1. Introduction -- 2. Literature Review -- 3. Parental Involvement in PIRLS-2011 -- 4. Modeling Parental Involvement -- 5. Relation between Parental Involvement and Student Achievement in PIRLS-2011 -- 6. Conclusion and Discussion -- References -- Appendix: Technical details on the implementation of the bi-factor model.Open AccessThis volume offers insights from modelling measures of parental involvement and their relationship with student reading literacy across countries, exploring and incorporating cultural differences. This is a significant contribution to a field where cross-cultural comparisons from a triangulated perspective are sparse. For readers interested in exploring the relationship between parental involvement and student attainment, the literature review provides a useful starting point. Meanwhile, for the more methodologically interested reader, this report presents state-of-the-art ways to identify and model cultural differential item functioning in international large-scale assessment (ILSA), illustrating the extent to which the parental involvement construct may be influenced by cultural differences and how this may affect the outcomes of cross-cultural comparisons. The framework is generic and should provide a solid foundation for future ILSA practices and secondary analyses. ILSA studies like the IEA’s Progress in International Reading Literacy Study (PIRLS) provide valuable data, containing both student achievement data and contextual background data from schools, teachers, students and parents for over 41 countries.