%0 Journal Article %1 Boeck1988 %A Boeck, Paul De %A Rosenberg, Seymour %D 1988 %J Psychometrika %K binary_factor_analysis %N 3 %P 361--381 %R 10.1007/BF02294218 %T Hierarchical classes: Model and data analysis %U https://doi.org/10.1007/BF02294218 %V 53 %X A discrete, categorical model and a corresponding data-analysis method are presented for two-way two-mode (objects × attributes) data arrays with 0, 1 entries. The model contains the following two basic components: a set-theoretical formulation of the relations among objects and attributes; a Boolean decomposition of the matrix. The set-theoretical formulation defines a subset of the possible decompositions as consistent with it. A general method for graphically representing the set-theoretical decomposition is described. The data-analysis algorithm, dubbed HICLAS, aims at recovering the underlying structure in a data matrix by minimizing the discrepancies between the data and the recovered structure. HICLAS is evaluated with a simulation study and two empirical applications.

@article{Boeck1988, abstract = {A discrete, categorical model and a corresponding data-analysis method are presented for two-way two-mode (objects {\texttimes} attributes) data arrays with 0, 1 entries. The model contains the following two basic components: a set-theoretical formulation of the relations among objects and attributes; a Boolean decomposition of the matrix. The set-theoretical formulation defines a subset of the possible decompositions as consistent with it. A general method for graphically representing the set-theoretical decomposition is described. The data-analysis algorithm, dubbed HICLAS, aims at recovering the underlying structure in a data matrix by minimizing the discrepancies between the data and the recovered structure. HICLAS is evaluated with a simulation study and two empirical applications.}, added-at = {2021-08-16T11:49:43.000+0200}, author = {Boeck, Paul De and Rosenberg, Seymour}, biburl = {https://www.bibsonomy.org/bibtex/2ebc805b34a8a476ba6cf955c8525883f/duerrschnabel}, day = 01, doi = {10.1007/BF02294218}, interhash = {f81f16fe2519af8f53afcff9f8414ebe}, intrahash = {ebc805b34a8a476ba6cf955c8525883f}, issn = {1860-0980}, journal = {Psychometrika}, keywords = {binary_factor_analysis}, month = sep, number = 3, pages = {361--381}, timestamp = {2021-08-16T11:49:43.000+0200}, title = {Hierarchical classes: Model and data analysis}, url = {https://doi.org/10.1007/BF02294218}, volume = 53, year = 1988 }