Approximating Ideology Scaling of Online Social Networks with Factor Analysis Identifying Dimensions with Survey Reference Frames

Ideological scaling is a ubiquitous tool for inferring political opinions of large samples of social media users. Two longstanding issues with these methods, when applied to social media data, are their computational complexity and the lack of inherent referential frames for inferred ideology positions. In this work we address both issues. First, we derive the explicit mathematical connection between the Bayesian inference of ideology positions and Factor Analysis approximation that results in efficient computation. We illustrate the quality of these approximations with synthetic data. Second, we show how the use of survey data for identification and calibration allows for positioning along several issue and ideology dimensions, while positioning social media users from different countries in common political spaces. We illustrate our method on X/Twitter friendship networks in France, Germany, Italy, and Spain, validating our results using text data.