Using Particle Physics to Estimate Non-linear Expressions of Latent Constructs

Abstract

Political scientists often use survey instruments to indirectly infer latent constructs such as social trust, political efficacy, and ideology. However, traditional techniques used to reconstruct latent quantities from survey data, such as principal components, factor analysis, and item response theory models, have limitations as they assume linearity among the underlying co-dependencies among a given set of survey items. This assumption does not hold for complex nonlinear expressions of latent constructs, such as when survey respondents from opposite ends of the ideological spectrum share a stance on a particular issue but for completely different reasons. For example, a left-leaning respondent may see cash benefits for child care as an important instrument for gender equality while conservatives welcome incentives for women to stay home and give birth to more children. To liberals, GMO’s might appear as environmental hazards while conservatives reject them as they could tamper with God’s eternal creation. To address such non-linearities, we propose a new method that models survey item-responses as force-directed statistical networks. By treating item responses as physical particles in finite space, a force-directed algorithm can detect complex, non-linear relationships within latent constructs. Generalized additive models and LOESS-fit models applied to the spatial equilibrium of item response particles can subsequently be used to calculate sparse, (non-)linear latent factors that optimally characterize this space. This method is flexible, allows for multiple scoring options, and outperforms traditional latent variable models in the presence of non-linear expressions of the underlying latent construct.