What limitations apply to test-of-fit
statistics used in RUMM2030?
- The Residual
test-of-fit statistic: is
constructed as a standard normalised residual, but is not perfectly
- a very positive
value implies poor discrimination;
- a very negative
value implies too good a discrimination.
- The Chi-square
test-of-fit: (and its
probability) is constructed as an approximate chi square but is not
perfectly distributed as the chi square.
the tests-of-fit employed by RUMM2030 for a Rasch analysis should be used relatively,
and not strictly absolutely according to external criteria.
How do RUMM2030 fit indices relate to OUTFIT
and INTFIT statistics used in other programs?
The outfit and infit statistics used in other
programs are similar to the Residual statistic in RUMM2030:
These values are differently weighted statistics
based on the residual between a person's response and the expected response
according to the model given the person and item estimates.
- The Outfit in these
programs is closer in value to that display in RUMM2030.
- All Residual
statistics displayed in RUMM2030 have an expected mean of 0 and a
standard deviation of 1 but, because they are approximations, the distributions
are not strictly normal.
- All of the
distributions of these Residuals:
- are affected by the
relative locations of the persons and the items;
- the number of
parameters estimated as well as
- the fit between the
data and the model.
- In all of these Residual
- a very negative value
implies overfit [Observations of means in successive class intervals
steeper than the ICC curve] for some reason [perhaps violation of local
- a very large value
implies underfit [Observations of means in successive class intervals
flatter than the ICC curve] of some kind [perhaps a violation of
- The chi square test of
fit formalises the graphical display of the ICC curves.