Analysis of paired comparison data based on experimental design: Expression using structural equation modeling

Paired comparison is a useful method for assessing ranks among several objects, and it enables us to obtain more reliable data than assessing objects one by one. But paired comparison principally provides information only about the ranks of the objects. On the other hand, experimental design provides a framework for elucidating causal associations. If we could analyze paired comparison data by the experimental design framework, it would be a very effective method. But experimental design, in its original form, is not readily applicable to paired comparison data. However, if we adopt the perspective of structural equation modeling (SEM), we can deal with paired comparison and experimental design in a unified way, because they are both submodels of SEM. The purpose of this study is to provide a new method to analyze causal connection of paired comparison data by using SEM. Here, two actual numerical examples are shown, one of which is obtained by within-subject design and the other is obtained by between-subject design.