The family approach to assessing fit in Rasch measurement

There has been a renewed interest in comparing the usefulness of a variety of model and non-model based fit statistics to detect measurement disturbances. Most of the recent studies compare the results of individual statistics trying to find the single best statistic. Unfortunately, the nature of measurement disturbances is such that they are quite varied in how they manifest themselves in the data. That is to say, there is not a single fit statistic that is optimal for detecting every type of measurement disturbance. Because of this, it is necessary to use a family of fit statistics designed to detect the most important measurement disturbances when checking the fit of data to the appropriate Rasch model. The early Rasch fit statistics (Wright and Panchapakasen, 1969) were based on the Pearsonian chi square. The ability to recombine the NxL chi squares into a variety of different fit statistics, each looking at specific threats to the measurement process, is critical to this family approach to assessing fit. Calibration programs, such as WINSTEPS and FACETS, that use only one type of fit statistic to assess the fit of the data to the model, seriously underestimate the presence of measurement disturbances in the data. This is due primarily to the fact that the total fit statistics (INFIT and OUTFIT), used exclusively in these programs, are relatively insensitive to systematic threats to unidimensionality. This paper, which focuses on the Rasch model and the Pearsonian chi-square approach to assessing fit, will review the different types or measurement disturbances and their underlying causes, and identify the types of fit statistics that must be used to detect these disturbances with maximum efficiency.