Adjusted principal component estimation for binary factor model

In economic decision-making, the binary factor model is widely employed to characterize decision processes and capture individuals' exposures to various factors. This paper reveals that when the binary response is factorized, additional factors emerge, including an augmented time-invariant item that can lead to overestimation of the individual effect. These findings explain why the principal component method often produces misleading estimates when applied to binary data. To address this issue, we develop an adjusted principal component (APC) method, which modifies the eigenvalue ratio test to determine factor numbers, estimates factors in the transformed model, and recovers estimates for the original binary model. It avoids parametric error distribution specifications and initial value selection, overcoming limitations of existing iterative methods. Extensive Monte Carlo experiments confirm APC's robustness. We then apply APC to analyze dividend initiation factors using S&P 500 data (1998-2016), demonstrating its practical effectiveness.