Centroid analysis: Inferring concept representations from open-ended word responses.

The present research proposes and evaluates a novel method - centroid analysis - for measuring representations and concepts at both individual and group levels by mapping open-ended responses onto a pre-existing semantic vector space. Centroid analysis allows us to retrace the target concept as the geometric center of the semantic vectors of the responses generated by this concept. At the group level, centroid analysis enables researchers to compare conceptual structures across different populations to investigate how factors such as language, culture, cognitive differences, educational background, or exposure to specific narratives shape shared representations. At the individual level, centroid analysis enables fine-grained assessments of how personal experiences, expertise, cognitive styles, and even temporary contextual influences affect conceptual representations. We evaluate this method using two distributional semantic models across several calculation methods, reference lexicon sizes, response types, and datasets with tasks ranging from single-word substitutions to single and multiple free associations and multiple feature generation. We conclude that at the group level, the best method to retrace the response-generating concept as a vector in a multi-dimensional semantic space from the averaged vectors of participant responses is to collect multiple free associations (70 unique and 245 total responses per target), use fastText for meaning-to-vector mapping for responses and targets, and to consider each response in the centroid calculation as often as it occurred in the data. At the individual level, the best results are achieved by employing fastText and considering at least eight responses per item per participant in the centroid calculation.