# Multiple imputation for missing count data in a time series from a panel study

I am trying to tackle a problem which deals with the imputation of missing data from a panel data study(Not sure if I am using 'panel data study' correctly - as I learned it today.) I have total death count data for years 2003 to 2009, all the months, male & female, for 8 different districts and for 4 age groups.

The dataframe looks something like this:

         District  Gender Year Month    AgeGroup TotalDeaths
Northern    Male 2006    11        01-4           0
Northern    Male 2006    11       05-14           1
Northern    Male 2006    11         15+          83
Northern    Male 2006    12           0           3
Northern    Male 2006    12        01-4           0
Northern    Male 2006    12       05-14           0
Northern    Male 2006    12         15+         106
Southern  Female 2003     1           0           6
Southern  Female 2003     1        01-4           0
Southern  Female 2003     1       05-14           3
Southern  Female 2003     1         15+         136
Southern  Female 2003     2           0           6
Southern  Female 2003     2        01-4           0
Southern  Female 2003     2       05-14           1
Southern  Female 2003     2         15+         111
Southern  Female 2003     3           0           2
Southern  Female 2003     3        01-4           0
Southern  Female 2003     3       05-14           1
Southern  Female 2003     3         15+         141
Southern  Female 2003     4           0           4


For the 10 months spread over 2007 and 2008 some of the total deaths from all districts were not recorded. I am trying to estimate these missing value through a multiple imputation method. Either using Generalized Linear Models or SARIMA models.

My biggest issue is the use of software and the coding. I asked a question on Stackoverflow, where I want to extract the data into smaller groups such as this:

         District  Gender Year Month    AgeGroup TotalDeaths
Northern    Male 2003     1        01-4           0
Northern    Male 2003     2        01-4           1
Northern    Male 2003     3        01-4           0
Northern    Male 2003     4        01-4           3
Northern    Male 2003     5        01-4           4
Northern    Male 2003     6        01-4           6
Northern    Male 2003     7        01-4           5
Northern    Male 2003     8        01-4           0
Northern    Male 2003     9        01-4           1
Northern    Male 2003    10        01-4           2
Northern    Male 2003    11        01-4           0
Northern    Male 2003    12        01-4           1
Northern    Male 2004     1        01-4           1
Northern    Male 2004     2        01-4           0


Going to

         Northern    Male 2006    11        01-4           0
Northern    Male 2006    12        01-4           0


But someone suggested I should rather bring my question here - perhaps ask for a direction? Currently I am unable to enter this data as a proper time-series/panel study into R. My eventual aim is to use this data and the amelia2 package with its functions to impute for missing TotalDeaths for certain months in 2007 and 2008, where the data is missing.

Any help, how to do this and perhaps suggestions on how to tackle this problem would be gratefully appreciated.

If this helps, I am trying to follow a similar approach to what Clint Roberts did in his PhD Thesis.

EDIT:

After creating the 'time' and 'group' variable as suggested by @Matt:

> head(dat)
District Gender Year Month AgeGroup Unnatural Natural Total time                    group
1 Khayelitsha Female 2001     1        0         0       6     6    1     Khayelitsha.Female.0
2 Khayelitsha Female 2001     1     01-4         1       3     4    1  Khayelitsha.Female.01-4
3 Khayelitsha Female 2001     1    05-14         0       0     0    1 Khayelitsha.Female.05-14
4 Khayelitsha Female 2001     1     15up         8      73    81    1  Khayelitsha.Female.15up
5 Khayelitsha Female 2001     2        0         2       9    11    2     Khayelitsha.Female.0
6 Khayelitsha Female 2001     2     01-4         0       2     2    2  Khayelitsha.Female.01-4


As you notice, there's actually further detail 'Natural' and 'Unnatural'.

You can use the Amelia package to impute the data (full disclosure: I am one of the authors of Amelia). The package vignette has an extended example of how to use it to impute missing data.

It seems as though you have units which are district-gender-ageGroup observed at the monthly level. First you create a factor variable for each type of unit (that is, one level for each district-gender-ageGroup). Let's call this group. Then, you would need a variable for time, which is probably the number of months since January 2003. Thus, this variable would be 13 in January of 2004. Call this variable time. Amelia will allow you to impute based on the time trends with the following commands:

library(Amelia)
a.out <- amelia(my.data, ts = "time", cs = "group", splinetime = 2, intercs = TRUE)


The ts and cs arguments simply denote the time and unit variables. The splinetime argument sets how flexible should time be used to impute the missing data. Here, a 2 means that the imputation will use a quadratic function of time, but higher values will be more flexible. The intercs argument here tells Amelia to use a separate time trend for each district-gender-ageGroup. This adds many parameters to the model, so if you run into trouble, you can set this to FALSE to try to debug.

In any event, this will get you imputations using the time information in your data. Since the missing data is bounded at zero, you can use the bounds argument to force imputations into those logical bounds.

EDIT: How to create group/time variables

The time variable might be the easiest to create, because you just need to count from 2002 (assuming that is the lowest year in your data):

my.data$time <- my.data$Month + 12 * (my.data$Year - 2002)  The group variable is slightly harder but a quick way to do it is using the paste command: my.data$group <- with(my.data,
as.factor(paste(District, Gender, AgeGroup, sep = ".")))


With these variables created, you want to remove the original variables from the imputation. To do that you can use the idvars argument:

a.out <- amelia(my.data, ts = "time", cs = "group", splinetime = 2, intercs = TRUE,
idvars = c("District", "Gender", "Month", "Year", "AgeGroup"))

• Thank you so much for your response! I've been playing with Amelia for a bit but gave up (prior to this). I've previously seen the vignette (but lost it somehow!) Just had a quick look at it and will throughly go through it. One problem I now have is that I'm uncertain on how to create the group and time variables. (I tried creating them for time series analysis/forecasting, but got a loop around it.) I'm sure it's in the vigette - so I'll get back to you if I'm struggling. Thanks again :) – OSlOlSO Jul 21 '11 at 9:24
• Glad it's useful. I added an example of how to create those variables. Hope that helps. – Matt Blackwell Jul 21 '11 at 18:25
• Thanks for the examples @Matt. For some strange reason it gave me an error when I used "ts=time" and "cs=group". I just replace "time" and "group" by the respective column number and then it worked. a.out=amelia(dat,ts=time,cs=group,splinetime=2,intercs=TRUE,idvars=c("District","Gender","Month","Year","AgeGroup"),bounds=bds) Amelia Error Code: 6 The 'ts' variable is out of the range of possible column numbers or is not an integer. – OSlOlSO Jul 21 '11 at 21:40
• For the bounds I followed the vignette and created bounds using: bds <- matrix(c(6, 7, 8,0, 0,0, 500, 500,500), nrow = 3, ncol = 3) I basically just chose 500 as a random upper limit. I did try just to not give a third column, but Amelia warned that it requires the third one. Is there perhaps a way to just specific a lower limit? – OSlOlSO Jul 21 '11 at 21:43
• I added an example of the data in the question - perhaps if this caused the Error? But I doubt it. – OSlOlSO Jul 21 '11 at 21:52