Degrees of freedom for S-X2 statistic

[Irshad Mujawar]

Hello Phil,

I observed that for the same model (e.g. Rasch ) S-X2 statistic's degrees of freedom are changing for different items.

How is it possible as I suppose the number of groups and number of estimated parameters will remain same across the all items .

What formula are you using to calculate degrees of freedom of S-X2 statistic?

Thank you,
Irshad

[Phil Chalmers]

Hi Irshad,

The S-X2 statistic is built conditional on the total score values, so if some total scores don't appear very often the tables with the expected values for each category will be sparse. Therefore, in order to fix this the categories are collapsed both across categories (for polytomous items only) and total scores. So, some items might have more sparseness than others, and therefore require more collapsing; thus, have lower degrees of freedom to work with.

That being said, if you are checking out the S-X2 to polytomous items I would recommend updating to the dev version. The CRAN version works fine, but it was a bit over zealous with collapsing across categories, where sometimes they collapsed to only a single expected value (which makes a chi^2 test useless for those particular scores). Doesn't seem to affect the statistic too much overall since the effect is pretty minor, but nonetheless a better implementation is available. Cheers.

Phil

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