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Residuals in normal regression are used to assess a model's goodness‐of‐fit (GOF) and discover directions for improving the model. However, there is a lack of residuals with a characterized reference distribution for censored regression. In this article, we propose to diagnose censored regression with normalized randomized survival probabilities (RSP). The key idea of RSP is to replace the survival probability (SP) of a censored failure time with a uniform random number between 0 and the SP of the censored time. We prove that RSPs always have the uniform distribution on (0, 1) under the true model with the true generating parameters. Therefore, we can transform RSPs into normally distributed residuals with the normal quantile function. We call such residuals by normalized RSP (NRSP residuals). We conduct simulation studies to investigate the sizes and powers of statistical tests based on NRSP residuals in detecting the incorrect choice of distribution family and nonlinear effect in covariates. Our simulation studies show that, although the GOF tests with NRSP residuals are not as powerful as a traditional GOF test method, a nonlinear test based on NRSP residuals has significantly higher power in detecting nonlinearity. We also compared these model diagnostics methods with a breast‐cancer recurrent‐free time dataset. The results show that the NRSP residual diagnostics successfully captures a subtle nonlinear relationship in the dataset, which is not detected by the graphical diagnostics with CS residuals and existing GOF tests.

Background For differential abundance analysis, zero-inflated generalized linear models, typically zero-inflated NB models, have been increasingly used to model microbiome and other sequencing count data. A common assumption in estimating the false discovery rate is that the p values are uniformly distributed under the null hypothesis, which demands that the postulated model fit the count data adequately. Mis-specification of the distribution of the count data may lead to excess false discoveries. Therefore, model checking is critical to control the FDR at a nominal level in differential abundance analysis. Increasing studies show that the method of randomized quantile residual (RQR) performs well in diagnosing count regression models. However, the performance of RQR in diagnosing zero-inflated GLMMs for sequencing count data has not been extensively investigated in the literature. Results We conduct large-scale simulation studies to investigate the performance of the RQRs for zero-inflated GLMMs. The simulation studies show that the type I error rates of the GOF tests with RQRs are very close to the nominal level; in addition, the scatter-plots and Q–Q plots of RQRs are useful in discerning the good and bad models. We also apply the RQRs to diagnose six GLMMs to a real microbiome dataset. The results show that the OTU counts at the genus level of this dataset (after a truncation treatment) can be modelled well by zero-inflated and zero-modified NB models. Conclusion RQR is an excellent tool for diagnosing GLMMs for zero-inflated count data, particularly the sequencing count data arising in microbiome studies. In the supplementary materials, we provided two generic R functions, called and , for calculating the RQRs given fitting outputs of the R package .