Interpretable Semantic Gradients in SSD: A PCA Sweep Approach and a Case Study on AI Discourse

TL;DR

This paper introduces a PCA sweep method for selecting the number of components in Supervised Semantic Differential analysis, enhancing interpretability and stability in analyzing AI discourse.

Contribution

The paper proposes a systematic PCA sweep procedure for component selection in SSD, reducing researcher degrees of freedom and improving interpretability and stability of semantic gradients.

Findings

Identified a stable Admiration-related gradient contrasting AI framings.

No robust gradient alignment found for Rivalry in the case study.

PCA sweep improves interpretability and stability over heuristic methods.

Abstract

Supervised Semantic Differential (SSD) is a mixed quantitative-interpretive method that models how text meaning varies with continuous individual-difference variables by estimating a semantic gradient in an embedding space and interpreting its poles through clustering and text retrieval. SSD applies PCA before regression, but currently no systematic method exists for choosing the number of retained components, introducing avoidable researcher degrees of freedom in the analysis pipeline. We propose a PCA sweep procedure that treats dimensionality selection as a joint criterion over representation capacity, gradient interpretability, and stability across nearby values of K. We illustrate the method on a corpus of short posts about artificial intelligence written by Prolific participants who also completed Admiration and Rivalry narcissism scales. The sweep yields a stable, interpretable Admiration-related gradient contrasting optimistic, collaborative framings of AI with distrustful and derisive discourse, while no robust alignment emerges for Rivalry. We also show that a counterfactual using a high-PCA dimension solution heuristic produces diffuse, weakly structured clusters instead, reinforcing the value of the sweep-based choice of K. The case study shows how the PCA sweep constrains researcher degrees of freedom while preserving SSD's interpretive aims, supporting transparent and psychologically meaningful analyses of connotative meaning.