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I have a followup question for multiple data imputation. So I been reading a bit about this method and I am still confused. So lets say I have m=5 datasets from multiple imputation. I extract the five data files and run them through an indexing model. So for my example, I need the missing data to be computed into one single variable output. The model calculates from three imputed variables to produce a single indexing measure. I use R for imputation and take the extracted data to Matlab (to be run through the model). Do I need to do the indexing for each single m=5 datasets?

So how would I pool the data together at the end? If I have only one variable from three imputed variables? Do I even need to do the pooling? Would justifying my process in data variable prediction and convergence as being sufficient without pooling?

If there is a reading I can look into that would be very helpful. I am so confused at this step. Any help will be appreciated.

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    $\begingroup$ Could you say a bit more about what you mean by your "indexing model"? Does the output of the "indexing model" include some measure of the variance of the result? $\endgroup$ – EdM Mar 25 '16 at 21:02
  • $\begingroup$ I am running the water indexing model and my data is purely numeric. They are just measures of water parameters. The index output does not measure variance. I will run a trend analysis at the end. Can't I just run the variance for all the datasets prior before I use them? Do I need to use all the datasets and can I just select one out of five based on the closeness of it to the original dataset? $\endgroup$ – Sasha Mar 25 '16 at 21:11
  • $\begingroup$ You have to use all of your datasets when you do multiple imputation. You combine analysis results across the five datasets. See the section entitled: "Combining Analysis Results": csos.jhu.edu/contact/staff/jwayman_pub/… $\endgroup$ – StatsStudent Mar 25 '16 at 21:37
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The simple answer here is that with multiple imputation you do your calculation on each of the imputed data sets and then pool the results over all the imputations. But there are a few additional considerations that you should consider for your particular application.

This seems to be the type of water quality index based on a Canadian approach to develop such indices, as explained in this report. A large set of chemical measurements is taken for water at different measuring stations over time, and subsets of these measurements are chosen to represent different aspects of water quality. For the chemicals involved in a particular index, the fraction of chemicals that are outside acceptable limits, the fraction of individual measurements outside the limits, and the magnitude of the deviations outside acceptable limits are combined into a scale with values from 1 to 100 for each station each year.

Notably, however, not all of the chemicals need to be measured at a particular station for a valid index, provided that a particular station has at least 4 of the chemicals measured at least 4 times a year (4 by 4 rule). Once that threshold is passed, the particular chemicals measured at that station are used without regard to chemicals that are not measured at that station.

So if you are trying to use such indices as they are defined, imputation should be limited in its scope. It would seem to make little sense to impute measurements for chemicals at a particular site that have never been measured at that site, or to impute data for a particular station based on measurements at stations that are geographically distant. You also need to deal carefully with measurements that were "non-detectable," as the index definition deliberately leaves such measurements out of the calculation if the detection limit is above the acceptable limit for that chemical.

As with any multiple imputation, it is important to consider the details of the imputation methods carefully, as the defaults used in packages like mice in R might not be appropriate for your particular application. If you perform imputations appropriately, the differences among the indices determined from the individual imputations will provide information about the uncertainty introduced by the imputations, even though each index value itself has no associated error.

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  • $\begingroup$ Thank you for the extended answer. It helps a bunch in this case. $\endgroup$ – Sasha Mar 26 '16 at 1:09

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