Table 1.

Data generating distributions for simulation.

Simulation	logit E[Y|A, W]	Ψ (P0)	P0(b0(W) = 0)	P0(b0(W) < 0)
N1	W1 + W2	0	l	0
N2	−0.2A[(W1 – z0.8)+]2	0	0.80	0.20
N3	−0.25A	0	0	l
A1	0.8A	0.19	0	0
A2	$A{W}_1^{+}-A{W}_2^{+}$	0.06	0.25	0.38
A3	AW1	0.09	0	0.50

Note: Decimals rounded to the nearest hundredth. For N2, z_0.8 ≈ 0.84 is the 80th percentile of a standard normal distribution. We use x⁺ to denote the positive part of a real number x.