NCA ceiling techniques
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.
