International large-scale educational assessments (ILSAs) have played a relevant role in educational policies targeting immigrant students across countries as their results are used by governments as input for decision-making purposes. Given the potential impact that ILSAs can have, the psychometric features of these assessments must be carefully assessed and empirical evidence about the extent to which the inferences made based on test results are valid must be collected. To do so, the first step is to determine if the test results have the same meaning across countries and groups of examinees that is, if the measures are invariant so that results can be compared directly among countries. The general purpose of this dissertation was to provide evidence about the extent to which the 2018 Programme for International Student Assessment (PISA) provides invariant measures of reading literacy, exposure to bullying, and sense of belonging at school for immigrant students from diverse cultural and linguistic backgrounds across the countries that host large populations of immigrants. Moreover, given that test performance can be impacted by non-cognitive variables, the constructs exposure to bullying and sense of belonging at school were analyzed as potential predictors of student performance in reading literacy. Two modeling approaches were implemented to evaluate measurement invariance: a traditional approach (multiple group confirmatory factor analysis) and a more contemporary approach that has shown to be more suitable to handle the complex features of ILSAs. The overall results showed that the alignment optimization procedure was a more suitable statistical tool than the traditional modeling technique -multiple-group confirmatory factor analysis- for the evaluation of measurement invariance when the data under analysis are collected through ILSAs since it can handle the features and complexities of these data while allowing for the incorporation of the immigration status into the analysis. The implications of the overall findings for educational policymakers, educators, test developers, and educational researchers were discussed along with five limitations that should be addressed in future studies.