Factor Analysis: Rotated Matrix

When conducting an exploratory factor analysis (EFA) or principal components analysis, researchers often perform a procedure to rotate the factor matrix. In communication research, it is relatively rare that a researcher would conduct a factor analysis without rotation. Rotation of the factor structure entails moving the factor axes in order to provide a new perspective on patterns in the underlying factor structure. Factor rotation provides many benefits. An unrotated factor solution simply tries to explain the maximum amount of variance with a minimal number of factors; however, most communication researchers use factor analysis in order to extract meaningful data that accurately represents the underlying nature of their data. Rotating the factor structure allows for the extraction of factors with face validity—the goal is to derive factors that accurately reflect reality. This results in factors that are both practically and theoretically useful.

Although factor analysis is a quantitative method, certain aspects of the data interpretation [Page 527]process are qualitative. Rotating the factor matrix allows for a full consideration of themes, trends, and patterns in the data. There are two types of factor rotation—orthogonal and oblique. Orthogonal rotation assumes that there is no overlap or correlation between the extracted factors. Oblique rotation assumes that there is overlap between the underlying constructs. Choosing the correct rotation method and solution depends largely on the goals of the researcher. For example, does the rotated solution accurately reflect preexisting assumptions about the data? Does the rotated data match a pattern that would be expected based on theory? Factor rotation allows researchers to better achieve the overarching goals of EFA and principal components analysis to extract meaningful, interpretable factors that allow for the connection of measured variables to latent theoretic or conceptual constructs. This entry examines some of the conceptual issues related to rotating factor, describes how to rotate factors, and provides examples for understanding factor rotation in the context of communications research.