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I am preparing my data for CFA and multiple regression. I want to see how different types of parental involvement influence children's motivation and academic results. I have a sample size of 5000 with about 20% missing data.

I am having problems with handling the missing data. I probably made the mistake of deleting all cases marked by participants as "refused to answer" which makes this data look the same as system missing values. I did not delete them permanently I have the orginal data set saved with all system missing values marked as "." non-response as "9" and refusal to response as "8". What I did was change all the "8" and "9" to ".". I can easily un-do this. I'm just wondering if that is necessary and if this might be the reason for for the significant result in Little's test When performing Missing data analysis, Little's MAR test came out significant meaning that the missing data is MNAR which makes multiple imputation impossible.

My question is: Would list-wise deletion of only the subjects who refused to answer be a solution to my problem? I would still be left with missing data although it would probably be system missing data making it MAR. Does this make multiple imputation ok? If this is not possible how do I go about handling data that is MNAR?

Kayetu
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    I think this question may benefit from being rewritten. Try giving more detail about the data, methodology and question. – Jon Jan 10 '17 at 17:55
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    While the context is not really clear, one thing is easy to answer: listwise deletion is almost always invalid (it is only valid under an assumption of MCAR, which I would by default assume to not be fullfilled except for in exceptional circumstances and which is definitely not fullfilled when missing data are not MAR). – Björn Jan 10 '17 at 18:00
  • I agree that the OP should edit the post. I am not aware of a formal test by Little that the OP refers to. Little and Rubin have defined three types of missing data formally. They are MCAR (missing completely at random), MAR (missing at random) and MNAR ( missing not at random). These definitions and how to apply imputation when they are assumed is covered in their book on missing data. In addition Don Rubin has a text devoted to multiple imputation. – Michael R. Chernick Jan 10 '17 at 18:20
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    Little's test is for MCAR, not MAR; see [this page](http://stats.stackexchange.com/q/105233/28500) for example. Replace observed data for a variable with 0s, missing with 1s, and do chi-square tests of associations of missingness with other variables. So failing Little's test does not by itself rule out MAR. It does, however, rule out listwise deletion, as noted by @Björn. – EdM Jan 10 '17 at 18:30
  • Kaya can you clarify what you mean by the sentence starting 'I probably made the mistake ...'? Have you deleted them permanently? – mdewey Jan 10 '17 at 18:41
  • Little's test for MCAR was introduced in this paper: Little, R. J. A. (1988) A test of missing completely at random for multivariate data with missing values. Journal of the American Statistical Association. – Michael R. Chernick Jan 10 '17 at 18:50
  • mdewey I did not delete them permanently I have the orginal data set saved with all system missing values marked as "." non-response as "9" and refusal to response as "8". What I did was change all the "8" and "9" to ".". I can easily un-do this. I'm just wondering if that is necessary and if this might be the reason for for the significant result in Little's test. – Kayetu Jan 10 '17 at 19:05

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