Likelihood ratio test in R (using base functions or lrtest function)

lrtest.Rmd

---
title: "R Notebook"
output: html_notebook
---

## An example of likelihood ratio tests in R

```{r setup}
library(lmtest)
library(palmerpenguins)
library(ggplot2)
```

## View data

Adelie penguin data was used.
Omitted the missing values assuming MCAR.

```{r}
adelie <- penguins[penguins$species == "Adelie" &
                     !is.na(penguins$bill_depth_mm) &
                     !is.na(penguins$bill_length_mm), ]
ggplot(adelie) +
  geom_point(aes(x = bill_depth_mm, y = bill_length_mm, colour = island))
ggsave("plot01.png", width = 640, height = 480, units = "px", dpi = 144)
```

### Models

Model1: bill_length_mm ~ bill_depth_mm
Model2: bill_length_mm ~ bill_depth_mm + island

```{r}
model1 <- lm(bill_length_mm ~ bill_depth_mm, data = adelie)
model2 <- lm(bill_length_mm ~ bill_depth_mm + island, data = adelie)
```

### Likelihood ratio test

using the base functions

```{r}
(logLik1 <- logLik(model1))
(logLik2 <- logLik(model2))
df1 <- attr(logLik1, "df")
df2 <- attr(logLik2, "df")
d2logLik <- 2 * (logLik2 - logLik1)
attributes(d2logLik) <- NULL
d2logLik
1 - pchisq(d2logLik, df = df2 - df1)
```

using the lrtest function

```{r}
lrtest(model1, model2)
```