The Andrich Rating scale model is a normative measurement model. It is based on a Rasch logistic model and conforms to the tenets of axiomatic measurement theory.
23 24 Consequently, if the estimated measures from the VA LV VFQ difficulty ratings are valid, the pattern of patient responses to the items must agree with the expectations of the model within the limits of statistical error.
30 Goodness of fit is evaluated with weighted mean square residual errors across items for each person, across persons for each item, and across all person–item encounters for the instrument.
30 Two different weighting schemes are used. First, for each person–item encounter, the squared residual error is normalized to the expected variance. This normalized squared residual, which is expected to be distributed as χ
2, is called the outfit statistic, because it is sensitive to outlying errors.
30 For the second weighting scheme, the mean square residual is normalized to the average expected variance. This normalized mean squared residual, which also is expected to be distributed as χ
2, is called the infit statistic, because it is most representative of inlying errors.
30 Because both fit statistics are expected to be distributed as χ
2, the weighted mean squares are transformed to an expected standard normal distribution using a Wilson-Hilferty transformation.
31 Thus, the transformed outfit and infit values for each item and person are presented as
z-scores with an expected mean of 0 and an expected SD of 1.