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

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

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

*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

ISSN: 1471-2105