Table 5.

Results for dragonfly population data (cf. Section 5.1).

	Component	Lower95	Median	Upper95	PSRF	${\mathcal{F}}_{+}$
( $y_1$) Exuviae:	(Intercept)	−4.11	1.20	6.38	1.017	0.672
	Treatment	−0.86	−0.13	0.58	1.001	0.384
	2016	−1.79	0.57	2.75	1.008	0.716
	2017	−2.64	−1.39	−0.32	1.004	0.009
	2018	−3.52	−1.95	−0.66	1.007	0.004
	Emersion (fraction)	−1.09	0.85	3.11	0.999	0.795
	pH	−0.68	0.11	0.88	1.013	0.595
	Redox (V)	−4.31	−0.12	4.20	1.013	0.474
	Oxygen (fraction)	−4.47	−2.66	−0.68	1.005	0.005
	EC (mS/cm)	−3.01	−0.71	1.59	0.999	0.264
	Temperature ( ${}^{\circ }$C)	−0.12	0.10	0.31	1.014	0.812
	Water depth (m)	−3.13	0.01	2.68	1.005	0.504
	Sludge thickness (m)	−4.92	−1.27	1.59	1.003	0.199
( $y_2$) Egg-laying females:	(Intercept)	−6.53	−1.43	3.31	1.029	0.281
	Treatment	−0.77	−0.05	0.78	1.004	0.463
	2016	−3.02	−0.74	1.90	1.015	0.266
	2017	−1.29	−0.22	0.76	0.998	0.355
	2018	−4.66	−2.65	−0.97	1.014	0.000
	Emersion (fraction)	−2.97	−0.68	1.99	1.020	0.319
	pH	−0.49	0.62	1.51	1.037	0.892
	Redox (V)	−3.96	0.80	4.93	1.002	0.620
	Oxygen (fraction)	−3.04	−1.18	0.81	1.015	0.101
	EC (mS/cm)	0.30	2.46	4.83	1.012	0.973
	Temperature ( ${}^{\circ }$C)	−0.41	−0.13	0.14	1.013	0.159
	Water depth (m)	−2.00	0.26	2.27	0.999	0.593
	Sludge thickness (m)	−2.94	−0.47	2.27	0.999	0.352
(θ) Correlation:		0.22	0.53	0.80	1.010
( $\mathit{\pi }$) Zero inflation:	${\pi }_1$: $(0,0)$	0.00	0.07	0.14	1.012
	${\pi }_2$: $(\mathrm{E}\mathrm{x}\mathrm{u}\mathrm{v}\mathrm{i}\mathrm{a}\mathrm{e},0)$	0.00	0.04	0.13	1.002
	${\pi }_3$: $(0,\mathrm{E}\mathrm{g}\mathrm{g}\mathrm{l}.\mathrm{f}\mathrm{e}\mathrm{m}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{s})$	0.00	0.05	0.14	1.005
( $\mathbf{\Sigma }$) Random effects:	${\mathrm{\Sigma }}_{11}$: Variance (Ex.)	0.23	1.94	5.24	0.999
	${\mathrm{\Sigma }}_{12}$: Covariance	−0.53	0.11	1.75	1.012
	${\mathrm{\Sigma }}_{22}$: Variance (Egg-l. f.)	0.00	0.09	1.76	1.012

Notes: The 1st and 3rd columns give the bounds of 95% posterior confidence intervals, computed as the 0.025 and the 0.975 empirical quantiles of the posterior samples; the 2nd column lists the posterior median. The 4th column lists the Gelman-Rubin potential scale reduction factors (PSRFs). The last column gives the fraction of posterior samples that were positive. High (low) fractions indicate that the majority of posterior samples were positive (negative), indicating a systematic effect. Covariates for which at least 80% of the sampled parameters had the same sign have been put in bold. The relative covariate effects on the marginal medians are listed in Table 6.