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?