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circus

circus is an R package provides functions for calcuating descriptive statistics using variance components from brms model objects.

Introduction

When quantitative measurements are hierarchically organized at multiple levels, intra-class correlations (ICC) can be used to express how strongly units of the same group resemble each other (McGraw & Wong 1996). ICC takes the form:

\begin{align*} \Large ICC &= \frac{\sigma_G}{(\sigma_G + \sigma_e)} \end{align*}

where \begin{align*} \sigma_G \end{align*} is the variance amoung units of a specific group and \begin{align*} \sigma_e \end{align*} is the residual variance. One application of ICC in biological literature is the calculation of heritability in quantitive genetics studies from animal models (Wilson et. al, 2010) or repeatability of behavioural traits in animal personality studies (Nakagawa & Schielzeth, 2010)

Currently circus supports one function get_icc() to compute ICC from random effects models.

Installation

circus is not currently on CRAN. For testing purposes only it can be downloaded through devtools as follows:

install.packages("remotes")
remotes::install_github("fontikar/circus", build_vignettes=T)

library(circus)

NOTE: This package is still under development so functions have not be extensively tested. Please reach out if you have any feedback.

How it works

As a simple example, we will fit an animal model using random regression to model the birth weight of mythical gryphons using brms. We will use the gryphon dataset and gryphonPed pedigree included in the circus package to estimate heritability of birth weight (BWT). We will also partition variance due to MOTHER identity and YEAR as mothers gave birth across different years by fitting these as random intercepts.

#Arrange the pedigree into an inverted relatedness matrix
inv.phylo <- MCMCglmm::inverseA(gryphonPed)
A <- solve(inv.phylo$Ainv)
rownames(A) <- rownames(inv.phylo$Ainv)

#Fitting the model
model <- brms::brm(
  BWT ~  1 + (1|ANIMAL) + (1|MOTHER) + (1|BYEAR), 
  data = gryphon,
  family = gaussian(), cov = list(ANIMAL = A),
  chains = 1, iter = 20)

NOTE: This fit is a very short run and is for demonstrative purposes only. It will result in warnings about convergence etc.

Heritability (h2) is the proportion of total variance in birthweight attributed to genetic differences among each individual (ANIMAL). Total variance is the sum of all variance components:

\begin{align*} \Large h^2 &= \frac{\sigma_{ANIMAL}}{(\sigma_{ANIMAL} + \sigma_{MOTHER} + \sigma_{BYEAR} + \sigma_{e})} \end{align*} 

#Compute ICC for the group variable "ANIMAL", this is heritability
get_icc(model, var = "ANIMAL")
#>        var  Estimate  Est.Error     Lower     Upper
#> icc ANIMAL 0.3183965 0.07118566 0.1866593 0.4701074

References

McGraw, K. O., & Wong, S. P. (1996). Forming inferences about some intraclass correlation coefficients. Psychological methods, 1(1), 30.

Wilson, A. J., Reale, D., Clements, M. N., Morrissey, M. M., Postma, E., Walling, C. A., Kruuk, L. E. B & Nussey, D. H. (2010). An ecologist's guide to the animal model. Journal of Animal Ecology, 79(1), 13-26.

Nakagawa, S., & Schielzeth, H. (2010). Repeatability for Gaussian and non-Gaussian data: a practical guide for biologists. Biological Reviews, 85(4), 935-956.