Distributional properties of the PIRLS-home resource for learning scale and observed effects on reading achievement
Are measurements of educational inequalities by latent indices without bias?
In Progress in International Reading Literacy Study (PIRLS) educational inequalities are measured, amongst others, through the relationship between students’ reading achievements and the home resource for learning (HRL) scale. By applying the partial credit model and using the WLE estimates for the person parameters it is accepted that the distribution of this latent variable is asymptotically normal within participating countries. This assumption is challenged from a theoretical perspective and through empirical findings. To find out how far the distributional properties of the HRL index influence the results of educational inequality measurements, the HRL index is rescaled for 21 European countries who participated in PIRLS 2011, assuming three different prior distributions of the latent index and using the EAP estimates for the person parameters. The predictive effects of these latent indices on students reading achievement were estimated with spline regressions. A positively skewed distribution of the latent index in the marginal maximum likelihood for estimating the item parameters results in the best fit of the scaling model in most countries. In addition, the pattern of signs of the estimated spline coefficients across the knots and the non-linear correlation between the latent index and student reading achievement varies considerably across the prior and empirical distributional properties of the latent index. Thus, by interpreting educational inequalities measured through the relationship between students’ reading achievements and the HRL scale in PIRLS, distributional properties of the HRL index should be taken into account.