Residual analysis for discrete correlated data in the multivariate approach - Fábio, Lizandra C.; Villegas, Cristian; Mamun, Abu Sayed Md. Al; Carrasco, Jalmar Manuel Farfan (Brazilian Journal of Biometrics, 2025)
The residual distributions obtained from discrete correlated and uncorrelated data cannot be well approximated to the standardized normal distribution. In this case, the efficiency in checking the adequacy of the model to the data and detecting outliers is not guaranteed. Thus, alternative measures for residual analysis have been considered in several classes of models and their properties have been assessed. In this paper, we investigate the empirical distribution of four residuals of the multivariate negative binomial regression (MNBR) model. In our study, we propose standardized weighted and standardized Pearson residuals; we also consider the standardized component of deviance and quantile residuals suggested by Fabio et al. (2012) and Fabio et al. (2023), respectively. Monte Carlo simulation results reveal that the concordance of the empirical distribution of the residuals to the standard normal distribution depends on the dispersion parameter. Furthermore, the impact on residual analysis when the random effect distribution is misspecified is explored. We concluded that the quantile and standardized weighted residuals presented better performances.