Item-Level Multiple Imputation to Produce a Total Score for a Measure?

#1
Hi, all, a quick question regarding multiple imputation . . .

The multiple imputation examples I've seen appear to opearate at the scale/inferential level of analysis, i.e. using all measures' total scores to predict other total scores and using imputed scale-level predictions in inferential stats.

Is it possible to use multiple imputation at an item-level within a measure for a single case in order to produce a total score for that measure for that case? For example, if I have Case #222's BDI-II measure, and items 3, 6, & 11 are missing (assuming MAR), can I impute those missing items via multiple imputation and produce a total BDI-II score for Case #222?

Thank you very much,
 
#2
The one study I've seen which addresses the question (Gottschall, West, & Enders, 2012) found that item-level imputation is actually preferable to scale level in that it provides eventual estimates which are consistently more reliable. One thing I like that they don't mention in the article is the ability using SPSS's multiple imputation command to easily constrain the interval and rounding of your imputed values to fit those of the scale. That said, there are some considerations to keep in mind, particularly when determining how many other items you want to consider when imputing values. Too many relative to your sample size and you'll have some serious efficiency and accuracy problems.
 

Lazar

Phineas Packard
#3
It depends. Missing data models involve a trade-off between complexity of the missing data model, amount of missing data, and the amount and quality of information you have in general. There is thus no inprincipal reason why you could not impute at the item level and treat the items as ordered categorical (this is possible in SPSS) thus no rounding or censoring required. However, such a model is complex and under many conditions will not run. In such cases you may then have to treat the items as continious or move to scale scores (Im not a particular fan of rounding or censoring for measures that are later assumed to be continous).

The other option is to utalise a model based approach like full-information-maximum-liklihood estimation or a Bayes approach which will deal with missing data on the fly so to speak.
 
#4
Thanks a bunch - here's what I'm trying to figure out, specifically: I've run a multiple imputation procedure for the measure's items, and SPSS produces a file w/ 25 imputed datasets (I chose 25 imputations); my understanding (which could be wrong) is that each dataset is produced in light of the previously produced dataset, and that appropriate multiple imputation utilizes the pooled datasets in all analyses for maximum accuracy. I'm not seeking to analyze data yet, I'm seeking to produce a single total score for a single case's measure; after this score is produced I would, place it in the scale-level dataset and run the inferential analyses on that dataset. I've considered simply plugging in the item-values from the 25th imputation to produce the case's score for the measure, but I suspect this would be no more appropriate than a single imputation . . .?
 

Lazar

Phineas Packard
#6
Thanks a bunch - here's what I'm trying to figure out, specifically: I've run a multiple imputation procedure for the measure's items, and SPSS produces a file w/ 25 imputed datasets (I chose 25 imputations); my understanding (which could be wrong) is that each dataset is produced in light of the previously produced dataset, and that appropriate multiple imputation utilizes the pooled datasets in all analyses for maximum accuracy. I'm not seeking to analyze data yet, I'm seeking to produce a single total score for a single case's measure; after this score is produced I would, place it in the scale-level dataset and run the inferential analyses on that dataset. I've considered simply plugging in the item-values from the 25th imputation to produce the case's score for the measure, but I suspect this would be no more appropriate than a single imputation . . .?

Ok a few points:
1. I think 25 is excessive (particularly if you have only a little missing data that is MCAR. Five is more than enough.
2. Successive models are independent random draws from a distribution defined by the missing data model. WE do pool the results as follows. Point estiamtes are given by the average across the N datasets. Standard errors are given by the average of the N datasets plus the between imputation variance in the point estimates. The purpose of this is to incorporate into the standard errors the uncertainty that comes from imputing missing values. If your missing data model is effective SEs will be largely uneffected. If your missing data model is trying to cope with lots of missing data then SEs will be much larger.
3. If you imputed at the item level then you would create scales scores within each imputed dataset. Thus with 5 imputations you will need to produce 5 scales scores. Your reasoning is correct that taking a single scale score will be no better than a single imputation.

One minor points:
1. In SPSS their is an option to save the iterations (it is the last tab in MI). Do so! Then graph these iterations for the means and the SD of the items that have considerable missing data. The plot should look like a hairy catapillar with no strange values (extremely large or very small values) and no trend upward or downward.