A method of factor extraction specific to a binary matrix, illustrated here as a person-by-item response matrix, is presented. The extraction procedure, termed ERGO, differs from the more commonly implemented dimensionalizing techniques, factor analysis and multidimensional scaling, by taking into consideration item difficulty. Utilized in the ERGO procedure is the calculation of a dominance matrix which, for either persons or items, has the important attribute of allowing directionality to be inferred between relations. ERGO iteratively adds items together, resulting in the construction of various sets of implicative chains representing dimensions. Having constructed these chains, the ERGO procedure orders the chains in terms of maximal number of items contributed. The chain evaluation procedure can best be explained as an attempt to maximize the number of items accounted for in a given dimensional solution. To give additional understanding of the ERGO process, an empirical example which utilizes social distance items (Bogardus, 1925) paired individually with three ethnic groups was analyzed for respondents representing four ethnic groups. The results demonstrated the ability of ERGO to (1) group items referring to the same ethnic group; (2) uncover hierarchically graded orders within each chain; (3) select the three chains that corresponded to the three ethnic groups; and (4) cluster individuals by ethnic group according to their scores. (Author/KS)