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. [ABSTRACT FROM AUTHOR]