Second, the results were analyzed using item-response theory (IRT).
Most ADL instruments have been developed using classic test
theory,
49 but it has several shortcomings. The main ones
are that the results are dependent on the sample of subjects tested,
that every item is assumed to have the same difficulty, and that the
ordinal ratings used produce an interval scale. IRT is a powerful
statistical tool that overcomes these problems and has gained wide
acceptance in the development of educational and psychological
instruments.
50 Recently, Massof
51 advocated its use in the development of vision disability measures and
Turano et al.
52 applied it to a low-vision mobility
measure. IRT assumes that there is an unobserved (latent) continuous
dimension of ability (θ) and that each person can be placed along
this dimension at a point that reflects the extent of his or her
ability. IRT estimates item characteristic curves for each item that
show the probability of a positive response on a specific item as a
function of ability (θ).
53 The shape of the curve for
each item is determined by two item parametersβ
i and α
i . Parameterβ
i represents the item difficulty, andα
i represents the item discriminating ability
of item
i. Formally, the proportion of people who have
amount of the ability who answer item
i correctly is given
as:
\[P_{i}({\theta}){=}\ \frac{e^{{\alpha}_{i}({\theta}-{\beta}_{i})}}{1{+}e^{{\alpha}_{i}({\theta}-{\beta}_{i})}}\]
In the simplest model of IRT, termed the one-parameter logistic
model or Rasch model, all the items are assumed to have equal
discriminating ability (α
i ). Thus, the
important parameters are person ability and item difficulty. Each of
these parameters may be transformed to an interval scale using the
logarithm of the odds ratio (log-odds), where the mean value is 0 and
the SD 1. The units on the log-odds scale are called logits. (See
Hambleton et al.
53 for a detailed description of IRT and
Massof
51 for a description of using the Rasch model
to develop a vision disabilty measure.) We used another statistical
analysis program (Bigsteps, ver. 2.82; Mesa Press, Chicago, IL) to
perform a Rasch analysis on the data.