Deterministic parallel analysis: An improved method for selecting factors and principal components

TL;DR

This paper introduces Deterministic Parallel Analysis (DPA), an improved, faster, and more reproducible method for selecting factors in PCA and factor analysis, addressing shadowing and threshold issues with proven consistency and real data validation.

Contribution

It proposes DPA, a deterministic and enhanced version of Parallel Analysis, with deflation and threshold adjustments, supported by theoretical proofs and empirical validation.

Findings

DPA is faster and more reproducible than traditional PA.

Deflation effectively mitigates shadowing effects.

Methods significantly improve factor detection accuracy in real data.

Abstract

Factor analysis and principal component analysis (PCA) are used in many application areas. The first step, choosing the number of components, remains a serious challenge. Our work proposes improved methods for this important problem. One of the most popular state-of-the-art methods is Parallel Analysis (PA), which compares the observed factor strengths to simulated ones under a noise-only model. This paper proposes improvements to PA. We first de-randomize it, proposing Deterministic Parallel Analysis (DPA), which is faster and more reproducible than PA. Both PA and DPA are prone to a shadowing phenomenon in which a strong factor makes it hard to detect smaller but more interesting factors. We propose deflation to counter shadowing. We also propose to raise the decision threshold to improve estimation accuracy. We prove several consistency results for our methods, and test them in simulations. We also illustrate our methods on data from the Human Genome Diversity Project, where they significantly improve the accuracy.