Appropriateness of calculating scale means based on available non-missing responses (i.e., person-mean imputation)

Question

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?

Answer 1

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.

Answer 2

Person-mean imputation with an minimum-item threshold is a simple strategy for retaining scale scores where participants miss the occasional response.

Some general principles

• If missing data is minimal (e.g., less than 5% of participants are missing 1 item on a 10 item scale), the method of dealing with missing data is unlikely to make a difference to substantive conclusions.
• From a first principle perspective, imputation methods should provide more robust estimates of missing item responses as they incorporate both item and person characteristics into estimating the missing response.
• Design studies to avoid sporadic item-missing data.

Conditions where person-mean imputation is more reasonable:

• Item means are all about the same
• The threshold number of missing items is low relative to the total number of items in the scale (e.g., a requirement for 19 out of 20 items is more appropriate than 10 out of 20 items)
• There is generally very little missing data; at the extreme level, there is no missing data, and person-mean imputation does not change the data at all
• the cause of missing data is due to random processes such as accidentally skipping items, not clearly indicating the response, and so on.
• A simple and standardised rule for calculating scale means is desired (e.g., a rule might be required for a test manual that can be applied in a standardised way across studies and samples)

Avoiding sporadic missing data for items in scales

At a broader level, person-mean imputation of item responses is a response to a problem that can often be avoided using various study design strategies:

• Computerised administration of questionnaires can prevent (where this is ethically permitted) participants skipping or missing items.
• If questionnaires are administered on paper and in person, the experimenter can review the questionnaire booklet to check for missing data before the participant leaves the room.

Answer 3

one more piece of advice: make sure the full 6-item composite scale is reliable & that none of the included items reduces scale reliability. If those conditions aren't satisfied, you shouldn't be averaging them even in cases where data are complete. If these conditions are satisfied, then using a subset of items for cases w/ missing data isn't going to bias your result (assuming you are averaging or adding z-score transformation of items, as you always should in forming aggregate likert scale); it is just going to make it noisier than it should be (b/c you are relying on fewer items & thus cancelling out less of the random measurement error associated with each individual item). (Best solution, though, is multiple imputation, again assuming composite scale is reliable.)