Association and dissociation
1. Association and dissociation
So far, we've talked exclusively about measures of association. But what about dissociation? What if reading one book predicts that an individual will not read another? In this video, we'll look at a metric that measures both.2. Using dissociation to pair ebooks
Let's return to the job we were hired to do in the exercises: help a start-up organize ebooks on a website. We're given four books to work with initially: The Hobbit, The Great Gatsby, Pride and Prejudice, and The Catcher in the Rye. We could approach this by suggesting that the company pair books that have high measures of association. We could also approach this by suggesting they separate books that don't typically appear together in reader libraries or are ``dissociated.'' In this video, we'll learn about a single metric that captures both association and dissociation.3. Introduction to Zhang's metric
The metric we'll discuss in this video was introduced in Zhang (2000) and has since become known as Zhang's metric. It is bounded from below by -1 and bounded from above by 1. A value of 1 indicates perfect association. Negative 1 indicates perfect dissociation. Zhang's metric is comprehensive in the sense that it measures both association and dissociation. It is also interpretable and has a definition in terms of simpler metrics.4. Defining Zhang's metric
Zhang's metric is defined as the difference between the confidence metrics of "if A then B" and "if NOT A then B," divided by the maximum of the confidence of "if A then B" and of "if NOT A then B." Let's unpack that slowly, starting with the numerator. First, we compute the confidence metric for the rule "if A then B," which measures the degree of association. And second, we subtract from that the confidence of "if NOT A then B," which means the dissociation between A and B. Both numbers will be non-negative. Finally, we divide by the maximum of the two confidence measures we computed. This will ensure that the value of the metric is never smaller than -1 and never larger than 1.5. Constructing Zhang's metric using support
When we construct Zhang's metric, we'll actually use a simpler form, which exclusively entails support calculations. In the version above, the numerator is given as the support of A and B less the product of the support of A and support of B. The denominator is the max of the support of A and B, multiplied by one minus the support of A, and the support of A multiplied by the support of B minus the support of A and B.6. Computing Zhang's metric
Let's say we decide to use Zhang's metric as a way to order our client's ebook site. We'll start with a test using The Hobbit as an antecedent and Pride and Prejudice as the consequent. We'll compute the support for each book, followed by the support for both books.7. Computing Zhang's metric
We'll then compute the numerator as the support of both books, less the product of their individual supports. The expression for the denominator is more complicated. First, we compute the support of both books, multiplied by one minus the support of the Hobbit. Next, we compute the support of the Hobbit, multiplied by the support of Pride and Prejudice minus the support of both. Finally, we compute the maximum of the two and then divide the numerator by the denominator to get Zhang's metric. Printing, we can see that the value is slightly positive, indicating weak, but positive association.8. Let's practice!
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