Dataset Information

A brief introduction to mixed effects modelling and multi-model inference in ecology.

ABSTRACT: The use of linear mixed effects models (LMMs) is increasingly common in the analysis of biological data. Whilst LMMs offer a flexible approach to modelling a broad range of data types, ecological data are often complex and require complex model structures, and the fitting and interpretation of such models is not always straightforward. The ability to achieve robust biological inference requires that practitioners know how and when to apply these tools. Here, we provide a general overview of current methods for the application of LMMs to biological data, and highlight the typical pitfalls that can be encountered in the statistical modelling process. We tackle several issues regarding methods of model selection, with particular reference to the use of information theory and multi-model inference in ecology. We offer practical solutions and direct the reader to key references that provide further technical detail for those seeking a deeper understanding. This overview should serve as a widely accessible code of best practice for applying LMMs to complex biological problems and model structures, and in doing so improve the robustness of conclusions drawn from studies investigating ecological and evolutionary questions.

SUBMITTER: Harrison XA

PROVIDER: S-EPMC5970551 | biostudies-other | 2018

REPOSITORIES: biostudies-other

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A brief introduction to mixed effects modelling and multi-model inference in ecology.

Harrison Xavier A XA Donaldson Lynda L Correa-Cano Maria Eugenia ME Evans Julian J Fisher David N DN Goodwin Cecily E D CED Robinson Beth S BS Hodgson David J DJ Inger Richard R

PeerJ 20180523

The use of linear mixed effects models (LMMs) is increasingly common in the analysis of biological data. Whilst LMMs offer a flexible approach to modelling a broad range of data types, ecological data are often complex and require complex model structures, and the fitting and interpretation of such models is not always straightforward. The ability to achieve robust biological inference requires that practitioners know how and when to apply these tools. Here, we provide a general overview of curr ...[more]

PMID: 29844961

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Project description:BACKGROUND: Different high-dimensional regression methodologies exist for the selection of variables to predict a continuous variable. To improve the variable selection in case clustered observations are present in the training data, an extension towards mixed-effects modeling (MM) is requested, but may not always be straightforward to implement.In this article, we developed such a MM extension (GA-MM-MMI) for the automated variable selection by a linear regression based genetic algorithm (GA) using multi-model inference (MMI). We exemplify our approach by training a linear regression model for prediction of resistance to the integrase inhibitor Raltegravir (RAL) on a genotype-phenotype database, with many integrase mutations as candidate covariates. The genotype-phenotype pairs in this database were derived from a limited number of subjects, with presence of multiple data points from the same subject, and with an intra-class correlation of 0.92. RESULTS: In generation of the RAL model, we took computational efficiency into account by optimizing the GA parameters one by one, and by using tournament selection. To derive the main GA parameters we used 3 times 5-fold cross-validation. The number of integrase mutations to be used as covariates in the mixed effects models was 25 (chrom.size). A GA solution was found when R2MM > 0.95 (goal.fitness). We tested three different MMI approaches to combine the results of 100 GA solutions into one GA-MM-MMI model. When evaluating the GA-MM-MMI performance on two unseen data sets, a more parsimonious and interpretable model was found (GA-MM-MMI TOP18: mixed-effects model containing the 18 most prevalent mutations in the GA solutions, refitted on the training data) with better predictive accuracy (R2) in comparison to GA-ordinary least squares (GA-OLS) and Least Absolute Shrinkage and Selection Operator (LASSO). CONCLUSIONS: We have demonstrated improved performance when using GA-MM-MMI for selection of mutations on a genotype-phenotype data set. As we largely automated setting the GA parameters, the method should be applicable on similar datasets with clustered observations.

Project description:BACKGROUND:Self-contained tests estimate and test the association between a phenotype and mean expression level in a gene set defined a priori. Many self-contained gene set analysis methods have been developed but the performance of these methods for phenotypes that are continuous rather than discrete and with multiple nuisance covariates has not been well studied. Here, I use Monte Carlo simulation to evaluate the performance of both novel and previously published (and readily available via R) methods for inferring effects of a continuous predictor on mean expression in the presence of nuisance covariates. The motivating data are a high-profile dataset which was used to show opposing effects of hedonic and eudaimonic well-being (or happiness) on the mean expression level of a set of genes that has been correlated with social adversity (the CTRA gene set). The original analysis of these data used a linear model (GLS) of fixed effects with correlated error to infer effects of Hedonia and Eudaimonia on mean CTRA expression. METHODS:The standardized effects of Hedonia and Eudaimonia on CTRA gene set expression estimated by GLS were compared to estimates using multivariate (OLS) linear models and generalized estimating equation (GEE) models. The OLS estimates were tested using O'Brien's OLS test, Anderson's permutation [Formula: see text]-test, two permutation F-tests (including GlobalAncova), and a rotation z-test (Roast). The GEE estimates were tested using a Wald test with robust standard errors. The performance (Type I, II, S, and M errors) of all tests was investigated using a Monte Carlo simulation of data explicitly modeled on the re-analyzed dataset. RESULTS:GLS estimates are inconsistent between data sets, and, in each dataset, at least one coefficient is large and highly statistically significant. By contrast, effects estimated by OLS or GEE are very small, especially relative to the standard errors. Bootstrap and permutation GLS distributions suggest that the GLS results in downward biased standard errors and inflated coefficients. The Monte Carlo simulation of error rates shows highly inflated Type I error from the GLS test and slightly inflated Type I error from the GEE test. By contrast, Type I error for all OLS tests are at the nominal level. The permutation F-tests have ?1.9X the power of the other OLS tests. This increased power comes at a cost of high sign error (?10%) if tested on small effects. DISCUSSION:The apparently replicated pattern of well-being effects on gene expression is most parsimoniously explained as "correlated noise" due to the geometry of multiple regression. The GLS for fixed effects with correlated error, or any linear mixed model for estimating fixed effects in designs with many repeated measures or outcomes, should be used cautiously because of the inflated Type I and M error. By contrast, all OLS tests perform well, and the permutation F-tests have superior performance, including moderate power for very small effects.

Dataset Information

A brief introduction to mixed effects modelling and multi-model inference in ecology.

Publications

A brief introduction to mixed effects modelling and multi-model inference in ecology.

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