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Table 2 Probability of rejecting the normality of RQRs based on SW normality test when \(n = 400\)

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 60 285 1068 2808 0.03 0.03 1 1 0.56 1 2475
2 59 28 108 287 0.04 0.04 1 1 0.50 1 2199
3 30 281 1072 2850 0.04 0.05 1 1 0.95 1 2596
4 29 27 107 287 0.04 0.04 1 1 0.90 1 2472
Scenario ZP \(Q_{0.05}\) \(Q_{0.5}\) \(Q_{0.95}\) ZMNB\(\dagger\) ZINB* ZMP ZIP NB Poisson N
1 60 285 1070 2825 0.04 0.04 1 1 0.57 1 2451
2 60 28 108 286 0.03 0.03 1 1 0.49 1 2212
3 30 280 1069 2843 0.04 0.04 1 1 0.95 1 2613
4 29 27 107 287 0.04 0.04 1 1 0.90 1 2485
Scenario ZP \(Q_{0.05}\) \(Q_{0.5}\) \(Q_{0.95}\) ZMNB\(\dagger\) ZINB\(\dagger\) ZMP* ZIP\(\dagger\) NB Poisson N
1 59 777 1012 1315 0.04 0.04 0.05 0.04 0.64 1 906
2 59 74 102 138 0.04 0.03 0.04 0.04 0.57 1 839
3 29 769 1011 1334 0.05 0.05 0.06 0.06 0.97 1 1065
4 29 73 102 139 0.04 0.05 0.06 0.04 0.94 1 960
Scenario ZP \(Q_{0.05}\) \(Q_{0.5}\) \(Q_{0.95}\) ZMNB\(\dagger\) ZINB\(\dagger\) ZMP\(\dagger\) ZIP* NB Poisson N
1 59 782 1015 1318 0.04 0.04 0.04 0.05 0.63 1 954
2 59 74 103 139 0.04 0.04 0.04 0.05 0.58 1 816
3 29 769 1015 1340 0.04 0.04 0.06 0.05 0.97 1 1015
4 28 73 102 139 0.04 0.04 0.05 0.05 0.95 1 936
  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. The three columns labelled by \(Q_\alpha\) show the average of the quantiles of non-zero counts for three \(\alpha\). ZP is the average zero percentage. N is the number of converged fittings over 3000 replicated datasets