non_linear_mlm_with_comparisons.Rmd

---
title: "post-hoc comparison with non-linear models"
author: "Clay Ford"
date: "2024-07-15"
output: html_document
---

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

## Get some data

Heights of Boys in Oxford. Data comes from the {nlme} package. This data frame contains the following columns:

- Subject: an ordered factor giving a unique identifier for each boy in the experiment
- age: a numeric vector giving the standardized age (dimensionless)
- height: a numeric vector giving the height of the boy (cm)


```{r}
data(Oxboys, package = "nlme")
```


## quick plot

Height obviously appears to be associated with age.

```{r}
library(ggplot2)
ggplot(Oxboys) +
  aes(age, height) +
  geom_line(aes(group = Subject)) + 
  geom_smooth(se = FALSE)
```

## fit a non-linear model

Model height as a function of age. A non-linear model is probably not necessary here, but we'll do it anyway.

```{r message=FALSE}
library(lme4)
m <- lmer(height ~ poly(age, 2) + (1 | Subject), data = Oxboys)
summary(m, corr = F)
```

## create a simple effect plot

```{r message=FALSE}
library(ggeffects)
plot(ggpredict(m, terms = "age [all]"))
```

## and now do post-hoc comparison 

Compare height at standardized age of 0.5 to -0.5. Notice we need to specify the age values to compare.

```{r message=FALSE}
library(emmeans)
emm <- emmeans(m, specs = "age", at = list(age = c(0.5, -0.5)))
contrast(emm, method = "pairwise")
```