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In educational assessments two types of missing responses can be discerned: items can be "not reached" or "skipped". Both types of omissions may be related to the test taker’s proficiency, resulting in non-ignorable missingness. This paper proposes to model not reached and skipped items as part of the response process, using IRTrees (De Boeck, & Partchev, 2012). A simulation study shows that this method can reduce bias when the missing responses are not ignorable. When applied to reading assessment data from the 2009 PISA assessments, the IRTree analysis shows that the tendency to skip items is negatively correlated with reading proficiency. Significant differences are found between IRTree estimates and estimates by a model that ignores the missing responses.