diff --git a/README.md b/README.md index 704897f..e7e4b3c 100644 --- a/README.md +++ b/README.md @@ -24,7 +24,7 @@ Introductory statistics are typically taught as a sequence of disconnected tests - [Generalised Additive Models (GAMs)](GAMs.pdf) - [An introduction to Bayesian modelling](Bayes_intro.pdf) - [Causal inference](causal-inference.pdf) - +- [Regression to the mean](regression-to-the-mean.pdf) ### Interactive tutorials, R scripts, etc diff --git a/regression-to-the-mean.Rmd b/regression-to-the-mean.Rmd new file mode 100644 index 0000000..6681505 --- /dev/null +++ b/regression-to-the-mean.Rmd @@ -0,0 +1,160 @@ +--- +title: "Regression to the mean" +# subtitle: "Nice subtitle here" +author: "Francisco Rodríguez-Sánchez" +institute: "https://frodriguezsanchez.net" +# date: "today" +aspectratio: 43 # use 169 for wide format +fontsize: 12pt +output: + binb::metropolis: + keep_tex: no + incremental: yes + fig_caption: no + pandoc_args: ["--lua-filter=hideslide.lua"] +urlcolor: blue +linkcolor: blue +header-includes: + - \definecolor{shadecolor}{RGB}{230,230,230} + # - \setbeamercolor{frametitle}{bg=black} + # - \logo{\includegraphics[height=2cm, width = 5cm]{logo.png}} # add logo to all slides + # - \titlegraphic{\vspace{6cm}\hfill\includegraphics[width=6cm]{logo.png}} # add logo to title slide +--- + + +```{r knitr_setup, include=FALSE, cache=FALSE} + +library("knitr") + +### Chunk options ### + +## Text results +opts_chunk$set(echo = FALSE, warning = FALSE, message = FALSE, size = 'tiny') + +## Code decoration +opts_chunk$set(tidy = FALSE, comment = NA, highlight = TRUE, prompt = FALSE, crop = TRUE) + +# ## Cache +# opts_chunk$set(cache = TRUE, cache.path = "knitr_output/cache/") + +# ## Plots +# opts_chunk$set(fig.path = "knitr_output/figures/") +opts_chunk$set(fig.align = 'center', out.width = '90%') + +### Hooks ### +## Crop plot margins +knit_hooks$set(crop = hook_pdfcrop) + +## Reduce font size +## use tinycode = TRUE as chunk option to reduce code font size +# see http://stackoverflow.com/a/39961605 +knit_hooks$set(tinycode = function(before, options, envir) { + if (before) return(paste0("\n \\", options$size, "\n\n")) + else return("\n\n \\normalsize \n") + }) + +``` + + +## Most biodiverse sites are losing more species + +WHY?? + +```{r} +include_graphics("images/RTM-1.png") +``` + +\scriptsize +\hfill Mazalla & Diekmann 2022 + + +## Most biodiverse sites are losing more species. Why? + +- Stronger competition + +- Humans destroying most species-rich sites + +- Establishment of new species favoured in poor sites + +. . . + +- No ecological cause, but stochastic variation (**regression to the mean**) + + +## A simulation for 100 sites + +:::::::::::::: {.columns align=center} + +::: {.column width="70%"} +- Simulate initial number of species: + + - \scriptsize `rnorm(n = 100, mean = 15, sd = 1)` + +- Simulate number of species at resurvey: + + - \scriptsize `rnorm(n = 100, mean = 15, sd = 1)` + +- **No change at all!** +::: + +::: {.column width="30%" } +```{r out.width="100%"} +include_graphics("images/hist_spp.png") +``` + +::: +:::::::::::::: + +## Regression to the mean + +Species-rich sites lose more species + +Species-poor sites gain more species + +Negative trend against baseline + +```{r out.width="100%"} +include_graphics("images/RTM-2.png") +``` + +\scriptsize +\hfill Mazalla & Diekmann 2022 + + +--- + +Whenever two sets of measurements are not perfectly correlated + +there will be regression towards the mean + +```{r} +set.seed(8) +dat <- data.frame(site = 1:100, + sp1 = rnorm(100, 5, 1)) |> + dplyr::mutate(sp2 = 2 + 0.5*sp1 + rnorm(100, 0, 0.3)) + +library(ggplot2) +ggplot(dat) + + aes(sp1, sp2) + + geom_point() + + geom_abline(intercept = 0, slope = 1) + + geom_smooth(method = "lm") + + coord_cartesian(xlim = c(2, 8), ylim = c(2, 8)) + + theme_minimal(base_size = 18) + + labs(x = "Initial", y = "Resurvey", title = "Number of species") +``` + + +## What to do? + +- Model outcome ~ baseline + +- Include baseline as predictor + + +## To learn more + +- [Mazalla & Diekmann 2022](https://doi.org/10.1111/jvs.13117) + +- [Kelly & Price 2005](https://doi.org/10.1086/497402) + diff --git a/regression-to-the-mean.pdf b/regression-to-the-mean.pdf new file mode 100644 index 0000000..aa9e00f Binary files /dev/null and b/regression-to-the-mean.pdf differ