Comment on 'Sparse Bayesian Factor Analysis when the Number of Factors is Unknown' by S. Fr\"uhwirth-Schnatter, D. Hosszejni, and H. Freitas Lopes

TL;DR

This paper discusses how sparsity and factor selection techniques from Bayesian factor analysis can be adapted to latent space models for network data, addressing identification issues inherent in these models.

Contribution

It demonstrates the application of Bayesian sparsity techniques to latent space models, proposing factor loading restrictions to improve identification.

Findings

Techniques can be applied to network latent space models

Factor loading restrictions aid in identification

Potential for broader applications in network analysis

Abstract

The techniques suggested in Fr\"uhwirth-Schnatter et al. (2024) concern sparsity and factor selection and have enormous potential beyond standard factor analysis applications. We show how these techniques can be applied to Latent Space (LS) models for network data. These models suffer from well-known identification issues of the latent factors due to likelihood invariance to factor translation, reflection, and rotation (see Hoff et al., 2002). A set of observables can be instrumental in identifying the latent factors via auxiliary equations (see Liu et al., 2021). These, in turn, share many analogies with the equations used in factor modeling, and we argue that the factor loading restrictions may be beneficial for achieving identification.