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. Author manuscript; available in PMC: 2018 Nov 1.
Published in final edited form as: J R Stat Soc Series B Stat Methodol. 2016 Oct 31;79(5):1509–1525. doi: 10.1111/rssb.12213

Table 1.

Simulation DGMs.

DGM 1: no positivity violations generated DGM 2: positivity violations generated
S ~ Ber(0.5) S~ Ber(0.5)
W1 ~ Ber(0.4 + 0.2S) W1 ~ Ber(0.3 + 0.5S)
W2 ~ N(0.1S, 1) W2 ~ N(0.5S, 1)
W3 ~ N(1 + 0.2S, 1) W3 ~ N(1 + S, 2)
A ~ Ber(0.5) A ~ Ber(0.5)
Z ~ Ber(−log(1.6) + log(4)A − log(11)W2 − log(1.3)W3) Z ~ Ber(−log(1.6)+log(4)A − log(2)W2 + log(2)W3)
Y ~ Ber(log(1.6) + log(1.9)Z − log(1.3)W3 − log(1.2)W1 + log(1.2)AW1) Y ~ Ber(log(1.6) + log(1.9)Z − log(1.3)W3 − log(1.2)W1 + log(1.2)AW1)