selecting one of a number of models of different dimensions is treated by finding its Bayes solution, and evaluating the leading terms of its asymptotic expansion.
Estimating the dimension of a model
TL;DR: In this paper, the problem of selecting one of a number of models of different dimensions is treated by finding its Bayes solution, and evaluating the leading terms of its asymptotic expansion.
Book
Generalized Linear Models
Peter McCullagh,John A. Nelder +1 more
TL;DR: In this paper, a generalization of the analysis of variance is given for these models using log- likelihoods, illustrated by examples relating to four distributions; the Normal, Binomial (probit analysis, etc.), Poisson (contingency tables), and gamma (variance components).
Book
Applied Regression Analysis
Norman R. Draper,Harry Smith +1 more
TL;DR: In this article, the Straight Line Case is used to fit a straight line by least squares, and the Durbin-Watson Test is used for checking the straight line fit.
Book
Applied Linear Statistical Models
TL;DR: Applied Linear Statistical Models 5e as discussed by the authors is the leading authoritative text and reference on statistical modeling, which includes brief introductory and review material, and then proceeds through regression and modeling for the first half, and through ANOVA and Experimental Design in the second half.