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I am currently running a multiple regression model using imputed data and have a few questions.

Background:

Using SPSS 18. My data appears to be MAR. Listwise deletion of cases leaves me with only 92 cases, multiple imputation leaves 153 cases for analysis. All assumptions met - one variable log transformed. 9 IV's 5 - 5 categorical, 3 scale, 1 interval. DV-scale. Using the enter method of standard multiple regression.

  • My DV is the difference of scores between a pre- score and a post score measure, both of these variables are missing a number of cases - should I impute missing values for each of these and then work out the differnce between them to calculate my DV (how do I go about doing this), or can I just impute data for my DV? Which is the most appropriate approach?
  • Should I run imputations on transformed data or skewed untransformed data?
  • Should I enter all variables into the imputation process, even if they are not missing data, or should I just impute data for the variables missing more than 10% of cases?

I have run the regression on the listwise deleted cases and my IV's account for very little of the variance in my DV, subsequently I have run the regression on a complete file following multiple imputation - The results are very similar, in that my 9 IV's still predict only approx 12% of the variance in my DV, however, now one of my IV'S indicates that it is making a significant contribution (this happens to be a log transformed variable)...

  • Should I report original data if there is little difference between my conclusions - i.e my IV's poorly predict the dv, or report the complete data?
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  • $\begingroup$ What does "scale" mean for SPSS, does it refer to ordinal data? $\endgroup$ – gung Jul 26 '12 at 15:43
  • $\begingroup$ Scale in SPSS formats typically means "interval/ratio" measures, see the VARIABLE LEVEL command. But that then leaves the question what the distinction between the 3 scale and the 1 interval question is? That being said though this should be enough information to effectively address your question. $\endgroup$ – Andy W Jul 26 '12 at 16:58
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    $\begingroup$ The only advice I could give is that predicting the change scores tends to be much harder than predicting the levels (so it is not surprising in many situations that a low R^2 occurs). See some nice discussion of pre-post designs here. Although that still totally does not answer your question! $\endgroup$ – Andy W Jul 26 '12 at 17:02
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  1. Whether you should impute both the pre- and post- scores, or the difference score, depends on how you analyze the pre-post difference. You should be aware there are legitimate limitations to analyses of difference scores (see Edwards, 1994, for a nice review), and a regression approach in which you analyze the residual for post- scores after controlling for pre-scores might be better. In that case, you would want to impute pre- and post- scores, since those are the variables that will be in your analytic model. However, if you're intent on analyzing difference scores, impute the difference scores, since it's unlikely you will want to manually compute difference scores across all your imputed data sets. In other words, whatever variable(s) you are using in your actual analytic model, is/are the variable(s) that you should use in your imputation model.
  2. Again, I would impute with the transformed variable, since that is what is used in your analytic model.
  3. Adding variables to the imputation model will increase the computational demands of the imputation process, BUT, if you have the time, more information is always better. Variables with complete data could potentially be very useful auxiliary variables for explaining MAR missingness. If using all your variables results in too time/computation demanding of an imputation model (i.e., if you have a big data set), create dummy variables for each cases's missingness for each variable, and see which complete variables predict those missingness variables in logistic models--then include those particular complete case variables in your imputation model.
  4. I wouldn't report the original (i.e., list-wise deleted) analyses. If your missingness mechanism is MAR, then MI is not only going to give you increased power, but it will also give you more accurate estimates (Enders, 2010). Thus, the significant effect with MI might be non-significant with list-wise deletion because that analysis is underpowered, biased, or both.

References

Edwards, J. R. (1994). Regression analysis as an alternative to difference scores. Journal of Management, 20, 683-689.

Enders, C. K. (2010). Applied Missing Data Analysis. New York, NY: Guilford Press.

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In my experience SPSS's imputation function is easy to use, both in creating datasets and in analyzing and pooling the resulting imputation datasets. However, its ease of use is its downfall as well. If you look at a similar imputation function in the R statistical software (see for example the mice package), you will see far more options. See Stef van Buurens website for an excellent explanation of multiple imputation in general (with or without using the mice package).

It is very important to note that these additional options are not 'luxury' choices for advanced users only. Some are essential in order to attain proper congeniality, specific models for specific missing variables, specific predictors for specific missing variables,imputation diagnostics, and more, which are not available in the SPSS imputation function.

As to your questions:

  1. imputation of pre- and post scores and passively replacing the missing differences is appropriate when you want to conserve the relation between the pre- and post scores, and the difference (as answered by jsakaluk). In your case this might be so when you want to build a model with the difference in pre and post score as outcome/dependent variable and the baseline (pre-score) as (one of the) predictors/indepenent variables.
  2. Any model used to replace missing values should abide by its assumptions. Meaning that to replace a continuous variable you need to adhere to the assumptions of a linear regression model (in the simplest case). for linear regression, and most other regression model, the predictor variables need not be normally distributed, the model's residuals however, do have to be! Some transformation might therefore be necessary if the latter is the case.
  3. See jsakaluk's answer. Do note however that SPSS uses massive imputation, which basically means all entered variables are used to replace variables with missing cases. If you only have one variable with missing this is no problem. If you have multiple however, this means the variables with missingness are also used to complete the other variables with missingness. This might not be a problem, but in some cases this creates feedback loops which bias your final imputation values. It is imperative to check this by looking for trends throughout the iterations of your imputation instead of 'stabilizing' replaced values.
  4. I agree with jsakaluk's answer on this one. If you decide to 'distrust' your complete data because you suspect selective missings, and solve or partly remedy this by using multiple imputation techniques (which I think would indeed be the least biased), then your multiple imputation results should be the main results you show. Regrettably, experience has shown reviewers or other interested people sometimes do want to see complete case analyses as well (so keep them at hand).
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