NCA ceiling techniques

What is a ceiling?

What is a floor?

What is a ceiling line?

What is a ceiling surface?

What is a ceiling technique?

What is the CE-FDH ceiling technique?

What is the CR-FDH ceiling technique?

What is the C-LP ceiling technique?

What is the CE-VRS ceiling technique?

What is the CR-VRS ceiling technique?

What is a ceiling?

A ceiling is the border between an empty space without observations and a full space with observations. This can be mathematically expressed as Y ≤ f(X), where Y is the outcome, X are the conditions, and f(X) is the ceiling function.

What is a floor?

A floor is the border between an empty space without observations and a full space with observations and that is mathematically expressed as Y ≥ f(X), where Y is the outcome, X are the conditions, and f(X) is the floor function.

What is a ceiling line?

A ceiling line is a ceiling in the two-dimensional space, where the ceiling function f(X) is a line.

What is a ceiling surface?

A ceiling surface is a ceiling in the three-dimensional space, where the ceiling function f(X) is a surface.

What is a ceiling technique?

A ceiling technique is a mathematical or statistical approach to approximate the ceiling (see table). In the NCA software package for R, the CE-FDH ceiling technique is the default ceiling technique for dichotomous and discrete (with few levels) necessary condition analysis or when a continuous ceiling is "jumpy". The CR-FDH ceiling technique is the default ceiling technique for discrete (with many levels) and continuous necessary condition analysis.

 Common ceiling Techniques in NCA Name in NCA software Name CE-FDH ce_fdh Ceiling Envelopment with Free Disposal Hull CR-FDH cr_fdh Ceiling Regression with Free Disposal Hull C-LP c_lp Ceiling - Linear Programming CE-VRS ce_vrs Ceiling Envelopment with Varying Return to Scale CR-VRS cr_vrs Ceiling Regression with Varying Return to Scale

What is the CE-FDH ceiling technique?

The Ceiling Envelopment – Free Disposal Hull (CE-FDH ) ceiling technique is a ceiling approximation obtained from the Free Disposal Hull (FDH) data envelopment technique that assumes that the ceiling is non-decreasing, resulting in a non-decreasing step function. In the NCA software package for R, the CE-FDH ceiling technique is the default ceiling technique for dichotomous and discrete (with few values) necessary conditions or when the border is 'jumpy'.

What is the CR-FDH ceiling technique?

The Ceiling Regression - Free Disposal Hull (CR-FDH) ceiling technique is a ceiling approximation that smooths the step function obtained by the CE-FDH technique by using OLS regression through the upper-left corners of the step function. In the NCA software package for R, the CR-FDH ceiling technique is the default ceiling technique for discrete (with many values) and continuous necessary conditions.

What is the C-LP ceiling technique?

The Ceiling - Linear Programming (C-LP) ceiling technique is a ceiling approximation that selects two upper left points from the step function obtained by the CE-FDH such that the empty space is maximum. The ceiling accuracy of this line is 100%. It can be used for simulations when there is no measurement error in the data.

What is the CE-VRS ceiling technique?

The Ceiling Envelopment - Varying Return to Scale (CE-VRS ) ceiling technique is a ceiling approximation obtained from Data Envelopment Analysis (DEA) that assumes that the ceiling is convex, resulting in a piecewise linear convex ceiling function.

What is the CR-VRS ceiling technique?

The Ceiling Regression - Varying Return to Scale (CE-VRS ) ceiling technique is a ceiling approximation that smooths the piecewise linear function obtained by the CE-VRS technique by using OLS regression through the corners of the piecewise linear function.