In international large-scale assessments, students may not be compelled to answer every test item: a student can decide to skip a seemingly difficult item or may drop out before the end of the test is reached. The way these missing responses are treated will affect the estimation of the item difficulty and student ability, and ultimately affect the country's score. In the Progress in International Reading Literacy Study (PIRLS), incorrect answer substitution is used. This means that skipped and omitted items are treated as incorrect responses. In the present study, the effect of this approach is investigated. The data of 2006, 2011, and 2016 cycles of PIRLS were analyzed using IRTree models in which a sequential tree structure is estimated to model the full response process. Item difficulty, students' ability, and country means were estimated and compared with results from a Rasch model using the standard PIRLS approach to missing values. Results showed that the IRTree model was able to disentangle the students' ability and their propensity to skip items, reducing the correlation between ability and the proportion of skipped items in comparison to the Rasch model. Nevertheless, at the country level, the aggregated scores showed no important differences between models for the pooled sample, but some differences within countries across cycles.