Randomized quantile residuals for diagnosing zero-inflated generalized linear mixed models with applications to...

Area of Science:

• Microbiome analysis
• Statistical modeling
• Bioinformatics

Background:

• Zero-inflated generalized linear models (GLMMs), particularly zero-inflated negative binomial (NB) models, are widely used for microbiome and sequencing count data.
• Accurate model fit is essential for estimating false discovery rates (FDR) in differential abundance analysis; model mis-specification can inflate false discoveries.
• Randomized quantile residuals (RQRs) are recognized for diagnosing count regression models, but their efficacy with zero-inflated GLMMs for sequencing data requires further investigation.

Purpose of the Study:

• To evaluate the performance of randomized quantile residuals (RQRs) in diagnosing zero-inflated generalized linear mixed models (GLMMs) for microbiome sequencing count data.
• To assess the reliability of RQR-based goodness-of-fit (GOF) tests in controlling Type I error rates.
• To demonstrate the practical application of RQRs in model selection for real microbiome datasets.

Main Methods:

• Large-scale simulation studies were conducted to assess the performance of RQRs for zero-inflated GLMMs.
• Goodness-of-fit tests utilizing RQRs were analyzed for their Type I error rates.
• Scatter-plots and Q-Q plots of RQRs were employed to visually assess model fit.
• RQRs were applied to diagnose six GLMMs fitted to a real microbiome dataset, focusing on Operational Taxonomic Unit (OTU) counts at the genus level.

Main Results:

• Simulation studies indicated that Type I error rates of GOF tests using RQRs closely matched nominal levels.
• RQR-derived scatter-plots and Q-Q plots proved effective in distinguishing between well-fitting and poorly-fitting models.
• Application to a real microbiome dataset demonstrated that zero-inflated and zero-modified NB models adequately captured OTU counts at the genus level after truncation.

Conclusions:

• Randomized quantile residuals (RQRs) are a valuable tool for diagnosing GLMMs applied to zero-inflated count data, especially in microbiome research.
• The study provides R functions (rqr.glmmtmb and rqr.hurdle.glmmtmb) for calculating RQRs using the glmmTMB package.
• Effective model diagnosis using RQRs enhances the reliability of differential abundance analysis in microbiome studies.