Table 1 Rasch approach to analysing the S-FHAI

1

Rating scale functioning:

Does the rating scale function consistently across the items?

• Average measures for each category and threshold on each item should advance monotonically

• Zstd values < 2.0 in outfit mean square (MnSq) values for step category calibrations [27]

Four items had less than 10 responses per category. Two categories were combined, and then only two items did not meet the criteria

2

Internal scale validity:

How closely do the item responses match the responses expected according to the Rasch model?

• Item goodness-of-fit values with MnSq values between 0.6 and 1.4 [28]

All items met the criterion

3

Internal scale validity:

Is the scale unidimensional?

• Principal component analysis, with the first component explaining ≥ 50 % of total variance and any additional component explaining < 5 % (or eigenvalue < 2.0) of the remaining variance [26]

First component explained 54.2 % of total variance, and second component explained 5.9 % (eigenvalue 3.25) of total variance

4

Person-response validity:

How closely do the individual responses match the responses expected according to the Rasch model?

• Person goodness-of-fit statistics with infit MnSq < 1.4 and Zsrd value ≤ 2.0 [29]

• ≤ 5 % of the sample fails to demonstrate acceptable goodness-of-fit values [29]

34 % of participants failed to demonstrate acceptable goodness-of-fit values

5

Person-separation reliability:

Can the S-FHAI distinguish between two distinct foot-health groups in the sample?

• Person-separation index ≥ 2.0 [30]

0.37

6

Differential test functioning (DIF):

Are the item difficulty calibrations stable in relation to gender and age?

• Mantel–Haenszel statistic for polytomous scales

using log-odds estimators in WINSTEPS software (P < 0.01) [31, 32]

Gender: all item difficulty calibrations were stable

Age: six items had DIF in relation to age