Epigenome-wide association studies can provide novel insights into the regulation of genes involved in traits and diseases. The rapid emergence of bisulfite-sequencing technologies enables performing such genome-wide studies at the resolution of single nucleotides. However, analysis of data produced by bisulfite-sequencing poses statistical challenges owing to low and uneven sequencing depth, as well as the presence of confounding factors. The recently introduced Mixed model Association for Count data via data AUgmentation (MACAU) can address these challenges via a generalized linear mixed model when confounding can be encoded via a single variance component. However, MACAU cannot be used in the presence of multiple variance components. Additionally, MACAU uses a computationally expensive Markov Chain Monte Carlo (MCMC) procedure, which cannot directly approximate the model likelihood.