Correlated component regression: Profiling student performances by means of background characteristics

Multicollinearity is one of the main problems when using regression analytic approaches to predict outcome variables. The application of traditional regression analytic approaches often provides unstable and unreliable estimates of the parameters when multicollinearity occurs. In this paper we apply a regression analytic method called correlated component regression (CCR), developed by Magidson (Correlated component regression: re-thinking regression in the presence of near collinearity. In Abdi et al. (eds) New perspectives in partial least squares and related methods, Springer, Heidelberg, pp 65-78, 2013), for characterizing student performances in PIRLS/TIMSS 2011 (Martin and Mullis, Methods and procedures in TIMSS and PIRLS 2011, TIMSS & PIRLS International Study Center, Chestnut Hill, 2013) through selected background characteristics, such as cultural and socioeconomic characteristics. On the basis of various criteria, we compare the findings of CCR with the results of OLS regression regarding the prediction of student performance values. An implemented cross-validation procedure and step-down algorithm are utilized to perform a special type of variable reduction. Thus, the results of our study will provide more reliable sets of background variables for characterizing large scale educational data in the domains of reading, mathematics, and science.