scMEDAL for the interpretable analysis of single-cell transcriptomics data with batch effect visualization using a deep mixed effects autoencoder

scRNA-seq data has the potential to provide new insights into cellular heterogeneity and data acquisition; however, a major challenge is unraveling confounding from technical and biological batch effects. Existing batch correction algorithms suppress and discard these effects, rather than quantifying and modeling them. Here, we present scMEDAL, a framework for single-cell Mixed Effects Deep Autoencoder Learning, which separately models batch-invariant and batch-specific effects using two complementary autoencoder networks. One network is trained through adversarial learning to capture a batch-invariant representation, while a Bayesian autoencoder learns a batch-specific representation. Comprehensive evaluations spanning conditions (e.g., autism, leukemia, and cardiovascular), cell types, and technical and biological effects demonstrate that scMEDAL suppresses batch effects while modeling batch-specific variation, enhancing accuracy and interpretability. Unlike prior approaches, the framework's fixed- and random-effects autoencoders enable retrospective analyses, including predicting a cell's expression as if it had been acquired in a different batch via genomap projections at the cellular level, revealing the impact of biological (e.g., diagnosis) and technical (e.g., acquisition) effects. By combining scMEDAL's batch-agnostic and batch-specific latent spaces, it enables more accurate predictions of disease status, donor group, and cell type, making scMEDAL a valuable framework for gaining deeper insight into data acquisition and cellular heterogeneity.