Best way to handle missing data?

Thanks for this suggestion, Malcolm.  Here is an example in which I use
Amelia/Zelig with the "africa" data set that is available in Amelia.
I extracted the average standard deviation of the random effects from the
result produced by Zelig.  (In this example, I am using the version of the
summary.MI function found here:
http://stackoverflow.com/questions/16571580/multi-level-regression-model-on-multiply-imputed-data-set-in-r-amelia-zelig-l)
 Perhaps this approach will work for my purposes.

# Get packages
require(Amelia)
require(Zelig)
require(ZeligMultilevel)

# Look at the data
data(africa)
head(africa)
summary(africa)
help(africa)

# Impute the missing data
africa.am <-
  amelia(x = africa,
         m = 30,
         cs = "country",
         ts = "year",
         logs = "gdp_pc")
summary(africa.am)
plot(africa.am)
missmap(africa.am)
names(africa.am)

# Create a model:
africa.z <-
  zelig(formula = gdp_pc ~ infl + tag(infl | country),
        data = africa.am$imputations,
        model = "ls.mixed")

# The combined fixed effects:
summary(africa.z)

# The average standard deviation of the random intercepts and slopes:
ran.ints <-
  sapply(africa.z,
         function(x)
           attributes(VarCorr(x$result)$country)$stddev["(Intercept)"])
mean(ran.ints)

ran.slopes <-
  sapply(africa.z,
         function(x)
           attributes(VarCorr(x$result)$country)$stddev["infl"])
mean(ran.slopes)



On Fri, Feb 27, 2015 at 4:47 AM, Malcolm Fairbrother <
M.Fairbrother at bristol.ac.uk> wrote:

Hi Bonnie,

I have not seen a formal treatment of this issue, but from the Amelia
documentation, my understanding is that if you want an estimate of the
random effects variance, you can just take the average of the estimates
from the model fitted to each imputed dataset. This is true for any
parameter, from the sounds of what Honaker, King, and Blackwell have
written.

 "you can combine directly and use as the multiple imputation estimate of
this parameter, q ?, the average of them separate estimates"

Even if Zelig doesn't report the RE variance estimates automatically,
they must be "in there" somewhere... I'm sure you can extract them. Or
maybe skip Zelig, and just use Amelia, and extract the estimated RE
variances from each fitted model (presumably using lme4)?

Cheers,
Malcolm


Date: Thu, 26 Feb 2015 21:20:33 -0800

From: Bonnie Dixon <bmdixon at ucdavis.edu>
To: Mitchell Maltenfort <mmalten at gmail.com>
Cc: "r-sig-mixed-models at r-project.org"
        <r-sig-mixed-models at r-project.org>
Subject: Re: [R-sig-ME] Best way to handle missing data?


I actually did try mice also (method "2l.norm"), but it seemed that
Amelia
was preferable for imputation.  Mice seems to only be able to impute one
variable, whereas Amelia can impute as many variables as have missing
data
producing 100% complete data sets as output.

However, most of the missing data in the data set I am working with is in
just one variable, so I could consider using mice, and just imputing the
variable that has the most missing data, while omitting observations that
have missing data in any of the other variables.  But the pooled results
from mice only seem to include the fixed effects of the model, so this
still leaves me wondering how to report the random effects, which are
very
important to my research question.

When using Amelia to impute, the packages Zelig and ZeligMultilevel can
be
used to combine the results from each of the models.  But again, only the
fixed effects seem to be included in the output, so I am not sure how to
report on the random effects.

Bonnie

On Thu, Feb 26, 2015 at 8:33 PM, Mitchell Maltenfort <mmalten at gmail.com>
wrote:

Mice might be the package you need


On Thursday, February 26, 2015, Bonnie Dixon <bmdixon at ucdavis.edu>

wrote:

Dear list;

I am using nlme to create a repeated measures (i.e. 2 level) model.

There

is missing data in several of the predictor variables.  What is the

best

way to handle this situation?  The variable with (by far) the most

missing

data is the best predictor in the model, so I would not want to

remove it.

I am also trying to avoid omitting the observations with missing data,
because that would require omitting almost 40% of the observations and
would result in a substantial loss of power.

A member of my dissertation committee who uses SAS, recommended that

I use

full information maximum likelihood estimation (FIML) (described here:

http://www.statisticalhorizons.com/wp-content/uploads/MissingDataByML.pdf

),
which is the easiest way to handle missing data in SAS.  Is there an
equivalent procedure in R?

Alternatively, I have tried several approaches to multiple imputation.
For
example, I used the package, Amelia, which appears to handle the

clustered

structure of the data appropriately, to generate five imputed

versions of

the data set, and then used lapply to run my model on each.  But I am

not

sure how to combine the resulting five models into one final result.

I

will need a final result that enables me to report, not just the fixed
effects of the model, but also the random effects variance components

and,

ideally, the distributions across the population of the random

intercept

and slopes, and correlations between them.

Many thanks for any suggestions on how to proceed.

Bonnie