  Psychiatry research seeks to understand the manifestations of psychopathology
in behavior, as measured in questionnaire data, by identifying a small number
of latent factors that explain them. While factor analysis is the traditional
tool for this purpose, the resulting factors may not be interpretable, and may
also be subject to confounding variables. Moreover, missing data are common,
and explicit imputation is often required. To overcome these limitations, we
introduce interpretability constrained questionnaire factorization (ICQF), a
non-negative matrix factorization method with regularization tailored for
questionnaire data. Our method aims to promote factor interpretability and
solution stability. We provide an optimization procedure with theoretical
convergence guarantees, and an automated procedure to detect latent
dimensionality accurately. We validate these procedures using realistic
synthetic data. We demonstrate the effectiveness of our method in a widely used
general-purpose questionnaire, in two independent datasets (the Healthy Brain
Network and Adolescent Brain Cognitive Development studies). Specifically, we
show that ICQF improves interpretability, as defined by domain experts, while
preserving diagnostic information across a range of disorders, and outperforms
competing methods for smaller dataset sizes. This suggests that the
regularization in our method matches domain characteristics. The python
implementation for ICQF is available at
\url{https://github.com/jefferykclam/ICQF}.
