Stata mi impute with scales

My data contains an Engagement measure (eng) that is calculated as the mean of 5 survey items (eng1 .. eng5). There is missingness at the item level. For non-imputed analyses, I can simply

Code:

egen eng = rowmean(eng1-eng5)

.

If I wanted to use multiple imputation on this dataset, I am unclear whether I should (1) impute with only the items first, then calculate means; or (2) calculate scale means, then impute. The drawback to the second method is that it might produce scale values that are no longer the means of the scale items. Therefore, the first method seems more right.

Unfortunately, when attempting to do this, Stata generates a lot of extra data columns like _1_eng1 that I assume correspond to the imputed value for eng1 in imputed "world" 1. Does this mean that I need to manually calculate scale values for every single dataset separately? Will the later

Code:

mi estimate

command know how to use these values when I attempt to do my final regression?

Separately, I am running into "incomplete" imputation rounds, which I don't know what to do with. Does that mean a particular iteration failed to converge, or that a certain cell imputed to a "missing" value?

Output follows:

Code:

            female: logistic regression
               age: predictive mean matching
           e1_last: predictive mean matching
           e2_last: predictive mean matching
           e3_last: predictive mean matching
           e7_last: predictive mean matching
           e8_last: predictive mean matching
        b_und_last: predictive mean matching
        b_val_last: predictive mean matching
       b_want_last: predictive mean matching
          ps1_last: predictive mean matching
          ps2_last: predictive mean matching
          ps3_last: predictive mean matching
          ps6_last: predictive mean matching

------------------------------------------------------------------
                   |               Observations per m            
                   |----------------------------------------------
          Variable |   Complete   Incomplete   Imputed |     Total
-------------------+-----------------------------------+----------
            female |        942           86        12 |      1028
               age |        914          114        25 |      1028
           e1_last |        679          349       189 |      1028
           e2_last |        683          345       187 |      1028
           e3_last |        682          346       187 |      1028
           e7_last |        682          346       189 |      1028
           e8_last |        679          349       191 |      1028
        b_und_last |        628          400       208 |      1028
        b_val_last |        626          402       211 |      1028
       b_want_last |        621          407       213 |      1028
          ps1_last |        687          341       185 |      1028
          ps2_last |        684          344       187 |      1028
          ps3_last |        682          346       187 |      1028
          ps6_last |        684          344       186 |      1028
------------------------------------------------------------------
(complete + incomplete = total; imputed is the minimum across m
 of the number of filled-in observations.)

Note: Right-hand-side variables (or weights) have missing values;
      model parameters estimated using listwise deletion.