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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