Testing measurement invariance of mathematics self-concept and self-efficacy in PISA using MGCFA and the alignment method

The aim of the study is to investigate the measurement invariance of mathematics self-concept and self-efficacy across 40 countries that participated in the Programme for International Student Assessment (PISA) 2003 and 2012 cycles. The sample of the study consists of 271,760 students in PISA 2003 and 333,804 students in PISA 2012. Firstly, the traditional measurement invariance testing was applied in the multiple-group confirmatory factor analysis (MGCFA). Then, the alignment analyses were performed, allowing non-invariance to a minimum to estimate all of the parameters. Results from MGCFA indicate that mathematics self-concept and self-efficacy hold metric invariance across the 80 groups (cycle by country). The alignment method results suggest that a large proportion of non-invariance exists in both mathematics self-concept and self-efficacy factors, and the factor means cannot be compared across all participating countries. Results of the Monte Carlo simulation show that the alignment results are trustworthy. Implications and limitations are discussed, and some recommendations for future research are proposed.