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I have some items, measured with 5-point Likert scale (e.g., Strongly Agree, Agree, Neutral, Disagree, Strongly Disagree), to model using Graded Response Model. However, the analysis runs extremely slow. Further analysis showed that some categories are answered with sample size less than 5. I wonder if it is appropriate to collapse/combine some response categories, so that it becomes a 3-point Likert scale (e.g., Agree, Neutral, Disagree)? Does the field reject this practice in general?

Some references to this issue will be useful. Thanks!

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  • $\begingroup$ Can you say more about your situation, your data, your analyses & your goals here? This is rather sparse & hard to follow. Can you paste in some sample data? $\endgroup$ – gung - Reinstate Monica Apr 12 '16 at 4:04
  • $\begingroup$ Perhaps it is useful to to show the number of responses in certain items: item1: 103 191 108 40 7; item5: 314 100 27 8 1 $\endgroup$ – Joseph Apr 12 '16 at 4:14
  • $\begingroup$ I <personally> recommend fitting Graded Rating Scale Model. You can fit the data to both GRM and GRSM and compare fits(AIC, BIC, etc.) to compare relative evidence of the model. If it's okay, GRSM is free of those sparse category problems in general. $\endgroup$ – KH Kim Apr 12 '16 at 4:43
  • $\begingroup$ Thanks. What is the difference between GRM and GRSM? $\endgroup$ – Joseph Apr 12 '16 at 5:14
  • $\begingroup$ GRM has different thresholds for each items, GRSM shares the thresholds throughout the items. Since the response categories are the same throughout items, GRSM seems appropriate choice. $\endgroup$ – KH Kim Apr 12 '16 at 20:35
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If 5 means 5 per items, I would rather fit GRSM or RS-GRM. You can fit the model with R package mirt with itemtype="grsmIRT". If the categories are collapsed automatically you can use survey.weights to prevent it. http://basicstatistics.tistory.com/entry/Fitting-GRSM-aka-RSGRM

But GRSM(RS-GRM) has rather strong constraints on parameters on GRM. So I think you should fit GRM and GRSM, and see the model fit to determine which model is more appropriate.

If you must stay with GRM, I think collapsing is appropriate. But it depends on what kind of result you want to get. It is known even if the category difficulties are very unstable, latent estimates could be very accurate. You can do some sensitivity check if you are suspicious.

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