Significant predictors of mathematical literacy for top-tiered countries/economies, Canada, and the United States on PISA 2012: Case for the sparse regression model

Background: National ranking from the triennial Programme of International Student Assessment (PISA) often serves as a barometer of national performance and human capital. Though excessive student- and school-level covariates (n > 700) may prove intractable for traditional least-squares estimate procedures, shrinkage methods may be more suitable for subset selection.

Aims: With a focus on the United States, this paper proposes sparse regression for PISA 2012 to discover salient student- and school-level predictor variables for mathematical literacy achievement.

Sample: The sparse regression analysis was conducted on 10 top-tiered OECD countries/economies, Canada, and the United States in mathematical literacy on the 2012 PISA. Two- and three-level hierarchical regression analyses were performed on Canadian and US students (N = 26,522) along with five of the ten top-tiered countries/economies (N = 58,385).

Methods: Using the 'least absolute shrinkage and selection operator' (LASSO) technique, the study (1) identified salient predictor variables of mathematical literacy performance for the top-tiered countries/economies, Canada, and the United States and (2) used these salient variables to perform two- and three-level hierarchical regression on data from Canada and the United States along with five top-tiered countries/economies. Weights and replicates were used to account for complex sample design. A weighted, two-level confirmatory factor analysis was performed to identify latent constructs. Missing data were handled through multiple imputation.

Results: Separate two-level hierarchical models accounted for 32-35% student-level and 58-70% school-level variance in Canada and the United States, respectively; three-level models accounted for 33% of level-one variance, 62-65% level-two variance, and 13-44% of level-three variance for the US/Canada and US/Canada/top-tiered students, respectively. Following top-tiered countries/economies, Canadian students had high levels of self-efficacy, were more likely to encounter advanced concepts in class, were less activity/small group-centred, and were more likely to consider truancy a learning hindrance. Factor analyses revealed a positive relation with rigour and class organization (teacher-centred) for top-tiered countries and Canada, though not for the United States. For all countries, there was a strong relation between rigour and self-beliefs.

Conclusion: Compared to top performers, a less rigorous curriculum, coupled with class and school factors, may explain lag in US performance.