Abstract: In a typical educational survey, a sample of students responds to items relating to one or more cognitive
domains, and to a questionnaire. The cognitive domains are scaled using an item response theory
model, and interest is in the conditional distribution of ability given student and school characteristics.
We propose a network model in which all questions (cognitive and background) are nodes, connected
by edges that encode the correlational structure. Interest is in modelling the joint distribution of all
questions. The network structure consists of three components. First the edges between cognitive items
encode the dimenstionality of the cognitive domains. Second the edges between questions from the
background questionnaire encode its structure. Third, edges between cognitive items and
questionnaire items provide information about Differential Item Functioning (DIF). We use this
framework to put DIF in educational surveys in a novel perspective.

Keywords: cognitive domain, Differential Item Functioning (DIF), educational surveys