Avoiding the misuse of BLUP in behavioral ecology: I. Multivariate modelling for individual variation (MCMCglmm tutorial)

Introduction

Overview

This tutorial accompanies our 2017 Behavioral Ecology paper, “Avoiding the misuse of BLUP in behavioral ecology”. Below, we provide worked examples of multivariate statistical methods for directly testing hypotheses about associations between individual variation in behaviour and other traits. Below, we will: - Test the correlation between two personality traits (behaviours measured repeatedly on individuals); - Test for an association between these personality traits and a measure of fitness (one value per individual).

In this version of the tutorial, we illustrate these models using the R package MCMCglmm, developed by Jarrod Hadfield. Visit the CRAN page for MCMCglmm here for links and citation info: https://cran.r-project.org/web/ packages/MCMCglmm/index.html. MCMCglmm fits generalised linear mixed modes (GLMMs) in a Bayesian framework, using Markov chain Monte Carlo techniques. We have also provided a separate tutorial for the R interface for ASReml, which fits GLMMs using maximum likelihood (and so is likely more familiar to lme4 users) but is commercially licensed software. Updates and further tutorials associated with this paper can be found at https://tomhouslay.com/tutorials/.

Aims

Please note that we do assume readers are familiar with the general principles of specifying mixed effects models, and in particular with the use of MCMCglmm for univariate mixed effects models. Readers unfamiliar with using univariate mixed effects models for modelling a single behavioural trait might prefer to start with Dingemanse & Dochtermann’s 2013 paper, ‘Quantifying individual variation in behaviour: mixed effects modelling approaches’. Readers unfamiliar with MCMCglmm should look at Jarrod Hadfield’s excellent course notes, available at the MCMCglmm CRAN page: https://cran.r-project.org/web/packages/MCMCglmm/index.html. We also use various methods for manipulating and visualising data frames using the tidyverse package (including tidyr, dplyr, ggplot2 etc) — more details on their use can be found at http://r4ds.had.co.nz/. In our tutorial, we aim to teach the following: - How to phrase questions of interest in terms of variances and covariances (or derived correlations or regressions); - How to incorporate more advanced model structures, such as: - Fixed effects that apply only to a subset of the response traits; - Traits which are measured a different number of times (e.g., repeated measures of behaviour and a single value of breeding success); - Interpreting MCMC credible intervals.

Tufte样式在Edward Tufte的书以及物理学家费曼的教科书很常见，它的一个显著特点就是边栏的使用。例如脚注和边栏注解，以及放在边栏里的小型插图。Tufte样式在LaTeX和HTML/CSS中都有实现¹。我们将这两种实现都纳入了tufte包。若需要LaTeX/PDF输出，使用输出格式tufte_handout即可，类似地，tufte_book可以用来输出PDF书，tufte_html生成HTML网页。这些输出格式可以在YAML元数据中指定，或者传给rmarkdown::render()函数。若对rmarkdown包不熟悉，可参见 Allaire et al. (2017)。

---
title: "一个Tufte样式示例"
author: "张三"
ctex: yes
output:
  tufte::tufte_handout:
    latex_engine: xelatex
  tufte::tufte_html: default
---

章节标题

Tufte样式不主张太深的章节目录，一般仅仅使用一级标题（Markdown中用一个井号#）和二级标题（两个井号）。

插图

边栏插图

插图在Tufte的书中非常常见，我们可以使用三种插图：边栏图、全宽图、主栏图。先说边栏图：使用knitr代码段选项fig.margin = TRUE即可将图形放置在边栏中，如：

library(ggplot2)
mtcars2 <- mtcars
mtcars2$am <- factor(
  mtcars$am, labels = c('automatic', 'manual')
)
ggplot(mtcars2, aes(hp, mpg, color = am)) +
  geom_point() + geom_smooth() +
  theme(legend.position = 'bottom')

## `geom_smooth()` using method = 'loess'

MPGhorsepower;

注意我们使用代码段选项fig.cap设定了图的标题。当然我们也可以设置图的长宽。

任意边栏内容

事实上我们可以在边栏中放置除了图之外的内容，此时我们不再使用```{r}写代码段，而是用```{marginfigure}。例如右边有一个微积分第一基本定理。

根据微积分第一基本定理我们知道，对$x \in [a, b]$有
$$\frac{d}{dx}\left( \int_{a}^{x} f(u)\,du\right)=f(x).$$

为了文本内容的可移植性（同样的内容可以生成HTML和LaTeX文档），我们建议边栏中不要放置太复杂的内容，简单的加粗、倾斜都没有问题，但不建议在边栏中使用列表、参考文献等内容。

全宽插图

代码段选项fig.fullwidth = TRUE可以使得一幅图占用全部页宽，例如：

ggplot(diamonds, aes(carat, price)) + geom_smooth() +
  facet_grid(~ cut)

## `geom_smooth()` using method = 'gam'

其它和图形有关的代码段选项仍然可以使用，一般情况下，全款图形的fig.width选项会较大，而fig.height相对较小。上图的尺寸是\(10 \times 2\)英寸.

主栏插图

默认情况下，R代码段生成的图形放置在主栏里，其标题放在边栏中，例如：

ggplot(diamonds, aes(cut, price)) + geom_boxplot()

边栏附注

Tufte样式的文档中，脚注会被自动转换为边栏附注²。脚注是带编号的，另一种边栏附注是不带编号的，这种附注需要用tufte包中的R函数margin_note()在knitr行内代码中生成。⊕,与边栏插图一样，边栏附注中我们也不建议写太复杂的内容，通常只是一句简单的文字。

参考文献

HTML输出中，参考文献默认也放在边栏中。例如这里我们可以引用(R Core Team 2016)。这个功能需要在YAML元数据中设置link-citations: yes，而且pandoc-citeproc程序的版本应该至少是0.7.2。若这两个条件不满足，参考文献会被放在文档末尾。

表格

我们可以用knitr包中的kable()函数生成简单的表格。HTML输出中表格的标题也会被放在边栏中。

knitr::kable(
  mtcars[1:6, 1:6], caption = 'mtcars数据的前几行。'
)

mtcars

	mpg	cyl	disp	hp	drat	wt
Mazda RX4	21.0	6	160	110	3.90	2.620
Mazda RX4 Wag	21.0	6	160	110	3.90	2.875
Datsun 710	22.8	4	108	93	3.85	2.320
Hornet 4 Drive	21.4	6	258	110	3.08	3.215
Hornet Sportabout	18.7	8	360	175	3.15	3.440
Valiant	18.1	6	225	105	2.76	3.460

引文

Markdown语法使用>来生成引文，如果需要在引文下面用行内代码以及quote_footer()函数加上一句引文来源，例如：

“多亏了我的律师，要不然我现在还在牢里。两个人一起挖确实比一个人快很多啊。”

— Joe Martin

如果不用这个函数的话，引文底部的话只是一个普通段落：

“伟人论道，凡人论事，小人论酒。”

— Fran Lebowitz

响应式页面

这个包生成的HTML页面是响应式的：如果页宽小于760像素，边栏内容会自动隐藏。此时我们可以点击脚注的序号显示它，其它边栏附注则可以通过点击圆圈加号的符号显示。

结语

希望诸位喜欢R Markdown的超级简洁性，同时我们感谢Tufte-CSS和Tufte-LaTeX项目的作者们，没有他们的辛勤劳动，就没有这个tufte包。这份文档的R Markdown源文档可以在Github上找到，或者直接使用RStudio菜单File -> New File -> R Markdown -> From Template新建一个文档，或直接从R里面打开这个Rmd文件：

file.edit(
  tufte:::template_resources(
    'tufte_ctex', '..', 'skeleton', 'skeleton.Rmd'
  )
)

Allaire, JJ, Joe Cheng, Yihui Xie, Jonathan McPherson, Winston Chang, Jeff Allen, Hadley Wickham, Aron Atkins, Rob Hyndman, and Ruben Arslan. 2017. Rmarkdown: Dynamic Documents for R. https://CRAN.R-project.org/package=rmarkdown.

R Core Team. 2016. R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. https://www.R-project.org/.

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1. 参见Github库tufte-latex和 tufte-css↩

2. 这里本来是一个脚注↩