# Studies with many questionnaires

The practical issue that most often occurs with missing data in questionnaire data, is that when studies use many questionnaires, that the number of variables will exceed the number of respondents. Since multiple imputation is based on regression, the same assumptions as in regressions apply. Accordingly, when the number of variables exceeds the number of subjects in the data, regression models cannot be estimated, and therefore estimating the imputed values will be problematic.

There are two possible methods to deal with this problem: parcel summary score imputation or passive imputation. The first methods is more pragmatic and can be performed in any statistical software package that can perform multiple imputation. Passive imputation requires a more advanced adaptation of the imputation process and is not possible in SPSS, however it can be performed in R. For the full paper see Eekhout et al (2016)

## Parcel summary imputation

When the number of variables in the imputation model exceeds the number of respondents in the data, which can be the case when many questionnaire scales are included in one study, the imputations cannot be estimated. In order for multiple imputation to work, the number of variables in the imputation model needs to be reduced somehow. For the imputation model, it is important to include all information from the analyses. If the imputation model is not compatible to the analysis model, bias can occur in analysis estimates. Reducing the number of variables in the imputation model, needs to be done carefully, without losing important information. One way to do this is to use parcel summary scores as predictors for the imputation of items from other scales. A parcel summary score for a questionnaire or scale is the average over the available items. In paragraph 8.1.2 it is stated that using the average of the available items as an imputation methods is not recommended. However, in this case we use the average of the available items (i.e. parcel summary scores) as a surrogate for the item scores itself. We use this information as a predictor to impute items from other scales. That way, information from other questionnaires is used in the imputation, but the number of variables is reduced (from all items to one parcel summary score). The parcel summary score multiple imputation can be performed in five steps:

- Step1: calculate the parcel summary scores for each questionnaire. For each questionnaire in the data, a temporary score is calculating by taking the average over the available item scores. This results in as many additional columns in the data as there are questionnaires. The goals is not to replace the total score of the questionnaire by this parcel summary score, because this temporary score is only used in the imputation process.
- Step 2: impute the item scores per questionnaire. The main dataset should be separated as many sub-datasets as there are questionnaires. Each sub-dataset contains the item scores of a questionnaire, the parcel summary scores of the other questionnaires and all other variables that should be used in the imputation model. In each of these sub-datasets the multiple imputation procedure can be performed, including the item scores of that questionnaire, the parcel summary scores of the other questionnaires and the other relevant variables for imputation. Make sure that the setting for the multiple imputations are each time the same (i.e. the number of iterations and the number of imputations).
- Step 3: Merge all imputed datasets. The imputed datasets created in step 2 should be merged into one main multiple imputation dataset with all imputed item scores.
- Step 4: Calculate the total scores for the questionnaires with the imputed item scores. In the merged main multiple imputation data the total scores are calculated with the imputed item scores.
- Step 5: Analyze the data and pool the results. In the final step the multiple imputed data is analyzed and the results from the analyses are pooled into one final result.

The downside of this methods, is that the multiple imputation procedure need to be performed multiple times. This results in multiple files with multiple imputed datasets that need to be merged after all imputation procedures are finished. This requires quite some time and good administration during the procedure. Nevertheless, this method results in optimal power for the analysis results, and incorporates all available item information in the missing data handling (REF). Furthermore, this procedure can be performed in any software package.

## Passive multiple imputation

A more advanced method to deal with imputing questionnaire data when many scale items are involved is passive multiple imputation. In passive multiple imputation, the derived variables (i.e. the total score of the items) are updated from recent imputed value during the imputation procedure. As can be reviewed in chapter 4 paragraph 4, the MICE algorithm generates imputations based on regression imputation models for each variable with missing data in a sequential process. The sequential process is performed until each variable with missing values is imputed, and then the iteration is finished. The imputation process is repeated for several iterations, until one imputed dataset is set aside. In each iteration, all item scores with missing values are imputed. In passive imputation, we can update the total score from the imputed item scores after each iterations. And since, for each variable with missing data a separate regression model is specified, it is also possible to adapt this regression model per variable. For the item scores of a questionnaire, we can use the other item scores of the questionnaires and the updated total scores form the other questionnaires as predictors in the imputation model. The process of updating the total scores between the iterations is the passive part of the imputation model. After the imputation procedure is completed, the total score should be recalculated from the imputed item scores before analyses can be performed.

This methods is more complicated, because it requires an adaptation of the imputation procedure. In SPSS this method cannot be used, however, in the MICE package in R it can. Other software packages that include options for passive imputation are the MI procedure in STATA (ref) and IVEware in SAS. The advantage is that in passive imputation, the missing data for all scales is handled in one procedure.

On this post shows how to passive imputation in R with the mice package.