Significant S_X2 item fit

[irukeru]

Hello I have run following model for my polytomous items in two factors. 

cfa2 <- mirt.model("F1 = 1,2,4,5

                   F2 = 3,6,7

                  COV = F1*F2")

mod2 <- mirt(dat, cfa2, itemtype = "graded", SE = T, TOL = 0.001)

I am getting well model fit indices, however, I am having trouble to interpret the results in itemfit. When I run the analysis for item fit, I am getting all S_X2 are significant which we do not want. I have checked some previous posts here, and some stated that large sample size is the reason for this results. So, my question is if you have any reference for it? and, how can I provide evidence for itemfit other than using S_X2?

> itemfit(mod2)

  item    S_X2 df.S_X2 RMSEA.S_X2 p.S_X2

1   K1 149.834      51      0.034      0

2   K2 134.221      52      0.030      0

3   K3  95.981      47      0.025      0

4   K4 136.955      51      0.031      0

5   K5  96.524      48      0.024      0

6   K6 105.127      39      0.031      0

7   K7  93.166      49      0.023      0

Thank you!

[Keri Simmons]

The S-X2 stat is for unidimensional models so I imagine this is what is causing the significant result.

On May 26, 2020, at 4:06 PM, irukeru <i.so...@gmail.com> wrote:



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[irukeru]

Thank you Keri. So, then my question is if there is any way to examine itemfit in multidimensional models. I am just learning MIRT and I appreciate for any source or anything to read and learn more. 

26 Mayıs 2020 Salı 16:48:32 UTC-4 tarihinde Keri Simmons yazdı:

The S-X2 stat is for unidimensional models so I imagine this is what is causing the significant result.

On May 26, 2020, at 4:06 PM, irukeru <i.so...@gmail.com> wrote:



Hello I have run following model for my polytomous items in two factors. 

cfa2 <- mirt.model("F1 = 1,2,4,5

                   F2 = 3,6,7

                  COV = F1*F2")

mod2 <- mirt(dat, cfa2, itemtype = "graded", SE = T, TOL = 0.001)

I am getting well model fit indices, however, I am having trouble to interpret the results in itemfit. When I run the analysis for item fit, I am getting all S_X2 are significant which we do not want. I have checked some previous posts here, and some stated that large sample size is the reason for this results. So, my question is if you have any reference for it? and, how can I provide evidence for itemfit other than using S_X2?

> itemfit(mod2)

  item    S_X2 df.S_X2 RMSEA.S_X2 p.S_X2

1   K1 149.834      51      0.034      0

2   K2 134.221      52      0.030      0

3   K3  95.981      47      0.025      0

4   K4 136.955      51      0.031      0

5   K5  96.524      48      0.024      0

6   K6 105.127      39      0.031      0

7   K7  93.166      49      0.023      0

Thank you!

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[Phil Chalmers]

The S-X2 statistic is fine for multidimensional models. It might seem strange though since the frequency tables are conditional on the sum-scores (which are notably less meaningful for multidimensional models) but, statistically speaking, there's nothing inherently wrong with using sum-scores for other purposes --- such as detecting item misfit. I don't know if there's a standard reference for the S-X2 statistic in particular, this is just another example of all models being wrong to certain degrees (in which case all p-values converge to 0) and becomes more obvious in larger sample sizes. The SEM literature on goodness-of-fit measures is full of such information, which is largely why so many different indicies exist. IRT (and virtual all other areas of statistical modeling) is no different. HTH.

Phil

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