The K-INDSCAL Model for Heterogeneous Three-Way Dissimilarity Data

Area of Science:

• Psychometrics
• Multidimensional Scaling
• Data Analysis

Background:

• Classical multidimensional scaling (e.g., INDSCAL) assumes subject homogeneity.
• Subject heterogeneity can lead to failure in identifying representative common spaces.
• Analyzing three-way dissimilarity data requires models that account for individual differences.

Purpose of the Study:

• To propose a novel weighted Euclidean distance model for analyzing heterogeneous three-way dissimilarity data.
• To introduce the mixture INDSCAL in K classes (K-INDSCAL) model to address limitations of existing methods.
• To develop a robust method for identifying common spaces within subject groups.

Main Methods:

• Development of the K-INDSCAL model, extending INDSCAL to specify K common homogeneous spaces.
• Incorporation of individual saliencies within the K-INDSCAL framework.
• Estimation of model parameters using a least-squares fitting context and a coordinate descent algorithm.
• Discussion of a parsimonious model to mitigate parameter instability.

Main Results:

• Demonstration that INDSCAL can fail with heterogeneous subjects.
• K-INDSCAL successfully identifies common spaces reflecting data structure in heterogeneous populations.
• The proposed model and estimation algorithm are validated using both artificial and real data.

Conclusions:

• K-INDSCAL offers a significant advancement for analyzing three-way dissimilarity data with heterogeneous subjects.
• The model effectively captures underlying common structures while accommodating individual differences.
• The developed method provides a valuable tool for researchers dealing with complex, multi-subject datasets.