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In R, there is a package called mice which multiply imputes a dataset.

For my situation, I imputed using the predictive mean matching (pmm) method using a time series that I acquired that details multiple different climate variables like average temperature, relative humidity, precipitation etc.

At some point I would like to combine the results of these multiply imputed datasets, but in the syntax of the mice packages in R I apparently need to fit a statistical model on each imputed dataset.

But why do I need this? I mean sure, I need to run a model on the completed dataset (artificial neural networks), but that comes after.

Examples on the internet use the lm() package, but that's not exactly what I need.

What should I do and why should I do it?

Example on the internet: https://datascienceplus.com/imputing-missing-data-with-r-mice-package/

Thanks to anyone who replies.

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  • $\begingroup$ Check out Amelia to do the multiple imputation and Zelig to run the models and put them together. $\endgroup$ – zbicyclist May 17 '17 at 11:32
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The imputed values on your datasets obtained through multiple imputation are predictions from statistical models themselves, and vary according to probabilistic distributions as any predictions from statistical models would.

The problem with using them as if they were observed data is that you will underestimate the variances and the covariances of the estimations in your model because the model doesn't account for the variance coming from your imputed variables being predictions.

Estimating your model several times across multiple imputed datasets and then combining the estimates of parameters and standard errors through a set of rules (e.g. the ones proposed by Rubin) allows you to reintroduce that variability in your models and avoid overestimating things like test statistics.

If you treat your imputed datasets as if they were observed data, you run the risk of underestimating standard errors and things that shouldn't be statistically significant will show up as being significant. This is why you don't do it.

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  • $\begingroup$ So in other words I have to do it in order to introduce the uncertainty of the imputed values? Then if that's the case, what model should I use? I don't think I can use ANNs as arguments for its parameters, but then again the formula argument is also a needed parameter which I can't just set a formula of response and predictors, because I don't know which ones to use. The only way I can is to actually clean it first then do a Pearson's test on it. $\endgroup$ – ace_01S May 18 '17 at 3:16
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    $\begingroup$ You estimate whatever model you want to estimate on each of the imputed datasets, then you use Rubin's rules (google or look at Alisson's Missing Data book p.30) to combine the estimates of coefficients and standard errors. The R function in mice does it all automatically, though, so you may want to use that if the model you intend to estimate is covered by it. $\endgroup$ – Kenji May 18 '17 at 9:35
  • $\begingroup$ Honestly with the methodology we're going for, which makes use of data in more than one time series to run the ANN, each time series having NAs (no exception), that's gonna be a hell of a lot of analysis. I really just need one imputed dataset and that's it. Having to run an ANN for each imputed dataset for one time series plus the same situation for every time series thereafter and then doing it for multiple different combinations, is a doozy. Can't I just average the values across the multiply imputed dataset? $\endgroup$ – ace_01S May 18 '17 at 10:50
  • $\begingroup$ Averaging data will inflate the correlations between variables in your dataset and will still give you a biased result. It doesn't mean that you can't do it, but it is not recommended. I'm not familiar with Neural Networks, though, so I have no idea of how they solve their missing data problems. What I know is that the way you want to do it would give biased estimates in most regression models. $\endgroup$ – Kenji May 18 '17 at 11:27
  • $\begingroup$ Any recommendation of other missing data techniques? For time series I mean, I've read some studies that do the average of the previous day and the next day. $\endgroup$ – ace_01S May 18 '17 at 12:00

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