The AIC model selection method applied to path analytic models compared using a d-separation test.
TL;DR: This paper explains how to use the AIC statistic for d-sep tests, gives a worked example, and includes instructions to implement the analysis in the R computing language.
Abstract: Classical path analysis is a statistical technique used to test causal hypotheses involving multiple variables without latent variables, assuming linearity, multivariate normality, and a sufficient sample size. The d-separation (d-sep) test is a generalization of path analysis that relaxes these assumptions. Although model selection using Akaike's information criterion (AIC) is well established for classical path analysis, this model selection technique has not yet been developed for d-sep tests. In this paper, I explain how to use the AIC statistic for d-sep tests, give a worked example, and include instructions (supplemental material) to implement the analysis in the R computing language.
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TL;DR: In this paper, the authors present an open-source implementation of structural equation models (SEM), a form of path analysis that resolves complex multivariate relationships among a suite of interrelated variables.
Abstract: Summary
Ecologists and evolutionary biologists rely on an increasingly sophisticated set of statistical tools to describe complex natural systems. One such tool that has gained significant traction in the biological sciences is structural equation models (SEM), a form of path analysis that resolves complex multivariate relationships among a suite of interrelated variables.
Evaluation of SEMs has historically relied on covariances among variables, rather than the values of the data points themselves. While this approach permits a wide variety of model forms, it limits the incorporation of detailed specifications. Recent developments have allowed for the simultaneous implementation of non-normal distributions, random effects and different correlation structures using local estimation, but this process is not yet automated and consequently, evaluation can be prohibitive with complex models.
Here, I present a fully documented, open-source package piecewiseSEM, a practical implementation of confirmatory path analysis for the r programming language. The package extends this method to all current (generalized) linear, (phylogenetic) least-square, and mixed effects models, relying on familiar r syntax. I also provide two worked examples: one involving random effects and temporal autocorrelation, and a second involving phylogenetically independent contrasts.
My goal is to provide a user-friendly and tractable implementation of SEM that also reflects the ecological and methodological processes generating data.
2,194 citations
Posted Content•
TL;DR: A user‐friendly and tractable implementation of SEM that also reflects the ecological and methodological processes generating data, and extends this method to all current (generalized) linear, (phylogenetic) least‐square, and mixed effects models, relying on familiar r syntax.
Abstract: Ecologists and evolutionary biologists are relying on an increasingly sophisticated set of statistical tools to describe complex natural systems. One such tool that has gained increasing traction in the life sciences is structural equation modeling (SEM), a variant of path analysis that resolves complex multivariate relationships among a suite of interrelated variables. SEM has historically relied on covariances among variables, rather than the values of the data points themselves. While this approach permits a wide variety of model forms, it limits the incorporation of detailed specifications. Here, I present a fully-documented, open-source R package piecewiseSEM that builds on the base R syntax for all current generalized linear, least-square, and mixed effects models. I also provide two worked examples: one involving a hierarchical dataset with non-normally distributed variables, and a second involving phylogenetically-independent contrasts. My goal is to provide a user-friendly and tractable implementation of SEM that also reflects the ecological and methodological processes generating data.
550 citations
Cites methods from "The AIC model selection method appl..."
...Shipley (2013) showed that the Fisher’s C statistic can be used to obtain a value of Akaike’s information criterion (AIC) using the following equation: AIC ¼ Cþ 2K eqn 2 whereC is from eqn (1), andK is the likelihood degrees of freedom (not to be confused with k, the number of independence claims…...
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TL;DR: In this article, the effects of above-and belowground biodiversity on multiple ecosystem functions (for example, ecosystem multifunctionality, EMF) were investigated on the Tibetan Plateau, China.
Abstract: Plant biodiversity is often correlated with ecosystem functioning in terrestrial ecosystems. However, we know little about the relative and combined effects of above- and belowground biodiversity on multiple ecosystem functions (for example, ecosystem multifunctionality, EMF) or how climate might mediate those relationships. Here we tease apart the effects of biotic and abiotic factors, both above- and belowground, on EMF on the Tibetan Plateau, China. We found that a suite of biotic and abiotic variables account for up to 86% of the variation in EMF, with the combined effects of above- and belowground biodiversity accounting for 45% of the variation in EMF. Our results have two important implications: first, including belowground biodiversity in models can improve the ability to explain and predict EMF. Second, regional-scale variation in climate, and perhaps climate change, can determine, or at least modify, the effects of biodiversity on EMF in natural ecosystems.
412 citations
TL;DR: A new method is used to quantify plumage colour of all ~6,000 species of passerine birds to determine the main evolutionary drivers of ornamental colouration in both sexes, and finds that conspecific male and female colour elaboration are strongly correlated.
Abstract: Classical sexual selection theory provides a well-supported conceptual framework for understanding the evolution and signalling function of male ornaments. It predicts that males obtain greater fitness benefits than females through multiple mating because sperm are cheaper to produce than eggs. Sexual selection should therefore lead to the evolution of male-biased secondary sexual characters. However, females of many species are also highly ornamented. The view that this is due to a correlated genetic response to selection on males was widely accepted as an explanation for female ornamentation for over 100 years and current theoretical and empirical evidence suggests that genetic constraints can limit sex-specific trait evolution. Alternatively, female ornamentation can be the outcome of direct selection for signalling needs. Since few studies have explored interspecific patterns of both male and female elaboration, our understanding of the evolution of animal ornamentation remains incomplete, especially over broad taxonomic scales. Here we use a new method to quantify plumage colour of all ~6,000 species of passerine birds to determine the main evolutionary drivers of ornamental colouration in both sexes. We found that conspecific male and female colour elaboration are strongly correlated, suggesting that evolutionary changes in one sex are constrained by changes in the other sex. Both sexes are more ornamented in larger species and in species living in tropical environments. Ornamentation in females (but not males) is increased in cooperative breeders--species in which female-female competition for reproductive opportunities and other resources related to breeding may be high. Finally, strong sexual selection on males has antagonistic effects, causing an increase in male colouration but a considerably more pronounced reduction in female ornamentation. Our results indicate that although there may be genetic constraints to sexually independent colour evolution, both female and male ornamentation are strongly and often differentially related to morphological, social and life-history variables.
280 citations
Smithsonian Institution1, Virginia Institute of Marine Science2, Åbo Akademi University3, Shoals Marine Laboratory4, Université du Québec à Chicoutimi5, University of Groningen6, Florida Gulf Coast University7, Stockholm University8, University of the Algarve9, University of Oslo10, University of Gothenburg11, University of Helsinki12, University of Nordland13, San Diego State University14, University of Alaska Fairbanks15, Hokkaido University16, University of British Columbia17, University of Washington18, College of Charleston19, University of California, Davis20
TL;DR: This work factorially added nutrients and reduced grazing at 15 sites across the range of the marine foundation species eelgrass to quantify how top-down and bottom-up control interact with natural gradients in biodiversity and environmental forcing, and finds that biodiversity is comparably important to global change stressors.
Abstract: Nutrient pollution and reduced grazing each can stimulate algal blooms as shown by numerous experiments. But because experiments rarely incorporate natural variation in environmental factors and biodiversity, conditions determining the relative strength of bottom–up and top–down forcing remain unresolved. We factorially added nutrients and reduced grazing at 15 sites across the range of the marine foundation species eelgrass (Zostera marina) to quantify how top–down and bottom–up control interact with natural gradients in biodiversity and environmental forcing. Experiments confirmed modest top–down control of algae, whereas fertilisation had no general effect. Unexpectedly, grazer and algal biomass were better predicted by cross-site variation in grazer and eelgrass diversity than by global environmental gradients. Moreover, these large-scale patterns corresponded strikingly with prior small-scale experiments. Our results link global and local evidence that biodiversity and top–down control strongly influence functioning of threatened seagrass ecosystems, and suggest that biodiversity is comparably important to global change stressors.
187 citations
Cites methods from "The AIC model selection method appl..."
...Models were compared via the Akaike Information Criterion (AIC), estimated from D-separation tests (Shipley 2013)....
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References
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Book•
19 Jun 2013
TL;DR: The second edition of this book is unique in that it focuses on methods for making formal statistical inference from all the models in an a priori set (Multi-Model Inference).
Abstract: Introduction * Information and Likelihood Theory: A Basis for Model Selection and Inference * Basic Use of the Information-Theoretic Approach * Formal Inference From More Than One Model: Multi-Model Inference (MMI) * Monte Carlo Insights and Extended Examples * Statistical Theory and Numerical Results * Summary
36,993 citations
Book•
28 Apr 1989
TL;DR: The General Model, Part I: Latent Variable and Measurement Models Combined, Part II: Extensions, Part III: Extensions and Part IV: Confirmatory Factor Analysis as discussed by the authors.
Abstract: Model Notation, Covariances, and Path Analysis. Causality and Causal Models. Structural Equation Models with Observed Variables. The Consequences of Measurement Error. Measurement Models: The Relation Between Latent and Observed Variables. Confirmatory Factor Analysis. The General Model, Part I: Latent Variable and Measurement Models Combined. The General Model, Part II: Extensions. Appendices. Distribution Theory. References. Index.
19,019 citations
Proceedings Article•
01 Jan 1973
TL;DR: The classical maximum likelihood principle can be considered to be a method of asymptotic realization of an optimum estimate with respect to a very general information theoretic criterion to provide answers to many practical problems of statistical model fitting.
Abstract: In this paper it is shown that the classical maximum likelihood principle can be considered to be a method of asymptotic realization of an optimum estimate with respect to a very general information theoretic criterion. This observation shows an extension of the principle to provide answers to many practical problems of statistical model fitting.
18,539 citations
Book•
01 Jan 1925
TL;DR: The prime object of as discussed by the authors is to put into the hands of research workers, and especially of biologists, the means of applying statistical tests accurately to numerical data accumulated in their own laboratories or available in the literature.
Abstract: The prime object of this book is to put into the hands of research workers, and especially of biologists, the means of applying statistical tests accurately to numerical data accumulated in their own laboratories or available in the literature.
11,308 citations
TL;DR: The class of generalized additive models is introduced, which replaces the linear form E fjXj by a sum of smooth functions E sj(Xj), and has the advantage of being completely auto- matic, i.e., no "detective work" is needed on the part of the statistician.
Abstract: Likelihood-based regression models such as the normal linear regression model and the linear logistic model, assume a linear (or some other parametric) form for the covariates $X_1, X_2, \cdots, X_p$. We introduce the class of generalized additive models which replaces the linear form $\sum \beta_jX_j$ by a sum of smooth functions $\sum s_j(X_j)$. The $s_j(\cdot)$'s are unspecified functions that are estimated using a scatterplot smoother, in an iterative procedure we call the local scoring algorithm. The technique is applicable to any likelihood-based regression model: the class of generalized linear models contains many of these. In this class the linear predictor $\eta = \Sigma \beta_jX_j$ is replaced by the additive predictor $\Sigma s_j(X_j)$; hence, the name generalized additive models. We illustrate the technique with binary response and survival data. In both cases, the method proves to be useful in uncovering nonlinear covariate effects. It has the advantage of being completely automatic, i.e., no "detective work" is needed on the part of the statistician. As a theoretical underpinning, the technique is viewed as an empirical method of maximizing the expected log likelihood, or equivalently, of minimizing the Kullback-Leibler distance to the true model.
2,708 citations