cld.qmd

---
title: "Compact Letter Displays"
author: "Clay Ford"
date: 2024-03-13
format:
  html:
    embed-resources: true
---

In Compact Letter Displays (CLD), groups that do not differ significantly from each other share the same letter, while groups that do show significant differences will have different letters.

Demonstrate using "pigs" data included with {emmeans} package.

- source: Source of protein in the diet (factor with 3 levels: fish meal, soybean meal, milk)
- percent: Protein percentage in the diet (numeric with 4 values: 9, 12, 15, and 18)
- conc: Concentration of free plasma leucine, in mcg/ml

```{r message=FALSE}
library(emmeans)
library(ggplot2)
library(multcomp)
data(pigs)
pigs$percent <- factor(pigs$percent)
```

Looks like most of the variability in conc is due to source, but percent contributes as well.

```{r}
plot.design(pigs)
```

Fit a 2-way ANOVA with no interaction. 

```{r}
pigs.lm <- lm(conc ~ source + percent, data = pigs)
car::Anova(pigs.lm)
```

Now use {emmeans} to estimate marginal means. 

```{r}
pigs.emm <- emmeans(pigs.lm, c("percent", "source"))
pigs.emm
```

Now generate compact letter displays using the `cld()` function from the {multcomp} package. The {emmeans} package provides a method for running this function on {emmeans} objects. This replicates the `emmeans()` output above with an extra columns for the letters.

```{r}
multcomp::cld(pigs.emm, Letters = LETTERS)
```

I like the note: 

> NOTE: If two or more means share the same grouping symbol,
      then we cannot show them to be different.
      But we also did not show them to be the same.

Save as a data frame so we can create the CLD plot.

```{r}
cld_df <- multcomp::cld(pigs.emm, Letters = LETTERS)
names(cld_df)
```

Now create the plot. Use `show.legend = F` in `geom_text()` to suppress a letter from appearing in the legend.

```{r}
ggplot(cld_df) +
  aes(x = percent, y = emmean, color = source) +
  geom_point(position = position_dodge(width = 0.9)) +
  geom_errorbar(mapping = aes(ymin = lower.CL, ymax = upper.CL), 
                              position = position_dodge(width = 0.9),
                width = 0.1) +
  geom_text(mapping = aes(label = .group, y = upper.CL * 1.05), 
            position = position_dodge(width = 0.9), 
            show.legend = F)
```

Recall: groups that do not differ significantly from each other share the same letter, while groups that do show significant differences will have different letters. For example, fish at 9 percent appears to be different from soy and skim at 9 percent.

See [this page](https://schmidtpaul.github.io/dsfair_quarto//ch/summaryarticles/compactletterdisplay.html) for R code to create fancier CLD plots and some interesting critiques of CLD. For example, the developer of the {emmeans} package [is on record](https://stats.stackexchange.com/a/508092/46334) saying, "Providing for CLDs _at all_ remains one of my biggest regrets in developing this package." [In another Stack Overflow answer](https://stackoverflow.com/a/70856238/2765195) he states, "IMO, almost anything is better than a CLD. They display non-findings rather than findings."

He instead suggests presenting simple comparisons in tabular form, like so:

```{r}
pairs(pigs.emm, by = "source")
pairs(pigs.emm, by = "percent")
```