Distributed leadership is one of the most prominent contemporary leadership theories in education. Its attraction in education is perhaps due to its potential to bring about school improvement. A review of the literature, however, reveals broadness in the way the construct is being conceptualized and operationalized; thus making it elusive. The elusive nature of distributed leadership could be down to the lack of attempts to unpack and measure this construct, and/or because of the contested definition of the term "leadership" itself. The purpose of this article is to elucidate this construct by addressing possible dimensionality issues. To do this, exploratory factor analysis was performed using Rasch (linearized) standardized residuals to examine the factor structure of distributed leadership. The analysis provided a lucid interpretation of the data to build a theoretical (measurement) model of distributed leadership. The distributed leadership instrument consists of 25 items, and the sample involved 1,232 schools leaders from Singapore. The findings indicated the presence of four possible factors of distributed leadership which include "bounded empowerment", "developing leadership," "shared decision" and "collective engagement."