Fleshing out case study of mixed-effects model

_freeze/mod_stats/execute-results/html.json

@@ -1,8 +1,8 @@
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-    "markdown": "---\ntitle: \"Analysis & Modeling\"\ncode-annotations: hover\n---\n\n\n## Overview\n\nGiven the wide range in statistical training in graduate curricula (and corresponding breadth of experience among early career researchers), we'll be approaching this module in a different way than the others. One half of the module will use a \"flipped approach\" where project teams will share their proposed analyses with one another. The other half of the module will be dedicated to analyses that are more common in--or exclusive to--synthesis research. Content produced by project teams during the flipped half may be linked in the [Additional Resources](https://lter.github.io/ssecr/mod_stats.html#additional-resources) section at the bottom of this module at the discretion of each team. Otherwise the content of this module will focus only on the non-flipped content.\n\n## Learning Objectives\n\nAfter completing this module you will be able to: \n\n- <u>Describe</u> proposed analytical methods to an interested audience of mixed prior experience\n- <u>Explain</u> nuance in interpretation of results of proposed analyses\n- <u>Compare</u> and contrast interpretation of results in synthesis work versus primary research\n- <u>Identify</u> statistical tests common in synthesis research\n- <u>Perform</u> some synthesis-specific analyses\n\n## Needed Packages\n\nIf you'd like to follow along with the code chunks included throughout this module, you'll need to install the following packages:\n\n\n::: {.cell}\n\n```{.r .cell-code}\n# Note that these lines only need to be run once per computer\n## So you can skip this step if you've installed these before\ninstall.packages(\"tidyverse\")\n```\n:::\n\n\n## Mixed-Effects Models\n\n\n\n## Multi-Model Inference\n\n\n\n## Meta-Analysis\n\n\n\n## Additional Resources\n\n### Papers & Documents\n\n- [Understanding ‘It Depends’ in Ecology: A Guide to Hypothesising, Visualising and Interpreting Statistical Interactions](https://onlinelibrary.wiley.com/doi/10.1111/brv.12939). Spake _et al._, 2023. **Biological Reviews** \n- [Improving Quantitative Synthesis to Achieve Generality in Ecology](https://www.nature.com/articles/s41559-022-01891-z). Spake _et al._, 2022.**Nature Ecology and Evolution**\n- [Doing Meta-Analysis with R: A Hands-On Guide](https://bookdown.org/MathiasHarrer/Doing_Meta_Analysis_in_R/)\n\n### Workshops & Courses\n\n- Matt Vuorre's [Bayesian Meta-Analysis with R, Stan, and brms](https://mvuorre.github.io/posts/2016-09-29-bayesian-meta-analysis/)\n\n### Websites\n\n- \n",
+    "markdown": "---\ntitle: \"Analysis & Modeling\"\ncode-annotations: hover\n---\n\n\n## Overview\n\nGiven the wide range in statistical training in graduate curricula (and corresponding breadth of experience among early career researchers), we'll be approaching this module in a different way than the others. One half of the module will use a \"flipped approach\" where project teams will share their proposed analyses with one another. The other half of the module will be dedicated to analyses that are more common in--or exclusive to--synthesis research. Content produced by project teams during the flipped half may be linked in the [Additional Resources](https://lter.github.io/ssecr/mod_stats.html#additional-resources) section at the bottom of this module at the discretion of each team. Otherwise the content of this module will focus only on the non-flipped content.\n\n## Learning Objectives\n\nAfter completing this module you will be able to: \n\n- <u>Describe</u> proposed analytical methods to an interested audience of mixed prior experience\n- <u>Explain</u> nuance in interpretation of results of proposed analyses\n- <u>Compare</u> and contrast interpretation of results in synthesis work versus primary research\n- <u>Identify</u> statistical tests common in synthesis research\n- <u>Perform</u> some synthesis-specific analyses\n\n## Needed Packages\n\nIf you'd like to follow along with the code chunks included throughout this module, you'll need to install the following packages:\n\n\n::: {.cell}\n\n```{.r .cell-code}\n# Note that these lines only need to be run once per computer\n## So you can skip this step if you've installed these before\ninstall.packages(\"tidyverse\")\n```\n:::\n\n\n## Mixed-Effects Models\n\nIn any statistical test there is at least one response variable (a.k.a. \"dependent\" variable) and some number of explanatory variables (a.k.a. \"independent\" variables). However, in biology our experiments often involve repeated sampling over time or at the same locations in order to gather enough replicates to do robust analysis. These variables are neither response nor explanatory variables but we might reasonably conclude that they affect our response and/or explanatory variables.\n\nIn essence we want to use a statistical tool that asks <u>what is the effect of the explanatory variable(s) on the response _when the variation due to these non-variable considerations are accounted for_</u>?' Such tests are called \"mixed-effects models.\" This name derives from considering explanatory variables \"fixed effects\" and these non-explanatory/response variables as \"random effects\". Including both fixed and random effects thus creates a model with \"mixed effects.\"\n\n### Mixed-Effects Case Study\n\nLet's imagine we are researching tarantula populations for several years in the Chihuahuan Desert. Our hypothesis is that the number of tarantulas (response variable) will be greater in sites further from the nearest road (explanatory variable). We select ten study sites of varying distances from the nearest road and intensively count our furry friends for several months at three plots within each site. We return to our sites--and their associated plots--and repeat this process each year for three years. After entering our data in MS Excel here's what we walk away with.\n\n\n\nWith our data in hand we now want to run some statistical tests and--hopefully--get some endorphine-inducing small _p_ values.\n\nIf we choose to simply ignore our possible random effects, our model would look something like this:\n\n```\ntarantula_count ~ road_dist_km\n```\n\n\n\nHowever, from our extensive time in the field we have developed a strong intuition that \n\n\n\n## Multi-Model Inference\n\n\n\n## Meta-Analysis\n\n\n\n## Additional Resources\n\n### Papers & Documents\n\n- [Understanding ‘It Depends’ in Ecology: A Guide to Hypothesising, Visualising and Interpreting Statistical Interactions](https://onlinelibrary.wiley.com/doi/10.1111/brv.12939). Spake _et al._, 2023. **Biological Reviews** \n- [Improving Quantitative Synthesis to Achieve Generality in Ecology](https://www.nature.com/articles/s41559-022-01891-z). Spake _et al._, 2022.**Nature Ecology and Evolution**\n- [Doing Meta-Analysis with R: A Hands-On Guide](https://bookdown.org/MathiasHarrer/Doing_Meta_Analysis_in_R/). Harrier _et al._ 2023.\n- [Mixed Effects Models and Extensions in Ecology with R](https://link.springer.com/book/10.1007/978-0-387-87458-6). Zuur _et al._, 2009.\n\n### Workshops & Courses\n\n- Matt Vuorre's [Bayesian Meta-Analysis with R, Stan, and brms](https://mvuorre.github.io/posts/2016-09-29-bayesian-meta-analysis/)\n\n### Websites\n\n- \n",
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mod_stats.qmd

@@ -31,6 +31,28 @@ install.packages("tidyverse")
 
 ## Mixed-Effects Models
 
+In any statistical test there is at least one response variable (a.k.a. "dependent" variable) and some number of explanatory variables (a.k.a. "independent" variables). However, in biology our experiments often involve repeated sampling over time or at the same locations in order to gather enough replicates to do robust analysis. These variables are neither response nor explanatory variables but we might reasonably conclude that they affect our response and/or explanatory variables.
+
+In essence we want to use a statistical tool that asks <u>what is the effect of the explanatory variable(s) on the response _when the variation due to these non-variable considerations are accounted for_</u>?' Such tests are called "mixed-effects models." This name derives from considering explanatory variables "fixed effects" and these non-explanatory/response variables as "random effects". Including both fixed and random effects thus creates a model with "mixed effects."
+
+### Mixed-Effects Case Study
+
+Let's imagine we are researching tarantula populations for several years in the Chihuahuan Desert. Our hypothesis is that the number of tarantulas (response variable) will be greater in sites further from the nearest road (explanatory variable). We select ten study sites of varying distances from the nearest road and intensively count our furry friends for several months at three plots within each site. We return to our sites--and their associated plots--and repeat this process each year for three years. After entering our data in MS Excel here's what we walk away with.
+
+
+
+With our data in hand we now want to run some statistical tests and--hopefully--get some endorphine-inducing small _p_ values.
+
+If we choose to simply ignore our possible random effects, our model would look something like this:
+
+```
+tarantula_count ~ road_dist_km
+```
+
+
+
+However, from our extensive time in the field we have developed a strong intuition that 
+
 
 
 ## Multi-Model Inference
@@ -47,7 +69,8 @@ install.packages("tidyverse")
 
 - [Understanding ‘It Depends’ in Ecology: A Guide to Hypothesising, Visualising and Interpreting Statistical Interactions](https://onlinelibrary.wiley.com/doi/10.1111/brv.12939). Spake _et al._, 2023. **Biological Reviews** 
 - [Improving Quantitative Synthesis to Achieve Generality in Ecology](https://www.nature.com/articles/s41559-022-01891-z). Spake _et al._, 2022.**Nature Ecology and Evolution**
-- [Doing Meta-Analysis with R: A Hands-On Guide](https://bookdown.org/MathiasHarrer/Doing_Meta_Analysis_in_R/)
+- [Doing Meta-Analysis with R: A Hands-On Guide](https://bookdown.org/MathiasHarrer/Doing_Meta_Analysis_in_R/). Harrier _et al._ 2023.
+- [Mixed Effects Models and Extensions in Ecology with R](https://link.springer.com/book/10.1007/978-0-387-87458-6). Zuur _et al._, 2009.
 
 ### Workshops & Courses