A Method for the Analysis of Hierarchical Dependencies between Items of a Questionnaire

This paper describes a method of explorative data analysis which allows to detect logical implications between items of a dichotomous questionnaire or test. These logical dependencies are organized to form a hierarchical structure (quasi-order) on the items. Our analysis method, which is called Inductive Item Tree Analysis, can be seen as a method of Boolean analysis. We discuss the relation of our method to other methods of Boolean analysis and to related methods of data analysis, like for example Guttman scaling and latent class analysis. The adequacy of our analysis method is tested in a simulation study. The results of this study show that the method is able to detect existing dependencies with high accuracy if enough data are available. We apply our method to some real data sets to demonstrate the advantages of an analysis of logical implications.