Impute missing multivariate data using robust sequential algorithm
impSeqRob(x, alpha=0.9)a matrix of the same form as x, but with all missing values filled in sequentially.
the original incomplete data matrix.
.The default is alpha=0.9.
SEQimpute starts from a complete subset of the data set Xc and estimates
sequentially the missing values in an incomplete observation,
say x*, by minimizing the determinant of the covariance of the augmented
data matrix X* = [Xc; x']. Then the observation x* is added to the complete data matrix
and the algorithm continues with the next observation with missing values.
Since SEQimpute uses the sample mean and covariance matrix it will be vulnerable
to the influence of outliers and it is improved by plugging in robust estimators of
location and scatter. One possible solution is to use the outlyingness measure as proposed
by Stahel (1981) and Donoho (1982) and successfully used for outlier
identification in Hubert et al. (2005). We can compute the outlyingness measure for
the complete observations only but once an incomplete observation is imputed (sequentially)
we could compute the outlyingness measure for it too and use it to decide if this observation
is an outlier or not. If the outlyingness measure does not exceed a predefined threshold
the observation is included in the further steps of the algorithm.
S. Verboven, K. Vanden Branden and P. Goos (2007). Sequential imputation for missing values. Computational Biology and Chemistry, 31, 320--327. K. Vanden Branden and S. Verboven (2009). Robust Data Imputation. Computational Biology and Chemistry, 33, 7--13.
data(bush10)
impSeqRob(bush10) # impute squentially missing data
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