Structural Equation Modelling: Testing for the Factorial Validity, Replication and Measurement Invariance of Students' Views on Mathematics

Abstract

In this study, we provide a detailed account of processes involved in applying structural equation modelling to validate a survey instrument – the students' view of mathematics instrument – in a new cultural setting. First, we tested the factorial validity of the instruments in Ghana for 12th-grade students (N = 2034, M = 18.49, standard deviation = 1.25; 58.2% girls). Second, in the event of model misfit, we proposed and tested an alternate factorial structure. Third, we cross-validated the new structure with an independent sample from the Ghanaian data set. Fourth, we evaluated the factorial invariance across students' gender. Initial reliability estimates and confirmatory factor analysis indicated that the data set does not fit the hypothesized model (seven-factors). Subsequent exploratory factor analysis indicated a four-factor structure for the data set. The study has important implications for studies using structural equation modelling to validate survey instruments and shows the methodological challenges associated with the importation of a Western survey instrument into a different cultural environment.