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Updated: Oct 28, 2026

Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills
Published on: September 17, 2019
Academic self-concept and ecological predictors of longitudinal change in reading achievement in Chile: evidence from
Sonia Salvo-Garrido1, Ana Moraga-Pumarino2, Manuel Mieres-Chacaltana3
1Departamento de Matemática y Estadística, Universidad de La Frontera, Temuco, Chile.
Background:
Reading achievement is a foundational educational outcome, yet longitudinal evidence remains limited on how students' reading achievement changes from primary to lower secondary education and how these changes are shaped by individual, family, school, and sociodemographic factors in unequal educational systems.
Methods:
This study examined longitudinal change in reading achievement from Grade 4 in 2015 to Grade 8 in 2019 in a national Chilean cohort of 123,827 students. Using linear mixed-effects models with repeated measures, we analyzed the contribution of students' academic self-concept, academic engagement and self-efficacy, family reading attitudes, parental education, cultural capital, parental educational expectations, school climate, school violence, students' self-reported sex, Indigenous status, and socioeconomic status.
Results:
Observed reading scores were lower at the Grade 8 assessment occasion than at the Grade 4 assessment occasion, with mean scores of 247.3 and 273.0 points, respectively, and the final model estimated a negative coefficient for the Grade 8 assessment indicator (B = -23.68, p < 0.001). Academic self-concept showed the largest positive association with reading achievement (B = 23.45, p < 0.001), followed by teacher regulation and normative guidance, parental educational expectations, parental education, classroom order and engagement, and family reading attitudes. School violence and peer aggression, perceived discrimination at school, and student-teacher aggression were negatively associated with achievement. The most parsimonious moderation model indicated that longitudinal change differed by the joint combination of time, sex, and Indigenous status, whereas socioeconomic status was mainly associated with achievement levels rather than change over time.
Conclusion:
These findings support an ecological and equity-oriented understanding of reading development, showing that longitudinal change in reading achievement is associated with academic self-beliefs, family literacy environments, school experiences, and structural inequalities.
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