Amelia (version 1.1-33)

amelia: AMELIA: Mutliple Imputation of Incomplete Multivariate Data

Description

Runs the bootstrap EM algorithm on incomplete data and creates imputed datasets.

Usage

amelia(data,m=5,p2s=1,frontend=FALSE,idvars=NULL,
       ts=NULL,cs=NULL,polytime=NULL,intercs=FALSE,
       lags=NULL,leads=NULL,startvals=0,tolerance=0.0001,
       logs=NULL,sqrts=NULL,lgstc=NULL,noms=NULL,ords=NULL,
       incheck=TRUE,collect=FALSE,outname="outdata",
       write.out=TRUE,archive=TRUE,arglist=NULL,keep.data=TRUE, 
       empri=NULL,casepri=NULL,priors=NULL,autopri=0.05, emburn=c(0,0),
       bounds=NULL,max.resample=100)

Arguments

data

an incomplete dataset, organized into either a data frame or a matrix.

m

the number of imputed datasets to create.

p2s

an integer value taking either 0 for no screen output, 1 for normal screen printing of iteration numbers, and 2 for detailed screen output. See "Details" for specifics on output when p2s=2.

frontend

a logical value used internally for the GUI.

idvars

a vector of column numbers or column names that indicates identification variables. These will be dropped from the analysis but copied into the imputed datasets.

ts

column number or variable name indicating the variable identifying time in time series data.

cs

column number or variable name indicating the cross section variable.

polytime

integer between 0 and 3 indicating what power of polynomial should be included in the imputation model to account for the effects of time. A setting of 0 would indicate constant levels, 1 would indicate linear time effects

intercs

a logical variable indicating if the time effects of polytime should vary across the cross-section.

lags

a vector of numbers or names indicating columns in the data that should have their lags included in the imputation model.

leads

a vector of numbers or names indicating columns in the data that should have their leads (future values) included in the imputation model.

startvals

starting values, 0 for the parameter matrix from listwise deletion, 1 for an identity matrix.

tolerance

the convergence threshold for the EM algorithm.

logs

a vector of column numbers or column names that refer to variables that require log-linear transformation.

sqrts

a vector of numbers or names indicating columns in the data that should be transformed by a sqaure root function. Data in this column cannot be less than zero.

lgstc

a vector of numbers or names indicating columns in the data that should be transformed by a logistic function for proportional data. Data in this column must be between 0 and 1.

noms

a vector of numbers or names indicating columns in the data that are nominal variables.

ords

a vector of numbers or names indicating columns in the data that should be treated as ordinal variables.

incheck

a logical indicating whether or not the inputs to the function should be checked before running amelia. This should only be set to FALSE if you are extremely confident that your settings are non-problematic and you a

collect

a logical value indicating whether or not the garbage collection frequency should be increased during the imputation model. Only set this to TRUE if you are experiencing memory issues as it can significantly slow down the

outname

a string indicating the prefix of the file to which Amelia will write the imputed datasets. You can also specify a path in front of the prefix if you do not wish your items stored in the working directory. The files will be written as .csv f

write.out

a logical value indicating whether or not you wish to have Amelia write your imputed datasets as comma-seperated value files. If TRUE, Amelia will use the outname arugment as the file prefix.

archive

a logical variable indicating whether a replication archive should be saved. This archive includes all of the settings, the results of each imputation and some information about the convergence. The output will be saved as 'amarchive.R

arglist

an output list from the amelia function or from a saved session from AmeliaView. Values from this list take precendent over any individually set arugments. See the Amelia manual for more information.

keep.data

a logical value indicating whether or not to keep the imputed datasets after each imputation. Useful if the datasets are large and you wish to avoid keeping them in memory after they have been written to a file.

empri

number indicating level of the empirical (or ridge) prior. This prior shinks the covariances of the data, but keeps the means and variances the same for problems of high missingness, small N's or large correlations among the variables. Should

casepri

indicator matrix of size kxk (where k is the number of cases) for the degree of similarity between two cases. For example, the [2,3] entry would indicate how similar cases 2 and 3 were. The indicators can be 0, 1, 2, or

priors

a four or five column matrix containing the priors for either individual missing observations or variable-wide missing values. See "Details" for more information.

autopri

allows the EM chain to increase the empirical prior if the path strays into an nonpositive definite covariance matrix, up to a maximum empirical prior of the value of this argument times $n$, the number of observations. Must be between 0 and

emburn

a numeric vector of length 2, where emburn[1] is a the minimum EM chain length and emburn[2] is the maximum EM chain length. These are ignored if they are less than 1.

bounds

a three column matrix to hold logical bounds on the imputations. Each row of the matrix should be of the form c(column.number, lower.bound,upper.bound) See Details below.

max.resample

an integer that specifies how many times Amelia should redraw the imputed values when trying to meet the logical constraints of bounds. After this value, imputed values are set to the bounds.

Value

• A list containing the imputed datasets in objects 1 through m. Thus, you can refer to any of the datasets by referencing output[[i]], where i is the number of the dataset you wish to reference. These datasets will be returned in the same format which you passed them. For example, if you passed a data frame to amelia you will have m data frames in the output list. If you passed a matrix, you will have m matrices in the output. Other objects in the list:
• code
  return code for the function. 0 indicates a successful run of Amelia. Other codes refer to various problems in data or settings. Please refer to the error message and the Amelia manual for help with errors.
• message
  error message. Only appears if return code is not 0.
• amelia.args
  list of the arguments used in the imputation along with a few diagnostics on each imputation.
• thetas
  a matrix of the output parameter matrices used to generate the imputed datasets.

Details

Multiple imputation is a method for analyzing incomplete multivariate data. This function will take an incomplete dataset in either data frame or matrix form and return m imputed datatsets with no missing values. The algorithm first bootstraps a sample dataset with the same dimensions as the original data, estimates the sufficient statistics (with priors if specified) by EM, and then imputes the missing values of sample. It repeats this process m times to produce the m complete datasets where the observed values are the same and the unobserved values are drawn from their posterior distributions.

You can provide Amelia with informational priors about the missing observations in your data. To specify priors, pass a four or five column matrix to the priors argument with each row specifying a different priors as such:

one.prior <- c(row, column, mean,standard deviation)

or,

one.prior <- c(row, column, minimum, maximum, confidence).

So, in the first and second column of the priors matrix should be the row and column number of the prior being set. In the other columns should either be the mean and standard deviation of the prior, or a minimum, maximum and confidence level for the prior. You must specify your priors all as distributions or all as confidence ranges. Note that ranges are converted to distributions, so setting a confidence of 1 will generate an error.

Setting a priors for the missing values of an entire variable is done in the same manner as above, but inputing a 0 for the row instead of the row number. If priors are set for both the entire variable and an individual observation, the individual prior takes precedence. If each imputation is taking a long time to converge, you can increase the empirical prior, empri. This value has the effect of smoothing out the likelihood surface so that the EM algorithm can more easily find the maximum. It should be kept as low as possible and only used if needed. Amelia assumes the data is distributed multivariate normal. There are a number of variables that can break this assumption. Usually, though, a transformation can make any variable roughly continuous and unbounded. We have included a number of commonly needed transformations for data. Note that the data will not be transformed in the output datasets and the transformation is simply useful for climbing the likelihood. Please refer to the Amelia manual for more information on the function or the options.