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Regional Economic Disparities as Determinants of Students’ Achievement in Italy: Data and methodology

In this paper, we model education as a “production process” characterized by some students’ characteristics (age, gender, nationality, etc.) as well as schools’ characteristics (public/private status, resources, etc.) as inputs, and students’ achievement as outputs.
While the Invalsi dataset contains information about INDij, there is a lack of adequate data for SESj and SCHj (school-level socio-economic conditions of families and schools’ resources): to solve this problem, we matched the Invalsi dataset with the TIMSS 2007 one (http://www.iea.nl/TIMSS2007.html; more detailed information about TIMSS 2007 data, with special reference to Italy, can be found in Invalsi 2008b). It is important to point out here that the reference years are different: while the Invalsi data concern the year 2008/09, the TIMSS data refer to 2006/07. However, the latter has been used only for the school-level variables, which can be considered as quite “stable” across years, especially in a very short period (two years).
Nevertheless, we lack information about SESij (student-level socio-economic status): as a consequence, the empirical models are not able to explain a relevant part of the individual achievements’ variations caused by the different socio-economic backgrounds of the individual students. Indeed, as the Invalsi and TIMSS data come from different years, we were not able to match individual students – but only schools. Polytechnic Colleges

At the end of the merging procedure, we have data for a sample of 21,336 students, sorted into 163 schools.
The methodological approach: the advantages of multilevel modelling
In this paper, we used a multilevel approach to analyse the schools and students performances. The choice is justified by the hierarchical nature of data, e.g. students nested within schools. In the context analysed here, the multilevel modelling has many advantages with respect to the traditional linear models. Such advantages are particularly strong when some circumstances occur, and more specifically:
i.    the data show highly structured hierarchies because students are nested within schools, and schools are nested within cities and regions. The most common error when not considering the hierarchical structure of data are:
a.    Ecological fallacy, that is interpreting at individual level some variables obtained by aggregating data at higher level (this problem is particularly relevant in the educational setting, as pointed out by Connolly, 2006);
b.    Atomistic fallacy, that is interpreting groups’ effect by using individual-level data.
Both the problems lead to an underestimation of standard errors, which in turn confounds the statistical significance of variables at higher levels (overestimation). Such underestimation of standard errors is especially high when the correlation of individuals within groups is high;
ii.    the ability to describe the determinants of students’ results is hampered by the potential endogeneity of the students’ covariates, as well as by non-considered covariates at school level. Such problems can be partially reduced by properly taking into account both students and schools’ characteristics;
iii.    there are problems concerning the different numbers of students analysed in the different schools;
iv.    techniques for ranking schools’ performances (e.g. Data Envelopment Analysis) are often subject to the impact of “extremes” (outlier observations).
In these and other cases the extensive literature about variance and mixed-effects models suggests that hierarchical models (and particularly multilevel models) offer solutions for studying the relationships between outputs (e.g. achievement scores, in our case) and contextual and organizational variables in complex hierarchical structures – considering both individual and aggregate levels of analysis.
In the previous literature about Italian schools, despite the many advantages of multilevel modelling, only Longobardi et al. adopted it. We follow this methodological approach instead, through the following operating steps.

This post was written by , posted on January 3, 2014 Friday at 12:06 pm