mathematics

Truncated regression model

Truncated regression model 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 Truncated regression model rather than just read about it. In short: Truncated regression models are a class of models in which the sample has been truncated for certain ranges of the dependent variable. That means observations with values in the dependent variable below or above certain thresholds are systematically excluded from the sample.

Key takeaways

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

Reference excerpt

Truncated regression models are a class of models in which the sample has been truncated for certain ranges of the dependent variable. That means observations with values in the dependent variable below or above certain thresholds are systematically excluded from the sample. Therefore, whole observations are missing, so that neither the dependent nor the independent variable is known. This is in contrast to censored regression models where only the value of the dependent variable is clustered at a lower threshold, an upper threshold, or both, while the value for independent variables is available. Sample truncation is a pervasive issue in quantitative social sciences when using observational data, and consequently the development of suitable estimation techniques has long been of interest in econometrics and related disciplines. In the 1970s, James Heckman noted the similarity between truncated and otherwise non-randomly selected samples, and developed the Heckman correction. Estimation of truncated regression models is usually done via parametric maximum likelihood method. More recently, various semi-parametric and non-parametric generalisation were proposed in the literature, e.g., based on the local least squares approach or the local maximum likelihood approach, which are kernel based methods.

See also Censored regression model Sampling bias Truncated distribution

References

Further reading Breen, Richard (1996). "Sample-Selection Models and the Truncated Regression Model". Regression Models : Censored, Samples Selected, or Truncated Data. Thousand Oaks: Sage. pp. 33–47. ISBN 0-8039-5710-6. Frölich, Markus (2002). Semiparametric Estimation of Selectivity Models. New York: Nova Science. ISBN 1-59033-277-6. King, Gary (1989). "Models with Nonrandom Selection". Unifying Political Methodology : the Likehood Theory of Statistical Inference. Cambridge University Press. pp. 208–230. ISBN 0-521-36697-6. Maddala, G. S. (1983). "Censored and Truncated Regression Models". Limited-Dependent and Qualitative Variables in Econometrics. New York: Cambridge University Press. pp. 149–196. ISBN 0-521-24143-X.

Worked examples

Example 1 — a first encounter with Truncated regression model

Start with the simplest possible case. Write down what Truncated regression model 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 Truncated regression model 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 Truncated regression model 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 Truncated regression model

In research: Truncated regression model 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 Truncated regression model 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: Truncated regression model is common in secondary-school and first-year university syllabi. It links to neighbouring topics Actuarial science, Econometrics stubs, Mathematical and quantitative methods (economics), so understanding it makes those chapters shorter.
In everyday life: Look for Truncated regression model 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 Truncated regression model in 20 minutes

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

Frequently asked questions

What is Truncated regression model in simple terms?

Why does Truncated regression model 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 Truncated regression model?

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 Truncated regression model.