Heterogeneity, school-effects and the North/South achievement gap in Italian secondary education: evidence from a three-level mixed model

Abstract

With the aim of assessing the extent of the differences in the context of Italian educational system, the paper applies multilevel modeling to a new administrative dataset, containing detailed information for more than 500,000 students at grade 6 in the year 2011/2012, provided by the Italian Institute for the Evaluation of Educational System. Data are grouped by classes, schools and geographical areas. Different models for each area are fitted, in order to properly address the heteroscedasticity of the phenomenon. The results show that it is possible to estimate statistically significant "school effects", i.e., the positive/negative association of attending a specific school and the student's test score, after a case-mix adjustment. Therefore, the paper's most important message is that school effects are different in terms of magnitude and types in the three geographical macro areas (Northern, Central and Southern Italy) and are dependent on specific students' and schools' characteristics.Keywords Child development · Multilevel models · School effectiveness · Valueadded model · Contextual effects · Education 1 Indeed, we are aware that the quality of schools is characterized by a wider set of dimensions (such as non-cognitive achievements, school climate, cognitive test scores in additional subjects, teachers' satisfaction, etc.). Thus, while the formulation "schools with higher tests" is somehow less intuitive, it is definitely more adequate for describing the real aspect that we are monitoring in this research. However to ease notation we use the word quality in the text.

Semiparametric Mixed Effects Models for Unsupervised Classification of Italian Schools

“…Agasisti et al . () and Masci et al . (, ) observed that the percentage of variability in student attainments in INVALSI tests explained by the random effect depends on the geographical macroarea and differs between mathematics and reading performances.…”

“…In this section, we present the semiparametric mixed effects model (Section 2.1), the EM algorithm for the estimation of its parameters (Section 2.2) and a simulation study (Section 2.3). Since we know from previous research on Italian data that there are patterns of student achievements across different Italian schools (Agasisti et al ., ; Masci et al ., , ), we are interested in evaluating how the association between previous and current student test scores changes across different Italian schools and, in particular, in identifying subpopulations of schools within which this association is identical. Therefore, the model that we develop is a two‐level linear model (in the application, students represent level 1 and schools represent level 2) with a discrete distribution with a finite number of support points on the random effects.…”

“…On the basis of previous literature, it is reasonable to think that there is a linear correlation between student scores at grade 6 and at grade 8 (Agasisti et al ., ; Masci et al ., , ). We therefore consider a semiparametric two‐level linear model (where students represent the first level and schools the second), with student test scores at grade 6 and the student socio‐economic index as random and fixed effects respectively, allowing both the intercept and the coefficient of student test scores at grade 6 to be random or school specific.…”

“…About 59% of schools are in northern Italy, 18% are in central Italy and 23% are in southern Italy. Geographical information is very relevant since many studies in Italy confirm that there are significant discrepancies between student and school performances across the three geographical macroareas (Agasisti et al ., ; Agasisti and Vittadini, ; Masci et al ., , ).…”

“…the number of subpopulations in which schools are grouped, with respect to the trend of achievements of their students. In the educational literature, multilevel linear models have already been applied to INVALSI data, with a view to estimating school value added, modelled by means of parametric distributions, after adjusting for student characteristics (Agasisti et al ., ; Masci et al ., , ; Sani and Grilli, ). Nonetheless, our method has a different scope since it does not seek to estimate individual value added for each school, but it looks for subpopulations of schools with homogeneous value added.…”