Handling missing data, skewness, and outliers in medical research: A robust factor analysis approach using the...

Addressing incomplete and non-normally distributed multivariate data poses significant challenges in medical research, particularly when the interest is in discovering underlying data structures. This article introduces a robust factor analysis framework for handling missing data by employing the canonical fundamental skew-$t$ factor analysis (CFUSTFA) model, which incorporates the canonical fundamental skew-$t$ distribution into the latent factors and error terms. This versatile framework accounts for skewness, heavy tails, and missing data, thereby enhancing the model's ability to capture complex structures commonly observed in biomedical datasets. For parameter estimation under the missing at random mechanism, we develop a computationally efficient alternating expectation-conditional maximization algorithm within the maximum likelihood framework. This approach facilitates the simultaneous imputation of missing values and the extraction of low-dimensional factor representations. Standard errors for parameter estimates are also derived using a general information matrix-based approach. The proposed methodology is validated through simulations and applied to a hepatitis C virus laboratory dataset exhibiting skewness, excess kurtosis, and missingness. Our findings highlight the capability of the CFUSTFA model to robustly capture complex, incomplete, and asymmetric biomedical data, offering enhanced inference and interpretability compared with existing factor analysis approaches.