The Programme for International Student Assessment comparative study of reading performance among 15-year-olds is reanalyzed using statistical procedures that allow the full complexity of the data structures to be explored. The article extends existing multilevel factor analysis and structural equation models and shows how this can extract richer information from the data and provide better fits to the data. It shows how these models can be used fully to explore the dimensionality of the data and to provide efficient, single-stage models that avoid the need for multiple imputation procedures. Markov Chain Monte Carlo methodology for parameter estimation is described.

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