Correlation partition coefficient based on a multivariate multilevel model
by
Maria Eugenia Ferrao
Universidade da Beira Interior

School effectiveness research is a major topic in Education. It is broadly accepted that a good criterion for measuring effectiveness is the use of value-added models (VAM). Value-added models or adjusted comparison of schools play an important role in order to produce more accurate estimates of the school effect on student development. The statistical specification of those models is still a matter of discussion. Many authors suggest that VAM should consider more than one outcome variable and argue about the most adequate metric. Model functional form and the set of control variables are not a matter of general agreement, either.

The research project 3EM is a longitudinal study that aims both at estimating the school effect and at identifying the characteristics of the effective schools in Portuguese compulsory education (region of Cova da Beira).

The main purpose of this paper is to show that by the time students get into school (baseline), two potential outcome variables are moderately correlated but all correlation is due to student level. Correlation partition coefficient (CFC) is figured out based on a multivariate multilevel model applied to the 1st year 3EM data, where the response variables are 3EMat score (a measure of math skills) and student intellectual level. The control variables are age, gender, socio-economic level and self-concept.

Keywords: multivariate multilevel model, value added model, variance partition, skills in maths, self-concept.

Date received: July 19, 2006