Comment on "commentary on: past and present issues in Rasch analysis: the FIM revisited".

We would like to thank Allen W. Heinemann and Anne Deutsch for their commentary (1) on our paper (2). We entirely concur with their reminder of the debt owed by many to the work of Benjamin Wright and Mike Linacre at the Measurement, Evaluation, Statistics and Assessment (MESA) Psychometric Laboratory in Chicago, USA. It was through their efforts that, by-and-large, the Rasch model was disseminated into the area of health. We also concur with their reminder that the earlier work had an overriding purpose of introducing the Rasch model and, particularly, to emphasize that ordinal raw scores are not interval measures. While the former is now well established and, with over 1500 Rasch papers indexed in MEDLINE, stands as a testament to their efforts, the latter remains a challenge, given the inertia in the health outcomes community, and the frequent application of mathematical operations to ordinal scales. It is interesting to note that in their Commentary Heinemann & Deutsch (1) raise important questions as to the magnitude of the difference made to person estimates by the various modifications that can be made through collapsing of categories, and deletion of items that do not fit model expectations. It may be that the difference is, in fact, small, but that difference may reflect a solution that does satisfy the model assumptions and expectations, as opposed to one that does not. This is akin to a p-value of 0.06, which may reflect, in a clinical trial, very little difference in the magnitude of effect compared with that associated with a p-value of 0.05, but nevertheless, by convention , would fail to show a significant difference. Should we be concerned about this, and report that the study did show an effect? With respect to the Rasch model, either the data fit the model, or they do not, and person estimates under the latter scenario, are not valid, irrespective of the magnitude of difference from a fitting solution. Good science dictates that we specify in advance the acceptable parameters of fit for our analysis, and make our judgements about fit accordingly. Of more concern is the wide range of " acceptable " fit parameters to be found in the literature. Relaxing fit requirements and ignoring, for example, scientific evidence with regard to the appropriate range of fit statistics for a given sample size, consistent with a 0.05 Type I error rate, is a continuing threat …