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EvoArt committed Sep 3, 2021
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# BetaDispersion


This is a small package aimed at providing equivalent functionality to `betadisper` in the R package `vegan`, namely multivariate test for homogeneity of variance (dispersion). This is often used in ecology to compare beta diversity between metacommunities. This analysis comes from work by [Mari Anderson (2006)](https://onlinelibrary.wiley.com/doi/10.1111/j.1541-0420.2005.00440.x). However, a number of tweaks have been made to the preferred way of performing the analysis since then. We aim to keep this package aligned with decisions made by [vegan devs](https://github.com/vegandevs/vegan/blob/master/R/betadisper.R). However, the current implementation only offers permutation tests for P-values, and only spatial medians (not centroids) are used.
This is a small package aimed at providing equivalent functionality to `betadisper` in the R package `vegan`, namely multivariate test for homogeneity of variance (dispersion). This is often used in ecology to compare beta diversity between metacommunities. This analysis comes from work by [Marti Anderson (2006)](https://onlinelibrary.wiley.com/doi/10.1111/j.1541-0420.2005.00440.x). However, a number of tweaks have been made to the preferred way of performing the analysis since then. We aim to keep this package aligned with decisions made by [vegan devs](https://github.com/vegandevs/vegan/blob/master/R/betadisper.R). However, the current implementation only offers permutation tests for P-values, and only spatial medians (not centroids) are used.

<img src="https://github.com/EvoArt/BetaDispersion.jl/blob/master/docs/disp.svg">

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* `F` = Global F-Statistic
* `pairwise_F` = pairwise F-statistics

Additionally, If [Turing.jl](https://turing.ml/stable/) is loaded before BetaDisp you can call `bayesdisp` on the `Disp` returned by `dispersion` to perform Bayesian inference to estimate mean and standard deviation of the residuals of each group. By default 4 chains are run simultaneously using the No U-turns (NUTS) sampler for 1000 iterations each. The function returns the Markov chains along with diagnostics, more details can be found [here](https://turinglang.github.io/MCMCChains.jl/dev/). Check the [source code](https://github.com/EvoArt/BetaDispersion.jl/blob/master/src/Bayes.jl) to see the function arguments. If fine control over model implementation is required, the user is urged to construct their model directly in Turing.jl.
Additionally, If [Turing.jl](https://turing.ml/stable/) is loaded before BetaDispersion you can call `bayesdisp` on the `Disp` returned by `dispersion` to perform Bayesian inference to estimate mean and standard deviation of the residuals of each group. By default 4 chains are run simultaneously using the No U-turns (NUTS) sampler for 1000 iterations each. The function returns the Markov chains along with diagnostics, more details can be found [here](https://turinglang.github.io/MCMCChains.jl/dev/). Check the [source code](https://github.com/EvoArt/BetaDispersion.jl/blob/master/src/Bayes.jl) to see the function arguments. If fine control over model implementation is required, the user is urged to construct their model directly in Turing.jl.

## Example usage

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