BaBooN (version 0.2-0)

BBPMM.row: (Multiple) Imputation of variable vectors

Description

‘BBPMM.row’ performs single and multiple imputation (MI) of metric scale variable vectors. For MI, parameter draws from a posterior distribution are replaced by a Bayesian Bootstrap step. Imputations are generated using Predictive Mean Matching (PMM) as described in Little (1988).

Usage

BBPMM.row(misDataPat, blockImp=length(misDataPat$blocks), M=10, outfile=NULL, manWeights=NULL, stepmod="stepAIC", verbose=TRUE,  tol=0.25, setSeed=NULL, ...)

Arguments

misDataPat

An object created by rowimpPrep that contains information on all identified missing-data patterns.

blockImp

A scalar or vector containing the number(s) of the block(s) considered for imputation. Per default only the last block is imputed.

M

Number of multiple imputations. If M=1, no Bayesian Bootstrap step is carried out.

outfile

A character string that specifies the path and file name for the imputed data sets. If outfile=NULL (default), no data set is stored.

manWeights

Optional argument containing manual (non-negative) weights for the PMM step. manWeights can either be a list containing a vector for each missingness pattern, or just a vector, if only one missingness pattern/block exists. In either case, the number of elements in the vector(s) must match the number of variables in the corresponding block. Note that the higher the weight the higher the importance of a good match for the corresponding variable's predictive means.

stepmod

Performs variable selection for each imputation model based on the either on Schwarz (Bayes) Information criterion (backward). Default="stepAIC".

verbose

The algorithm prints information on weighting matrices and imputation numbers. Default=TRUE.

tol

Imported argument from function qr that specifies the tolerance level for linear dependencies among the complete variables and defaults to 0.25.

setSeed

Optional argument to fix the pseudo-random number generator in order to allow for reproducible results.

...

Further arguments passed to or from other functions.

Value

call

The call of BBPMM.row

mis.num

Vector containing the numbers of missing values per column.

modelselection

Chosen model selection method for the function call.

seed

Chosen seed value for the function call.

impdata

A list containing M completed data sets.

weightMatrix

A list containing weight matrices for all imputations and blocks.

model

A list containing the lm-objects for all imputations and blocks.

pairlist

A list containing the donor/recipient pairlist data frames for all imputations and blocks.

indMatrix

A matrix with the same dimensions as the incomplete data containing flags for missing values.

FirstSeed

First .Random.Seed before imputation starts.

LastSeed

Last .Random.Seed after function is done.

ignoredvariables

TRUE / FALSE indicator whether variables were ignored during imputation.

Details

The simultaneous imputation of several variables is useful for missing-by-design patterns, such as data fusion or split questionnaire designs. The predictive means of the imputation variables are weighted by the inverse of the covariance matrix of the residuals from the regression of these variables on the complete variables. The intuitive idea behind is that distances between predictive means should be punished more severely, if the particular variable can be explained well by the (completely observed) imputation model variables. Through partialization and subsequent usage of the residuals the weight matrix is transformed into a diagonal matrix. The calculated weights can be adjusted by manual weights. Since the weight matrix is a Mahalanobis type of distance matrix, the weights are in the denominator and therefore the lower the weight, the higher the influence. As this is somewhat counterintuitive, the reciprocal of the manual weights is taken. Therefore, the higher the manual weight the higher in the influence of the corresponding variable's predictor on the overall distance. To identify the missing-by-design patterns it is necessary to transform the raw data set via rowimpPrep. The donor/recipient ID pairlist for each imputation and identified pattern (‘block’) is stored. In general, weightMatrix, model and pairlist are list objects named ‘M1’ to ‘M’, and each in return is a list object named ‘block1’ to ‘block’. model contains another list object with lm-objects for all variables in a particular block. Unlike BBPMM this algorithm is not based on sequential regression. Therefore, imputed variables are conditionally independent given the completely observed variables (of which at least one must exist).

References

Eddelbuettel, D. and Francois, R. (2011) Rcpp: Seamless R and C++ Integration. Journal of Statistical Software, Vol. 40, No. 8, pp. 1--18. URL http://www.jstatsoft.org/v40/i08/. Eddelbuettel, D. and Sanderson, C. (2014) RcppArmadillo: Accelerating R with high-performance C++ linear algebra. Computational Statistics and Data Analysis, Vol. 71, March 2014, pp. 1054--1063.

Koller-Meinfelder, F. (2009) Analysis of Incomplete Survey Data -- Multiple Imputation Via Bayesian Bootstrap Predictive Mean Matching, doctoral thesis.

Little, R.J.A. (1988) Missing-Data Adjustments in Large Surveys, Journal of Business and Economic Statistics, Vol. 6, No. 3, pp. 287-296. Raghunathan T.E. and Lepkowski, J.M. and Van Hoewyk, J. and Solenberger, P (2001) A multivariate technique for multiply imputing missing values using a sequence of regression models. Survey Methodology, Vol. 27, pp. 85--95. Rubin DB (1981) The Bayesian Bootstrap. The Annals of Statistics, Vol. 9, pp. 130--134. Rubin, D.B. (1987) Multiple Imputation for Non-Response in Surveys. New York: John Wiley & Sons, Inc. Van Buuren, S. and Brand, J.P.L. and Groothuis-Oudshoorn, C.G.M. and Rubin, D.B. (2006) Fully conditional specification in multivariate imputation. Journal of Statistical Computation and Simulation, Vol. 76, No. 12, pp. 1049--1064. Van Buuren, S. and Groothuis-Oudshoorn, K. (2011) mice: Multivariate Imputation by Chained Equations in R. Journal of Statistical Software, Vol. 45, No. 3, pp. 1--67. URL http://www.jstatsoft.org/v45/i03/. Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth Edition. New York: Springer.

See Also

rowimpPrep, BBPMM

Examples

### sample data set with non-normal variables and a single
### missingness pattern
set.seed(1000)
n <- 50
x1 <- round(runif(n,0.5,3.5))
x2 <- as.factor(c(rep(1,10),rep(2,25),rep(3,15)))
x3 <- round(rnorm(n,0,3))
y1 <- round(x1-0.25*(x2==2)+0.5*x3+rnorm(n,0,1))
y1 <- ifelse(y1<1,1,y1)
y1 <- ifelse(y1>4,5,y1)
y2 <- y1+rnorm(n,0,0.5)
y3 <- round(x3+rnorm(n,0,2))
data <- as.data.frame(cbind(x1,x2,x3,y1,y2,y3))
misrow1 <- sample(n,20)
data[misrow1, c(4:6)] <- NA

### preparation step
impblock <- rowimpPrep(data)

### imputation
imputed.data <- BBPMM.row(impblock, M=5)