Estimating and interpreting more than two consensus components in projective mapping: INDSCAL vs. multiple factor analysis (MFA)

- The INDSCAL and MFA gave very similar results for two components.
- The MFA was slightly better than INDSCAL for estimating the consensus configuration for more than 2 dimensions.
- Using singular vectors can give a more relevant measure of similarity of configurations.
- It is important to consider more than two consensus components.

In this paper a general framework is proposed for understanding and analysing more than two consensus components in projective mapping (also known as Napping®) studies. Focus is on how two models, multiple factor analysis (MFA) and individual differences scaling (INDSCAL) based on the weighted Euclidean model (WEM), relate to each other and to the general framework. The stability of the consensus configurations of both methods are compared. The relations between the results of the two methods are investigated using the RV coefficient and an alternative index called SMI which gives equal weight to the axes regardless of the relative size of the singular values. The methods are tested and compared using three datasets and simulations.