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I designed a survey (mostly Likert scales) and began to collect responses. After collecting several responses I decided to include an additional scale comprised of 9 items. The newly added scale will be an important predictor. My dependent variables are themselves Likert scales. I will do ordinal probit regression.

Collection before adding the new item was ~200, but total sample size is expected to be ~500.

Should my data be considered to be MCAR, MAR, or MNAR? What is the best way to handle such missing data?

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If the participant characteristics don't change over time, then assuming MCAR is probably reasonable for this situation. Under that assumption you could exclude any participants without the new scale from the regression analysis and the results would still be valid, although with reduced sample size. Alternatively, you could try multiple imputation to replace the missing measurements for the first 200 participants. That can be a bit dangerous with so much missing data, but if the data is MCAR I think it should be ok. If there are strong relationships between the other scale questions and the missing scale question then I would try multiple imputation, but it's hard to say without knowing the details.

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  • $\begingroup$ Thank you! I believe the assumption of no meaningful change in participant characteristics is reasonable. But it may be that earlier participants are more diligent than newer ones (my scales are all beliefs/behavior related). In the latter case, should I make some adjustment for the multiple imputation procedure? Could you point me to a reference for multiple imputation in R that acknowledges the issue of having so much missing data? $\endgroup$
    – harg
    Sep 25 '21 at 18:19
  • $\begingroup$ @harg If you think patients may be changing over time you could try including a time covariate/interaction in the imputation models. It may be hard to assess how important that is. You might need to try it both ways and see if results are different. In R the most common MI package is mice and the author's book is a good reference for MI, stefvanbuuren.name/fimd. There's basically no way to avoid the issue of that much missing data. The more missing, the more the results depend on the assumptions and method of the replacements. You could try multiple methods and see if results differ $\endgroup$ Sep 26 '21 at 23:06

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