Table 2.

Estimated type I error rates at the significance level of 5% for GLMM-MiRKAT/aGLMM-MiRKAT based on the random slope model with Gaussian, Binomial or Poisson responses (Unit: %).

	n = 20			n = 50
${\rho }_{j{\ne j}^{\prime }}$	L	M	H	L	M	H
Gaussian
KJ	5.10	4.96	5.12	4.87	4.98	5.04
KBC	5.11	4.89	4.97	5.10	4.88	5.03
KU	5.03	4.95	5.13	5.03	5.03	5.10
K0.5	5.07	4.91	4.90	4.89	4.91	5.09
KW	4.96	4.95	4.87	4.83	5.03	5.01
adaptive	4.97	4.94	5.01	4.94	4.86	5.04
Binomial
KJ	5.08	4.80	5.01	5.09	5.02	4.83
KBC	4.93	4.94	5.1	4.89	5.02	4.88
KU	5.04	4.99	5.04	5.07	5.40	4.83
K0.5	5.02	4.97	4.84	5.00	5.08	4.96
KW	4.89	5.07	5.02	4.96	5.08	4.85
adaptive	4.99	4.94	4.85	4.86	5.11	4.82
Poisson
KJ	5.01	4.98	4.76	4.93	5.10	4.90
KBC	5.16	4.76	5.02	5.03	5.03	5.02
KU	4.90	5.06	4.92	5.09	5.19	4.93
K0.5	5.14	4.87	5.10	4.85	4.88	5.10
KW	5.12	4.82	5.28	4.86	5.06	5.18
adaptive	5.05	4.70	4.88	5.00	4.94	4.78

K_J: Jaccard dissimilarity; K_BC: Bray-Curtis dissimilarity; K_U: Unweighted UniFrac distance; K_0.5: Generalized UniFrac distance (θ = 0.5); K_W: Weighted UniFrac distance; adaptive: adaptive GLMM-MiRKAT (aGLMM-MiRKAT). L: low within-cluster correlation (${\rho }_{j{\ne j}^{\prime }}$ = $\frac{(1+j^2)}{(j^2+3)}$); M: medium within-cluster correlation (${\rho }_{j{\ne j}^{\prime }}$ = $\frac{(1+j^2)}{(j^2+2)}$); H: high within-cluster correlation (${\rho }_{j{\ne j}^{\prime }}$ = $\frac{(1+j^2)}{(j^2+\frac{5}{3})}$).