# Statistical methods for analysing multivariate abundance data This package provides tools for a model-based approach to the analysis of multivariate abundance data in ecology (Warton 2011), where 'abundance' should be interpreted loosely - as well as counts you could have presence/absence, ordinal or biomass (via `manyany`), etc. There are graphical methods for exploring the properties of data and the community-environment association, flexible regression methods for estimating and making robust inferences about the community-environment association, 'fourth corner models' to explain environmental response as a function of traits, and diagnostic plots to check the appropriateness of a fitted model (Wang et. al 2012). There is an emphasis on design-based inferences about these models, e.g. bootstrapping rows of residuals via `anova` calls, or cross-validation across rows, to make multivariate inferences that are robust to failure of assumptions about correlation. Another emphasis is on presenting diagnostic tools to check assumptions, especially via residual plotting. ## Details The key functions available in this package are the following. For graphical display of the data: - **`plot.mvabund`**: draw a range of plots for Multivariate Abundance Data - **`boxplot.mvabund`**: draw a range of plots of Model Formulae for Multivariate Abundance Data - **`meanvar.plot`**: draw mean-variance plots for Multivariate Abundance Data For estimating and displaying Linear Models: - **`manylm`**: Fitting Linear Models for Multivariate Abundance Data - **`summary.manylm`**: summarizie Multivariate Linear Model Fits for Abundance Data - **`anova.manylm`**: obtain ANOVA for Multivariate Linear Model Fits for Abundance Data - **`plot.manylm`**: plot diagnostics for a `manylm` Object For estimating and displaying Generalized Linear Models: - **`manyglm`**: fit Generalized Linear Models for Multivariate Abundance Data - **`summary.manyglm`**: summarize Multivariate Generalized Linear Model Fits for Abundance Data - **`anova.manyglm`**: obtain Analysis of Deviance for Multivariate Generalized Linear Model Fits for Abundance Data - **`plot.manyglm`**: plot diagnostics for a `manyglm` Object Other generic functions like `residuals`, `predict`, `AIC` can be applied to `manyglm` objects. For estimating and displaying 'fourth corner models' with species traits as well as environmental predictors: - **`traitglm`**: predict abundance using a GLM as a function of traits as well as environmental variables - **`anova.traitglm`**: obtain Analysis of Deviance for a fourth corner model of abundance Other generic functions like `plot`, `residuals`, `predict`, `AIC` can be applied to `traitglm` objects. Note `traitglm` can work slowly, as it fits a single big model to vectorised data (then wants to resample it when you call `anova.traitglm`). For fitting more flexible models: - **`manyany`**: simultaneously fit univariate models to each response variable from 'any' input function - **`anova.manyany`**: simultaneously test for a community-level effect, comparing two or more `manyany` objects - **`glm1path`**: fit a path of Generalised Linear Models with L1 ('LASSO') penalties - **`cv.glm1path`**: choose the value of the L1 penalty in a `glm1path` fit by cross-validation Other generic functions like `residuals`, `predict`, `AIC` can be applied to `manyany` and `glm1path` objects. These functions also can be on the slow side, especially if all rare species are included. For providing a data structure: - **`mvabund`**: create a mvabund object - **`mvformula`**: create Model Formulae for Multivariate Abundance Data Example datasets: - **`Tasmania`**: meiobenthic community data from Tasmania. Used to demonstrate test for interaction. - **`solberg`**: solberg species counts with a 3-level treatment factor. - **`spider`**: hunting spiders counts from different sites. - **`tikus`**: solberg nematode counts from Tikus island. - **`antTraits`**: ant counts from Eucalypt forests, with trait measurements. For more details, see the documentation for any of the individual functions listed above. ## References Brown AM, Warton DI, Andrew NR, Binns M, Cassis G and Gibb H (2014) The fourth corner solution - using species traits to better understand how species traits interact with their environment, **Methods in Ecology and Evolution** 5, 344-352. Warton D.I. (2008a). Raw data graphing: an informative but under-utilized tool for the analysis of multivariate abundances. **Austral Ecology** 33, 290-300. Warton D.I. (2008b). Penalized normal likelihood and ridge regularization of correlation and covariance matrices. **Journal of the American Statistical Association** 103, 340-349. Warton D.I. (2011). Regularized sandwich estimators for analysis of high dimensional data using generalized estimating equations. **Biometrics**, 67, 116-123. Warton DI, Shipley B & Hastie T (2015) CATS regression - a model-based approach to studying trait-based community assembly, **Methods in Ecology and Evolution** 6, 389-398. Warton D. I., Wright S., and Wang, Y. (2012). Distance-based multivariate analyses confound location and dispersion effects. **Methods in Ecology and Evolution**, 3, 89-101. Wang Y., Neuman U., Wright S. and Warton D. I. (2012). mvabund: an R package for model-based analysis of multivariate abundance data. **Methods in Ecology and Evolution**, 3, 471-473. ## Author(s) David Warton David.Warton@unsw.edu.au , Yi Wang and Ulrike Naumann. ## See Also `plot.mvabund`, `meanvar.plot`, `manyany`, `manylm`, `manyglm`, `traitglm`, `summary.manylm`, `anova.manyany`, `anova.manylm`, `anova.traitglm`, `anova.manyglm`, `plot.manylm` ## Examples ```r require(graphics) ## Load the spider dataset: data(spider) ## Create the mvabund object spiddat: spiddat <- mvabund(spider$abund) X <- as.matrix(spider$x) ## Draw a plot of the spider data: plot(spiddat, col="gray1", n.vars=8, transformation="sqrt", xlab=c("Hunting Spider"), ylab="Spider Species", scale.lab="s", t.lab="t", shift=TRUE, fg= "lightblue", col.main="red", main="Spiders") ## A mean-variance plot, data organised by year, ## for 1981 and 1983 only, as in Figure 7a of Warton (2008a): data(tikus) tikusdat <- mvabund(tikus$abund) year <- tikus$x[,1] is81or83 <- year==81 | year==83 meanvar.plot(tikusdat~year,legend=TRUE, subset=is81or83, col=c(1,10)) ## Create a formula for multivariate abundance data: foo <- mvformula( spiddat~X ) ## Create a List of Univariate Formulas: fooUni <- formulaUnimva(spiddat~X) fooUniInt <- formulaUnimva(spiddat~X, intercept=TRUE) ## Find the three variables that best explain the response: best.r.sq( foo, n.xvars= 3) ## Fit a multivariate linear model: foo <- mvformula( spiddat~X ) lm.spider <- manylm(foo) ## Plot Diagnostics for a multivariate linear model: plot(lm.spider,which=1:2,col.main="red",cex=3,overlay=FALSE) ## Obtain a summary of test statistics using residual resampling: summary(lm.spider, nBoot=500) ## Calculate a ANOVA Table: anova(lm.spider, nBoot=500) ``` package

mvabund-package