[Rasch] Sample Size and Item Fit Question

Petroski, Greg PetroskiG at health.missouri.edu
Wed Sep 3 05:07:48 EST 2008

I am fitting the Partial Credit Model to items with 4 ordinal response
options using WinSteps.  There are a large number of items in this
inventory and the sample size is fairly large with N = 1,300 subjects.
Virtually all the Infit & Outfit ZSTD statistics are significant -- by a
mile.  I also fit the Generalized Partial Credit & Graded Response
models to this data using PARSCALE and even with these more general
models nearly every item misfits with p < 0.02.  I believe all of this
apparent misfit is a sample size artifact.  Plots of the empirical and
model ICCs look pretty good and with N = 300-500 most items appear to
fit, even the more restricted PCM.

That is the back ground.  My question is when to use the LOCAL = option
in Winsteps and how to interpret these, especially ZEMP from LOCAL=Y.  I
don't yet really understand what WinSteps is doing with LOCAL=Y but the
but using it would "apparently" make for a gigantic difference in how a
reader sees fit.  For example, an item with INFIT ZSTD = 4.0  and item
with items with ZSTD > 4.6 and OUTFIT ZSTD= 5.0 have INFIT and OUTFIT
ZEMP values of .7 and .6, respectively.  The raw INFIT and OUTFIT
mean-squares for this item are 1.1 and 1.2, respectively.

So how does one interpret ZEMP, and whatever it is doing, does this seem
like cheating?  And, when sample sizes get bit should one abandon the
test statistics altogether and just be guided by mean-square values and
various published guidelines for them?

Greg Petroski
School of Medicine
Univeristy of Missouri

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