This question came up in a consulting context, and I was interested in your thoughts.

### Context

One strategy for dealing with occasional missing data when calculating scale means looks like this in the language of SPSS:

`COMPUTE depmean = mean.4(dep1, dep2, dep3, dep4, dep5, dep6). EXECUTE. `

I.e., calculate the mean of a psychological scale such as depression by taking the mean of six items.

If a participant has four or more non-missing items, return the mean of the non-missing items.

If the participant has three or fewer non-missing items, return missing.

Of course the number of items in the scale and the threshold number items for calculating the mean can vary.

### Question

- In general, under what conditions, would you see this method of dealing with missing data to be appropriate?
- If you perceive it to be inappropriate, what alternative procedure would you recommend?

#### Best Answer

Some years ago, I thought it might be a good idea to apply person-mean imputation (person-mean substitution or case-mean imputation) in case of item non-response. Nowadays, however, it seems obvious to me that this approach assumes that all scale items share similar characteristics (similar variance, standard deviation, item difficulty, etc.). In other words, I would be concerned if some respondents do not answer difficult/sensitive/… items.

Bono et al (2007: 7) are less concerned about this approach:

"Person-mean imputation requires substitution of the mean of all of an individual’s completed items for those items that were not completed on a given scale. This differs from item-mean where the mean response of the whole sample that responded to the item is substituted. Person-mean imputation could result in different substitutions for each person with missing items. On the plus side, because it does not substitute a constant value, it does not artificially reduce the measure’s variability and is less likely to attenuate the correlation. A disadvantage is that it tends to inflate the reliability estimates as the number of missing items increases. However, when the numbers of either respondents with missing items or items missing within scales are 20% or less, both item-mean imputation and person-mean imputation provide good estimates of the reliability of measures."

You also might want to check

Craig K. Enders (2010): Applied Missing Data Analysis. (Google books link)

Downey RG, King C. (1998): Missing data in Likert ratings: A comparison of replacement methods.

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