---
title: "FW 536 — Day 3 afternoon lab (model selection) — Your Name"
author: "Your Name Here"
date: "`r Sys.Date()`"
output:
  html_document:
    self_contained: true
    toc: true
    toc_depth: 3
    toc_float: true
    code_folding: show
    theme: cosmo
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE, message = FALSE, warning = FALSE)
```

# Day 3 afternoon lab — Model selection problem set

This template matches the afternoon (Part 2) problems in
[`problem_set.html`](problem_set.html#afternoon). Read each problem statement there,
write your work below, **Knit** to HTML, and upload the `.html` to the matching
Canvas assignment.

For setup help see the [R Markdown tutorial](../rmarkdown_tutorial.html).

---

# Setup

```{r}
# Load packages you'll need. Add or remove as appropriate.
library(ggplot2)
library(dplyr)
library(lme4)
library(nlme)
library(AICcmodavg)
library(MuMIn)
library(boot)          # cross-validation (cv.glm)
options(na.action = "na.fail")   # required by MuMIn::dredge()
```

```{r data}
# Problem 10 uses the real trophic-position data (fixed factors this time).
dat <- read.csv("data/qcbs_w6_data.csv")
dat$Fish_Species <- as.factor(dat$Fish_Species)
dat$Lake         <- as.factor(dat$Lake)
dat$Z_Length     <- scale(dat$Fish_Length)[, 1]
```

---

# Problem 7 — What does $\Delta\text{AIC} = 1.5$ actually mean?

> Simulate a strong real effect plus a pure-noise predictor and record how often
> the junk model lands within 2 AIC units of the correct one.

**My work:**

```{r}
# Your R code here
```

**Answer / biological interpretation:**


---

# Problem 8 — Type I error of AIC / AICc / BIC on pure noise

> Response unrelated to three predictors; `dredge()` every subset; record how often
> the top model retains a noise variable under each criterion.

**My work:**

```{r}
# Your R code here (options(na.action = "na.fail") is set above)
```

**Answer / biological interpretation:**


---

# Problem 9 — BIC vs AIC on a weak-but-real effect

> Three predictors (strong / modest / weak). Report the proportion of 500 reps in
> which each criterion retains each predictor.

**My work:**

```{r}
# Your R code here
```

**Answer / biological interpretation:**


---

# Problem 10 — AIC vs LOOCV on the trophic-position data (qcbs_w6_data.csv)

> Rank candidate fixed-effect models by AICc and by LOOCV MSE (`cv.glm`), compute
> Akaike weights, and compare the best model's CV MSE to `var(Trophic_Pos)`.

**My work:**

```{r}
# Your R code here (dat data frame is loaded above)
```

**Answer / biological interpretation:**


---

# Problem 11 — Multimodel inference and the "right question" trap

> From the AICc table, confirm the Akaike weights, discuss averaging coefficients
> vs predictions, and re-frame the temperature question as an evidence ratio.

**My work:**

```{r}
# Your R code here
```

**Answer / biological interpretation:**


---

# (Optional) Embed a photo of hand-written work

For problems easier to do on paper, photograph and embed:

```{r, echo=FALSE, eval=FALSE, out.width="60%", fig.cap="Hand-derivation for Problem N"}
knitr::include_graphics("images/problemN_derivation.jpg")
```

(Change `eval=FALSE` to `eval=TRUE` after saving an image. See the
[R Markdown tutorial](../rmarkdown_tutorial.html) for details.)

---

# Submission checklist

- [ ] Answered every afternoon (Part 2) problem from `problem_set.html`.
- [ ] Loaded `qcbs_w6_data.csv` from `data/` for the AIC-vs-CV problem.
- [ ] Knitted to HTML without errors.
- [ ] Photos (if any) embedded with `self_contained: true` in the YAML.
- [ ] Uploaded the `.html` to the matching Canvas assignment.