MCDA Toolkit for Stata

This repository contains Stata commands for Multi-Criteria Decision Analysis (MCDA).

Aim

The goal of this toolkit is to provide Stata users with robust, user-friendly tools to perform Multi-Criteria Decision Analysis. These methods are essential for ranking or selecting alternatives when multiple, often conflicting, criteria must be considered.

Methodology: TOPSIS

The primary command in this toolkit, mcda_topsis, implements the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) (Hwang and Yoon, 1981).

TOPSIS ranks alternatives based on their geometric distance from both the Positive Ideal Solution (PIS) and the Negative Ideal Solution (NIS). The chosen alternative should have the shortest distance from the PIS and the farthest distance from the NIS.

Core Logic:

1. Normalization: Criteria are normalized to a 0-1 scale using Min-Max normalization.
2. Weighting: User-defined weights are applied to the normalized criteria to reflect relative importance.
3. Ideal Solutions: The algorithm identifies the PIS (best values for all criteria) and the NIS (worst values).
4. Distance Calculation: The Euclidean distance of each alternative from both PIS and NIS is calculated.
5. Relative Closeness: A final score (0 to 1) is generated based on the relative closeness to the ideal solution.

Installation

You can install the latest version of the MCDA Toolkit directly from this GitHub repository using Stata's net install command:

net install mcda_topsis, from("https://raw.githubusercontent.com/emawbgit/MCDA/main/") replace

Description

The mcda_topsis command processes a set of numeric variables and outputs rankings based on the TOPSIS algorithm.

Key Features:

• Min-Max Normalization: Automatically standardizes criteria to a 0-1 scale.
• Domain Weighting: Allows weights to be assigned to groups of variables (domains), which are then automatically split among members.
• Flexible Directionality: Easily specify "benefit" criteria (higher is better) vs "cost" criteria (lower is better).

Syntax

mcda_topsis varlist [if] [in] [, options]

Options

Main

• weights(numlist): Specify the importance of each criterion.
• direction(numlist): Specify direction for each variable (1 for benefit, -1 for cost).
• domains(numlist): Specify domain IDs to split weights across groups of variables.

Output

• generate(names): Specify names for the generated score and rank variables (default: topsis_score, topsis_rank).

Examples

1. Basic Ranking

sysuse auto, clear
mcda_topsis mpg price weight, weights(0.4 0.3 0.3) direction(1 -1 -1)

2. Domain-Based Weighting

In this example, a weight of 0.5 is assigned to Domain 1 (containing mpg and gear_ratio) and split between them.

mcda_topsis mpg gear_ratio price, weights(0.5 0.5 0.5) domains(1 1 2)

Reporting Bugs or Desiderata

If you encounter any issues or bugs, please open an issue on the GitHub repository. Please include your Stata version and a sample of your data.

Author

Emanuele Clemente

License

MIT