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.