Xiaoyue Niu's contribution to the Discussion of ‘Vintage Factor Analysis with Varimax Performs Statistical Inference’ by Rohe & Zeng

原文摘要

I want to congratulate Rohe and Zeng on solving a long-time puzzle (and fight between statisticians and practitioners) of ‘why/whether the varimax rotation works’. Their inspiring results have some implications in the literature of latent space models for social networks (Hoff, 2021; Hoff et al., 2002). One of the appealing features of the latent space model is that one can extract the latent factors and analyse the unobserved features through the latent positions. However, it is a random orientation that we are interpreting due to the rotational invariance. It is less problematic if we are only interested in the relative locations. It becomes more of an issue when we are analysing dynamic networks or trying to compare networks across different subjects. In those situations, we need a ‘true’ orientation. A common approach is to pick a (random) orientation and perform Procrustes transformation, which could potentially diminish some of the structural changes and signals. Some more sophisticated effort towards solving the nonidentifiability issue includes Poworoznek et al. (2021), which also utilizes varimax. This rotational invariance happens because we assume normal factors, mostly due to computational convenience. If we are willing to move away from normality to something leptokurtic (such as a t-distribution), we would be able to have an ‘identifiable latent space model’. In fact, the normal mixture that Handcock et al. (2007) used is leptokurtic so the factor version of their clustering model is identifiable and could potentially be extended to a dynamic model to study latent position changes without the trouble of matching the orientations.

摘要来源：OpenAlex 索引摘要（稿件版本未注明）