Misfits: People and their problems. What might it all mean?

In the analysis of data, which arise from the administration of multiple choice tests or survey instruments and which are assumed to conform to a measurement model such as Rasch, it is normal practice to check item fit statistics in order to ensure that the items used in the instrument cohere to form a unidimensional trait measure. However, checking whether individuals also fit the measurement model appears to be less common. It is shown that poor person-fit compromises item parameter estimates and so it is argued that person-fit should be checked routinely in the calibration of instruments and in scoring individuals. Unfortunately, the meanings that can be ascribed to person-fit statistics for attitude instruments is not clear. A proposal for seeking the required clarity is developed.