All Rasch analyses were performed with a computer program (Winsteps, ver. 3.66) and by applying the Andrich rating scale model with an item-grouping level in which all items that share the same response scale (all except 4, 5, and 26) were analyzed together as a single group.
47 First, Rasch analysis was used to investigate how the response categories were used and whether any were disordered or whether neighboring categories were indistinguishable to respondents and could be merged. Second, we established whether the A&SQ behaves consistently among predefined subgroups within the sample. We were particularly interested in whether individuals with and without strabismus would respond differently to any item within the A&SQ. These differences were tested by using differential item functioning (DIF) and establishing whether item response bias was found within different subgroups, despite having equal levels of the underlying trait (i.e., VR-QoL).
45,47 The following predefined subgroups were evaluated: strabismus (presence or absence), sex (male or female), age (presbyopic, >45 years; prepresbyopic, 45 years or younger), and the presence or absence of spectacles for distance viewing. The χ
2 test comparing the mean level of item difficulty between each of these subgroups was used to identify significant levels of DIF.
47 Third, the usefulness of each item from the questionnaire (i.e., how well it fit the model) was determined; we examined how well each item matched the VR-QoL of the participants and whether removal of some items and/or merging of some response scales could lead to an improved instrument. Finally, Rasch analysis was used to determine whether the data were unidimensional.
39,45,46,41–43 Principal components analysis (PCA) of the residuals (i.e., observed responses minus their expected responses, as indicated by the Rasch model) was used to assess the dimensionality of the A&SQ.
48 PCA decomposes the item correlation matrix to first indicate what proportion of variance of the residuals is explained by the principal component. If it explains a large amount of the variance of the data, say >60%, then it is likely that the dataset is unidimensional. Patterns within the variance that are unexplained by the principal component suggest that a second construct is being measured. An eigen-value greater than 2.0 suggests a second dimension, as this is greater than the magnitude seen with random data. We finally examined any items that could form a second dimension and determined whether their number and inherent qualities suggest that an important second dimension is being measured (Linacre JM, personal communication, October 2008).