Factor analysis is a powerful technique for investigating multidimensionality in observational data, but it fails to construct interval measures. Rasch analysis constructs interval measures, but only indirectly flags the presence of multidimensional structures. Simulation studies indicate that, for responses to complete tests, construction of Rasch measures from the observational data, followed by principal components factor analysis of Rasch residuals, provides an effective means of identifying multidimensionality. The most diagnostically useful residual form was found to be the standardized residual. The multidimensional structure of the Functional Independence Measure (FIMSM) is confirmed by means of Rasch analysis followed by factor analysis of standardized residuals.