Table 3. Summary of models.

Flow term	Fit ?	Intercept			d.f.	Log lik.	AIC
undirected	yes	−4.5	2.21	1.36	8	−999.8	0.0
directed	yes	−4.7	1.94	1.52	8	−1017.9	36.3
internal	yes	−4.0	2.20	1.42	8	−1005.4	11.3
internal	no	−3.8	2.17	1.40	7	−1005.6	9.7
none	no	−3.9	2.16	1.82	6	−1012.1	20.6

The models chiefly differ by how contact is assumed to depend on flows. In the null model, denoted by none, contact was independent of flows. In the internal model, contact was a function of within-state flows. In the directed model, contact was a function of flows moving into a state and within-state flows. In the undirected model, contact was a function of within-state flows and both flows into and out of a state. The column “Fit ?” indicates whether we estimated the value of , which corresponds to risk that is independent of the number of infective farms. The symbol denotes the dispersion parameter of the negative binomial response. The symbol denotes the standard deviation of the random effect of (geographic) state on transmission rates. The abbreviation d.f. is for degrees of freedom (i.e., the number of parameters estimated). AIC gives the AIC (Akaike information criteria) of a model minus the lowest AIC of all models.