Structure Measure & Andrich Thresholds 3.2 June 19th, 2013, 6:35pm

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uve
 Posted: July 8th, 2012, 9:53pm
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 Mike,I understand that when GROUPS is selected, the Structure Measure for a category is the sum of the item measure and the Andrich Threshold for that category. I'm just not sure what the differences are in interpretation. For example, what information does Structure Measure provide that I can't glean from Andrich Threshold? Also, when GROUPS is not selected then the two sets of data are identical. This doesn't make sense to me in light of the fact that Structure Measure for a category is a sum of two data sets. I'd greatly appreciate any additional information you could provide.
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Mike.Linacre
 Posted: July 8th, 2012, 10:58pm
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 Uve, Winsteps includes considerable duplication of numbers, but from slightly different perspectives. No one uses all the numbers. In fact, surely most people (including me) ignore most of the numbers. We focus on the numbers that are important to us.Probably the focus here is on the different ways that the estimates for the Rating-Scale model and the Partial Credit model are presented. This is largely driven by historical accident. Initially, those models had different motivations and different audiences. They were conceptualized to be fundamentally different models. Only later was it realized that the differences between the models are algebraically trivial. But it was too late!So now, for the Rating-Scale model, the convention is to report the Andrich thresholds relative to the item difficulties. Since these are the same for all items, only one set of numbers is reported, often called "taus".  So "Structure measures = Andrich thresholds"For the Partial Credit model, the Andrich thresholds, which differ for each item, the Andrich Thresholds are usually combined with the item difficulties and often called "deltas". Winsteps also reports the the thresholds relative to item difficulties. So "Structure measures" = (item difficulty + Andrich threshold).Does this help?
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uve
 Posted: July 9th, 2012, 6:54pm
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 Thanks Mike, that helps. With a hammer I hammer nails and with a saw I cut wood. To me, each of these data sets is a tool. So with your explanation in mind, at this point I'm trying to distinquish the different uses/purpose of the Structure Measure tool from the Andrich Threshold tool when using the partial credit analysis.
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Mike.Linacre
 Posted: July 9th, 2012, 10:07pm
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 Uve, the difference between those two is really your audience. Do they think in terms of (item difficulty) + (Andrich threshold) [the original "Rating Scale" way of thinking] or (item difficulty + Andrich threshold) [the original "Partial Credit" way of thinking] ?
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