Generalized Procrustes Analysis (GPA)

Generalized Procrustes analysis (GPA) iteratively translates, rotates and scales several configurations, such as each assessor's product-by-attribute ratings, to their mean so that they agree as closely as possible.

일반화 Procrustes 분석(GPA)은 평가자별 제품×속성 평가 같은 여러 배치를 평균 배치에 최대한 일치하도록 반복적으로 이동, 회전, 확대하는 기법입니다.

Do the assessors on my sensory panel perceive the products in the same way once differences in scale use are removed?

척도 사용 습관 차이를 없애면 관능 패널의 평가자들이 제품을 같은 방식으로 지각하나요?

Generalized Procrustes analysis removes each assessor's level, orientation and range of scale use and builds a consensus configuration of the products. The share of total variance captured by the consensus, residuals by assessor and product, and a permutation test show how strong the agreement is and which assessors deviate.

When to use Generalized Procrustes Analysis (GPA)

• Several assessors rate the same products on the same attributes
• Assessors differ in how they use the rating scale
• You want a consensus product map and to identify outlying assessors

When to use something else

• Assessors use different attribute sets and you want block weights and RV coefficients: use Multiple Factor Analysis (MFA)
• Only two configurations are compared: use Procrustes analysis with PROTEST

Assumptions and requirements

• Every retained assessor rated all products (others are dropped)
• Rows refer to the same products across assessors
• Product orders are exchangeable within attributes under the permutation null

What the analysis reports

• Consensus configuration on principal axes
• Assessor scaling factors and residual sums of squares
• Variance explained by the consensus
• Permutation test of the consensus proportion

How to report it

A generalized Procrustes analysis of [K] assessors rating [P] products on [A] attributes showed that the consensus accounted for [value]% of the total variance (permutation test, p = [value]).

Related methods

• Procrustes Analysis
• Multiple Factor Analysis (MFA)
• Principal Component Analysis

Run Generalized Procrustes Analysis (GPA) on Quorant