ing structural zeros
zeros &lt;- 0+ (Caesar &gt;0)
zeros[1,,1,1] &lt;- 1
structable(zeros)

# fit model excluding possible structural zeros
Caesar.mod0s &lt;- loglm(~Infection + (Risk*Antibiotics*Planned), 
                      data=Caesar, 
	                    start=zeros)
Caesar.mod0s

anova(Caesar.mod0, Caesar.mod0s, test="Chisq")

mosaic (Caesar.mod0s)

# what terms to add?
add1(Caesar.mod0, ~.^2, test="Chisq")

# add Association of Infection:Antibiotics
Caesar.mod1 &lt;- update(Caesar.mod0, ~ . + Inf