Figure 1.

Directed Acyclic Graph of the latent class model. Every node is, if necessary, indexed by the department number ($i\in \left[1;N_{\mathit{Dpt}}\right]$) and the herd number ($j\in \left[1;Nher{d}_i\right]$). Plain arrows represent stochastic links and dotted arrows represent deterministic links. Observed data (grey oval) include $n_{\mathit{ij}}$, which is a vector of eight dimensions corresponding to the number of animals in each of the eight combinations of the three tests results. Measured covariables include $Nsampl{e}_{\mathit{ij}}$ the number of animals sampled in the $j^{\mathit{th}}$ herd of the $i^{\mathit{th}}$ department. Latent variables (white ovals) include the within-herd prevalence ($WH{P}_{\mathit{ij}}$), the herd latent status of each herd ($Herdstatu{s}_{\mathit{ij}}$) and $P_{\mathit{ij}}$ the conditional true prevalence (in positive herds only). Unknown parameters (white ovals) include the Se and Sp values of the three ELISA tests, the conditional dependence terms (modelled according to Wang et al. [33]), the between-herd prevalence ($BH{P}_i$) in each department, and the hyper-parameters of the within-herd prevalence beta distribution (${\gamma }_P$ and ${\mu }_P$).