The Rasch model is a theoretical mathematical description of how fundamental measurement should operate with social/psychological variables. Rasch suggested the use of chi-square fit statistics to determine how well any set of empirical data met the requirements of his model. Rasch analysis programs usually report fit statistics as two chi-square ratios: infit and outfit mean square statistics. Rasch factor analysis involves, first, a regular Rasch analysis procedure, followed by a factor analysis of the residuals that remain after the linear Rasch measure has been extracted from the data set. The presence of factor loadings in the analysis of residuals would suggest the presence of more than one underlying test dimension. In spite of the requirements of journal editors and reviewers for unambiguous interpretation of indicators of misfit, the routine application of some cutoff criteria for acceptable fit statistics always risks undervaluing the theory-driven process of developing measures in the human sciences.