Recovery of subsampled dimensions and configurations derived from napping data by MFA and MDS

Napping is a multivariate sensory method in which participants physically place stimuli on a large sheet of paper and orient them so that the distance between pairs represents a measure of dissimilarity. The two-dimensional nature of the task may be a limitation to the ability of this and similar methodologies to recover information about complex stimuli. In the first investigation, eight simulated three-dimensional stimuli were created with two different levels for each attribute. Simulated napping experiments had groups of participants attend to two of the dimensions with different probabilities. Multiple factor analysis (an analytical multivariate statistical procedure that can be thought of as a principle components analysis on the individuals) and MDS-INDSCAL (a variation on multidimensional scaling that finds a common configuration through reducing a stress measure associated with lack of fit) recovered full dimensionality from these data, although MFA had trouble when attention was the most unbalanced. In the second experiment, a human napping experiment was designed using custom three-dimensional stimuli: shapes with two levels each of size, color, and shape attributes. This experiment confirmed the results of Experiment 1, as both MDS-INDSCAL and MFA analyses again recovered the full dimensionality of the stimuli.