Skip to main content

Table 1 Probability of rejecting the normality of RQRs based on SW normality test when \(n = 100\)

From: Randomized quantile residuals for diagnosing zero-inflated generalized linear mixed models with applications to microbiome count data

Scenario ZP \(Q_{0.05}\) \(Q_{0.5}\) \(Q_{0.95}\) ZMNB* ZINB\(\dagger\) ZMP ZIP NB Poisson N
1 59 320 1075 2711 0.04 0.05 1 1 0.29 1 1604
2 59 32 109 275 0.04 0.03 1 0.99 0.18 1 1312
3 31 302 1078 2800 0.04 0.04 1 1 0.84 1 1720
4 31 29 107 280 0.05 0.05 1 0.99 0.75 1 1552
Scenario ZP \(Q_{0.05}\) \(Q_{0.5}\) \(Q_{0.95}\) ZMNB\(\dagger\) ZINB* ZMP ZIP NB Poisson N
1 58 317 1079 2727 0.04 0.04 1 1 0.28 1 1580
2 58 31 108 274 0.04 0.04 1 1 0.17 1 1276
3 31 301 1071 2783 0.05 0.04 1 1 0.85 1 1691
4 31 30 107 279 0.04 0.04 1 1 0.73 1 1535
Scenario ZP \(Q_{0.05}\) \(Q_{0.5}\) \(Q_{0.95}\) ZMNB\(\dagger\) ZINB\(\dagger\) ZMP* ZIP\(\dagger\) NB Poisson N
1 55 807 1036 1335 0.03 0.04 0.05 0.04 0.42 1 398
2 56 76 103 138 0.04 0.06 0.06 0.04 0.25 1 339
3 28 768 1008 1320 0.04 0.05 0.05 0.05 0.93 1 633
4 30 73 101 138 0.03 0.04 0.06 0.03 0.83 1 405
Scenario ZP \(Q_{0.05}\) \(Q_{0.5}\) \(Q_{0.95}\) ZMNB\(\dagger\) ZINB\(\dagger\) ZMP\(\dagger\) ZIP* NB Poisson N
1 55 793 1020 1318 0.03 0.05 0.03 0.05 0.42 1 390
2 54 74 102 138 0.04 0.04 0.06 0.05 0.30 1 338
3 28 781 1020 1341 0.04 0.03 0.04 0.04 0.92 1 617
4 29 72 102 139 0.03 0.04 0.04 0.04 0.84 1 451
  1. *Represents the true data generating model and \({\dagger}\) represents the models that theoretically contain or are very close to the true data generating model. ZP is the average zero percentages. The three columns labelled by \(Q_\alpha\) show the average of the quantiles of non-zero counts for three \(\alpha\). N is the number of converged model fittings over 3000 replicated datasets