Truncated data is a dataset in which some values are excluded as a matter of deliberate selection. It is different from censored data, in which certain values in the data sample are unknown due to some random cause. Truncation is similar to but distinct from the concept of statistical censorship. It can be thought of as an underlying sample with all values outside the limits completely omitted, without even a count of the omitted ones being maintained.
Truncating data values means removing values from a dataset that are below or above a certain value. In computer science, this term is often used in reference to data types or variables, such as numbers and floating-point strings. Truncation in IT refers to “cutting something or removing parts of it to make it shorter”. Truncated data is data for which measurements are only reported if they are above a lower limit, below an upper limit, or between a lower and upper limit.
In econometrics, truncated dependent variables are variables for which observations cannot be made for certain values in some range. In addition, truncation is performed on some other types of user technologies, for example, on email platforms, where a user can see the message that a certain email has been “truncated”. Modeling median income values would involve truncating income above and below specific amounts. Censoring data means collecting only partial information about data values, and truncating data means removing data values from a dataset altogether.
Generally, the values that insurance adjusters receive are truncated to the left, censored to the right, or both. In practice, if the truncated fraction is too small, the effect of truncation could be ignored when analyzing the data. Several operating systems or programming languages use truncate as a command or function to limit the size of a field, dataflow, or file. The estimation of such a truncated regression model can be done in parametric or semiparametric and non-parametric frames.
This represents an example of data truncation because anyone who has a GPA below a certain threshold is simply excluded from the dataset. In Stan, these data can be modeled following a truncated normal distribution for observations.