Open Access
December 2016 Exploiting TIMSS and PIRLS combined data: Multivariate multilevel modelling of student achievement
Leonardo Grilli, Fulvia Pennoni, Carla Rampichini, Isabella Romeo
Ann. Appl. Stat. 10(4): 2405-2426 (December 2016). DOI: 10.1214/16-AOAS988


We illustrate how to perform a multivariate multilevel analysis in the complex setting of large-scale assessment surveys, dealing with plausible values and accounting for the survey design. In particular, we consider the Italian sample of the TIMSS&PIRLS 2011 Combined International Database on fourth grade students. The multivariate approach jointly considers educational achievement in Reading, Mathematics and Science, thus allowing us to test for differential associations of the covariates with the three outcomes, and to estimate the residual correlations among pairs of outcomes within and between classes. Multilevel modelling allows us to disentangle student and contextual factors affecting achievement. We also account for territorial differences in wealth by means of an index from an external data source. The model residuals point out classes with high or low performance. As educational achievement is measured by plausible values, the estimates are obtained through multiple imputation formulas.


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Leonardo Grilli. Fulvia Pennoni. Carla Rampichini. Isabella Romeo. "Exploiting TIMSS and PIRLS combined data: Multivariate multilevel modelling of student achievement." Ann. Appl. Stat. 10 (4) 2405 - 2426, December 2016.


Received: 1 March 2016; Revised: 1 July 2016; Published: December 2016
First available in Project Euclid: 5 January 2017

zbMATH: 06688782
MathSciNet: MR3592062
Digital Object Identifier: 10.1214/16-AOAS988

Keywords: Hierarchical linear model , large-scale assessment data , multiple imputation , plausible values , school effectiveness , secondary data analysis

Rights: Copyright © 2016 Institute of Mathematical Statistics

Vol.10 • No. 4 • December 2016
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