TEST-OF-FIT STATISTICS
Question:
What limitations apply to test-of-fit
statistics used in RUMM2030?
Explanation:
- The Residual
test-of-fit statistic: is
constructed as a standard normalised residual, but is not perfectly
normally distributed:
- 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.
Overall:
the tests-of-fit employed by RUMM2030 for a Rasch analysis should be used relatively,
and not strictly absolutely according to external criteria.
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Question:
How do RUMM2030 fit indices relate to OUTFIT
and INTFIT statistics used in other programs?
Explanation:
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
statistics:
- 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
independence], and
- 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
unidimensionality].
- The chi square test of
fit formalises the graphical display of the ICC curves.
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