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

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

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

*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

ISSN: 1471-2105