Table 1.

Simulation scenarios: True model parameters when $x_1$ and $x_2$ are independently generated from a Bernoulli distribution with response probability 0.5. Note that “sc” denotes scenarios.

sc.	${\mathit{\beta }}_0$	${\mathit{\beta }}_1$	${\mathit{\beta }}_2$	${\mathit{\gamma }}_0$	${\mathit{\gamma }}_1$	${\mathit{\gamma }}_2$	Overall		$\mathit{x}=(1,1)$		$\mathit{x}=(1,0)$		$\mathit{x}=(0,1)$		$\mathit{x}=(0,0)$
							${\mathit{p}}_{\mathit{A}}$	${\mathit{p}}_{\mathit{B}}$	${\mathit{p}}_{\mathit{A}}$	${\mathit{p}}_{\mathit{B}}$	${\mathit{p}}_{\mathit{A}}$	${\mathit{p}}_{\mathit{B}}$	${\mathit{p}}_{\mathit{A}}$	${\mathit{p}}_{\mathit{B}}$	${\mathit{p}}_{\mathit{A}}$	${\mathit{p}}_{\mathit{B}}$
1	0	0	0	0	0	0	0.500	0.498	0.496	0.493	0.503	0.502	0.500	0.500	0.499	0.498
2	−0.5	0.5	0	0	0	0	0.407	0.398	0.502	0.488	0.497	0.499	0.318	0.302	0.310	0.296
3	−0.5	1	0	0	0	0	0.499	0.499	0.695	0.689	0.691	0.694	0.313	0.300	0.299	0.309
4	−1	0	0.5	0	0	0	0.231	0.233	0.302	0.311	0.157	0.155	0.312	0.312	0.155	0.157
5	−1	0	2	0	0	0	0.501	0.496	0.845	0.836	0.159	0.157	0.844	0.838	0.156	0.152
6	−0.5	0.5	0.5	0	0	0	0.498	0.500	0.689	0.696	0.499	0.503	0.500	0.493	0.303	0.308
7	−0.5	1	1	0	0	0	0.658	0.656	0.932	0.931	0.695	0.698	0.688	0.692	0.314	0.305
8	−0.5	−0.5	0.5	0	0	0	0.321	0.319	0.312	0.304	0.159	0.159	0.500	0.497	0.303	0.312
9	−0.5	−1	1	0	0	0	0.344	0.345	0.313	0.309	0.069	0.070	0.699	0.695	0.300	0.312
10	0	0	0	−0.5	0	0	0.312	0.499	0.310	0.505	0.311	0.501	0.315	0.497	0.309	0.491
11	−0.5	0.5	0	−0.5	0	0	0.235	0.404	0.304	0.503	0.314	0.501	0.158	0.308	0.158	0.305
12	−0.5	−0.2	0	−0.5	0	0	0.138	0.276	0.114	0.242	0.115	0.240	0.158	0.307	0.163	0.317
13	−0.5	0	0	−0.5	−0.5	0	0.112	0.311	0.067	0.315	0.069	0.318	0.160	0.304	0.150	0.303
14	−0.5	0	0	−0.5	0.5	0	0.234	0.309	0.306	0.307	0.315	0.308	0.156	0.309	0.164	0.312
15	−0.5	0.5	0	−0.5	−0.5	0	0.158	0.401	0.156	0.493	0.158	0.498	0.155	0.304	0.159	0.310
16	−1	0	0.5	−0.5	0	0	0.113	0.233	0.158	0.306	0.069	0.158	0.156	0.309	0.067	0.157
17	−1	0	2	−0.5	0	0	0.378	0.504	0.685	0.842	0.068	0.166	0.691	0.841	0.065	0.159
18	−1	0	2	−0.5	0	0.5	0.453	0.500	0.837	0.839	0.071	0.161	0.841	0.837	0.068	0.161
19	0.5	0.5	−0.5	−0.5	0.5	−0.5	0.500	0.680	0.499	0.692	0.841	0.839	0.160	0.494	0.497	0.694
20	0.5	0.5	−0.5	−0.65	0.5	0.5	0.625	0.680	0.802	0.692	0.800	0.840	0.444	0.491	0.449	0.690