---
title: "Interest measures"
author: "Michael Hahsler"
output:
  rmarkdown::html_vignette:
    toc: true
vignette: >
  %\VignetteIndexEntry{Interest measures}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(collapse = TRUE, comment = "#>")
library(arules)
set.seed(1234)
```

No single measure identifies every useful association. Support and confidence
describe prevalence and conditional probability, while measures such as lift
and leverage compare observed co-occurrence with what would be expected under
independence.

```{r}
trans <- transactions(list(
  T1 = c("tea", "cookies", "milk"),
  T2 = c("tea", "cookies"),
  T3 = c("coffee", "cookies"),
  T4 = c("tea", "milk"),
  T5 = c("coffee", "milk"),
  T6 = c("tea", "cookies", "milk"),
  T7 = c("coffee", "cookies"),
  T8 = c("tea", "cookies")
))

rules <- apriori(
  trans,
  parameter = list(support = 0.25, confidence = 0.5),
  control = list(verbose = FALSE)
)
```

The quality data frame already contains the measures calculated during mining.

```{r}
head(quality(rules))
```

Different measures answer different questions:

* **Support** is the proportion of transactions containing both sides.
* **Confidence** estimates the conditional probability of the right-hand side.
* **Coverage** is the support of the left-hand side.
* **Lift** is confidence divided by the right-hand-side support; values above
  one indicate positive association.

A rare rule can have high lift but little practical impact, while a rule with
high confidence may simply predict a very common consequent. It is therefore
often useful to consider several measures together.

`arules` implements many commonly used measures. The complete list is in
[A Probabilistic Comparison of Commonly Used Interest Measures for Association Rules](https://mhahsler.github.io/arules/docs/measures).

## Calculating additional measures for rules

`interestMeasure()` calculates additional measures. Supply the transactions
for measures that require counts not stored with the rules.

```{r}
measures <- interestMeasure(
  rules,
  measure = c("leverage", "phi"),
  transactions = trans
)
head(measures)
```

Here, leverage is the observed joint support minus the support expected under
independence. Phi is the correlation between the left- and right-hand sides of
a rule; it is undefined for some rules.

Add selected measures as new columns in the quality data frame.

```{r}
quality(rules) <- cbind(
  quality(rules),
  interestMeasure(
    rules,
    measure = c("leverage", "phi"),
    transactions = trans
  )
)
```

The new measures can now be used to filter and sort rules.

```{r}
inspect(head(sort(rules, by = "leverage"), 3))
```

## Other vignettes

* [Getting started with arules](getting-started.html)
* [Preparing transaction data](preparing-transaction-data.html)
* [Mining and pruning association rules](mining-and-pruning-rules.html)
* [Item hierarchies](item-hierarchies.html)