  We propose a new graphical model to describe the comorbidity of allergic
diseases. We present our model in two versions. First, we introduce a
generative model that correctly reflects the variables' causal relationship.
Then we propose an approximation of the generative model by another
misspecified model that is computationally more efficient and easily
interpretable. We will focus on the misspecified version, which we consider
more practical. We include in the model two directed graphs, one graph of known
dependency between the main binary variables (diseases), and a second graph of
the dependence between the occurrence of the diseases and their symptoms. In
the model, we also consider additional auxiliary variables. The proposed model
is evaluated on a cross-sectional multicentre study in Poland on the ECAP
database (www.ecap.pl). An assessment of the stability of the proposed model
was obtained using bootstrap and jackknife techniques.
