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Recursive partitioning

Recursive partitioning is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Recursive partitioning rather than just read about it. In short: Recursive partitioning is a statistical method for multivariable analysis. Recursive partitioning creates a decision tree that strives to correctly classify members of the population by splitting it into sub-populations based on several dichotomous independent variables.

Recursive partitioning — main illustration
Recursive partitioning — illustration

Key takeaways

  • Recursive partitioning belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Recursive partitioning to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Recursive partitioning from memory before moving on to harder problems.

Reference excerpt

Recursive partitioning is a statistical method for multivariable analysis. Recursive partitioning creates a decision tree that strives to correctly classify members of the population by splitting it into sub-populations based on several dichotomous independent variables. The process is termed recursive because each sub-population may in turn be split an indefinite number of times until the splitting process terminates after a particular stopping criterion is reached. Recursive partitioning methods have been developed since the 1980s. Well known methods of recursive partitioning include Ross Quinlan's ID3 algorithm and its successors, C4.5 and C5.0 and Classification and Regression Trees (CART). Ensemble learning methods such as Random Forests help to overcome a common criticism of these methods – their vulnerability to overfitting of the data – by employing different algorithms and combining their output in some way. This article focuses on recursive partitioning for medical diagnostic tests, but the technique has far wider applications. See decision tree. As compared to regression analysis, which creates a formula that health care providers can use to calculate the probability that a patient has a disease, recursive partition creates a rule such as 'If a patient has finding x, y, or z they probably have disease q'. A variation is 'Cox linear recursive partitioning'.

Advantages and disadvantages Compared to other multivariable methods, recursive partitioning has advantages and disadvantages.

Advantages are: Generates clinically more intuitive models that do not require the user to perform calculations. Allows varying prioritizing of misclassifications in order to create a decision rule that has more sensitivity or specificity. May be more accurate. Disadvantages are: Does not work well for continuous variables May overfit data.

Examples Examples are available of using recursive partitioning in research of diagnostic tests. Goldman used recursive partitioning to prioritize sensitivity in the diagnosis of myocardial infarction among patients with chest pain in the emergency room.

See also Decision tree learning

References

Illustrations

Recursive partitioning: A recursive partitioning tree showing survival of passengers on the Titanic ("sibsp" is the number of spouses or siblings aboard). The figures under the leaves show the probability of survival and the percentage of observations in the leaf. Summarizing: Your chances of survival were good if you were (i) a female or (ii) a young boy without several family members.
A recursive partitioning tree showing survival of passengers on the Titanic ("sibsp" is the number of spouses or siblings aboard). The figures under the leaves show the probability of survival and the percentage of observations in the leaf. Summarizing: Your chances of survival were good if you were (i) a female or (ii) a young boy without several family members.

Worked examples

Example 1 — a first encounter with Recursive partitioning

Start with the simplest possible case. Write down what Recursive partitioning claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Recursive partitioning before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Recursive partitioning ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Recursive partitioning

In research
Recursive partitioning appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Recursive partitioning in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Recursive partitioning is common in secondary-school and first-year university syllabi. It links to neighbouring topics Biostatistics, Statistical classification, so understanding it makes those chapters shorter.
In everyday life
Look for Recursive partitioning outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Recursive partitioning in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Recursive partitioning means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Recursive partitioning out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Recursive partitioning in simple terms?

Recursive partitioning is a statistical method for multivariable analysis. Recursive partitioning creates a decision tree that strives to correctly classify members of the population by splitting it into sub-populations based on several dichotomous independent variables.

Why does Recursive partitioning matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Recursive partitioning?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Recursive partitioning.

Tags

  • Biostatistics
  • Statistical classification

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