Assessing Construct Validity in Math Achievement: An Application of Multilevel Structural Equation Modeling (MSEM).

The purpose of the present study was to model math achievement at both the person and university levels of the analyses in order to understand the optimal factor structure of math competency. Data involved 2,881 students who took a national mathematics examination as part of their entry at the university public system in Saudi Arabia. Four factors from the National math examination comprised the math achievement measure, namely, numbers and operations, algebra and analysis, geometry and measurement, and, statistics and probabilities. Data were analyzed using the aggregate method and by use of Multilevel Structural Equation Modeling (MSEM). Results indicated that both a unidimensional and a 4-factor correlated model fitted the data equally well using aggregate data, where for reasons of parsimony the unidimensional model was the preferred choice with these data. When modeling data including clustering, results pointed to alternative factor structures at the person and university levels. Thus, a unidimensional model provided the best fit at the University level, whereas a four-factor correlated model was most descriptive for person level data. The optimal simple structure was evaluated using the Ryu and West (2009) methodology for partially saturating the MSEM model and also met criteria for discriminant validation as described in Gorsuch (1983). Furthermore, a university level variable, namely the year of establishment, pointed to the superiority of older institutions with regard to math achievement. It is concluded that ignoring a multilevel structure in the data may result in erroneous conclusions with regard to the optimal factor structure and the tests of structural models following that.