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Chris Bradley, Robert W Massof; Problems using the Andrich model to estimate visual ability measures. Invest. Ophthalmol. Vis. Sci. 2017;58(8):1358.
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© ARVO (1962-2015); The Authors (2016-present)
The Andrich rating scale model is used by many vision researchers to estimate person measures, item measures and population thresholds from a set of ratings people assign to items on visual function questionnaires. A major problem with the Andrich model is that it often estimates disordered population thresholds. Users of the model are often advised to merge neighboring rating categories and redo the analysis until estimated thresholds come out ordered. We have developed a new rating scale model called the Axiomatic Rating Scale (ARS) model that derives from first principles a polytomous Rasch model that not only estimates person measures and item measures on an invariant scale, but also naturally estimates ordered population thresholds. Our goal is to determine whether claims made in prior studies that estimate visual ability measures using the Andrich model would be contradicted by the ARS model.
We applied both the Andrich model and the ARS model to the Activity Inventory (AI), a visual function questionnaire that includes items from most other visual function questionnaires. There were 510 items and 3163 persons whose ratings we analyzed.
Estimated person and item measures were highly correlated between the Andrich and ARS models. Item measure r2 = 0.925 while person measure r2 = 0.796. The estimated population thresholds of the two models were highly dissimilar, with those of the Andrich model being highly disordered, while those of the ARS model were ordered. There was closer agreement between the Thurstone thresholds of the Andrich model and the ARS model thresholds.
Past analysis of visual function questionnaires using the Andrich model are unlikely to be contradicted by the ARS model as long as the analysis does not depend on the estimated population thresholds of the Andrich model. Any such analysis that depends on the estimated population thresholds of the Andrich model will require re-analysis using the ARS model.
This is an abstract that was submitted for the 2017 ARVO Annual Meeting, held in Baltimore, MD, May 7-11, 2017.
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