Efficient computational methods for the estimation of ideal points in social sciences

Estimation of ideological positions among voters, legislators and social media users is central to many subfields in the social sciences. To achieve this, a particular class of Item-Response theory (IRT) models, called ‘ideal points’ models, employs a range of collective choice data: roll call votes, co-sponsorship records, social media engagement data, or word occurrences in speech. Estimation challenges in such models include model identification, data volume and sparsity, while inference robustness against noise is unknown, and ideological position measurements inherently lack ground truth data. These have led to several estimation approaches, from Markov Chain Monte Carlo (MCMC), which is computationally costly in large settings, to fast, albeit less flexible, factor analysis approximations. We formulate a unifying framework for a large family of ideal point models across disciplines and examine their computational complexity and accuracy under noisy data. We examine several synthetic scenarios and first introduce, from signal processing, the Iterated Conditional Modes estimation method for IRT models. Finally, we illustrate the applicability of our framework in a multi-dimensional ideal points inference problem for nearly 20,000,000 X (previously Twitter) users in France, the UK, and the US, along several ideology and issue dimensions calibrated with survey data.