The importance of non-cognitive skills for academic achievement and future success has been emphasized but the invariance among the relationships of these constructs across different groups and countries is rarely studied. In this study, we used a novel approach, psychometric network analysis, to analyze the invariance of connections between non-cognitive skills measured in an international large-scale assessment--the 2018 Program for International Student Assessment (PISA). We focused on four different countries in terms of immigration contexts (Australia, Canada, and Germany) and analyzed the invariance of connections among non-cognitive skills for immigrant and native students within these countries. While Australia and Canada were the examples of traditional immigration countries, Belgium and Germany represented the post-war immigration countries with less selective immigration policy. We found significant differences in the network structure among countries and immigrant status (i.e., native vs. first-generation immigrant). Interestingly, we found that the primary split occurred between countries with different immigration policies. That is, the network tree structures of Canada and Australia were more similar to one another while the network tree structures of Germany and Belgium resembled each other. The results provided empirical evidence that non-cognitive constructs are not universal across countries selected, immigrants, and native students. The findings also underscored the importance of considering within-country and cross-country differences in order to design effective educational interventions relying on non-cognitive skills for targeting distinct cultural groups of interest.