Procrustes Analysis

Procrustes analysis translates, rotates and optionally scales one configuration to best match another by minimizing the residual sum of squares, and PROTEST tests the resulting Procrustes correlation by permutation.

Procrustes 분석은 잔차 제곱합이 최소가 되도록 한 배치를 이동, 회전, 필요하면 확대하여 다른 배치에 맞추고, PROTEST로 그 Procrustes 상관을 순열 검정하는 기법입니다.

Do two ordinations or measurement sets of the same objects show the same overall pattern?

같은 대상에 대한 두 서열화 결과나 두 측정 묶음이 전체적으로 같은 패턴을 보이나요?

Procrustes analysis superimposes one configuration onto another using the rotation from a singular value decomposition, giving a residual sum of squares, a symmetric m² and the Procrustes correlation. PROTEST permutes the rows of one configuration to judge whether the agreement exceeds chance, and per-object residuals show where the configurations disagree.

When to use Procrustes Analysis

• Comparing two ordinations or coordinate sets of the same objects
• Assessing concordance between two data sets, such as species and environment ordinations
• Finding which objects fit poorly after superimposition

When to use something else

• There are more than two configurations: use Generalized Procrustes Analysis (GPA)
• The hypothesis concerns pairwise distances: use the Mantel test

Assumptions and requirements

• Rows of both configurations refer to the same objects in the same order
• Objects are exchangeable under the null hypothesis for PROTEST

What the analysis reports

• Procrustes correlation and symmetric m²
• Non-symmetric residual sum of squares, RMSE, scale and rotation matrix
• PROTEST permutation p-value
• Residual per object

How to report it

A Procrustes analysis of the two configurations (N = [n]) gave a Procrustes correlation of r = [value] (m² = [value]); PROTEST ([value] permutations) gave p = [value].

Related methods

• Generalized Procrustes Analysis (GPA)
• Mantel and Partial Mantel Tests
• Canonical Correlation Analysis

Run Procrustes Analysis on Quorant