Imputation by predictive mean matching with distance aided donor selection

Imputes univariate missing data using predictive mean matching.

Usage

mice.impute.midastouch(
  y,
  ry,
  x,
  wy = NULL,
  ridge = 1e-05,
  midas.kappa = NULL,
  outout = TRUE,
  neff = NULL,
  debug = NULL,
  ...
)

Arguments

y

Vector to be imputed

ry

Logical vector of length length(y) indicating the the subset y[ry] of elements in y to which the imputation model is fitted. The ry generally distinguishes the observed (TRUE) and missing values (FALSE) in y.

x

Numeric design matrix with length(y) rows with predictors for y. Matrix x may have no missing values.

wy

Logical vector of length length(y). A TRUE value indicates locations in y for which imputations are created.

ridge

The ridge penalty used in .norm.draw() to prevent problems with multicollinearity. The default is ridge = 1e-05, which means that 0.01 percent of the diagonal is added to the cross-product. Larger ridges may result in more biased estimates. For highly noisy data (e.g. many junk variables), set ridge = 1e-06 or even lower to reduce bias. For highly collinear data, set ridge = 1e-04 or higher.

midas.kappa

Scalar. If NULL (default) then the optimal kappa gets selected automatically. Alternatively, the user may specify a scalar. Siddique and Belin 2008 find midas.kappa = 3 to be sensible.

outout

Logical. If TRUE (default) one model is estimated for each donor (leave-one-out principle). For speedup choose outout = FALSE, which estimates one model for all observations leading to in-sample predictions for the donors and out-of-sample predictions for the recipients. Mind the inappropriateness, though.

neff

FOR EXPERTS. Null or character string. The name of an existing environment in which the effective sample size of the donors for each loop (CE iterations times multiple imputations) is supposed to be written. The effective sample size is necessary to compute the correction for the total variance as originally suggested by Parzen, Lipsitz and Fitzmaurice 2005. The objectname is midastouch.neff.

debug

FOR EXPERTS. Null or character string. The name of an existing environment in which the input is supposed to be written. The objectname is midastouch.inputlist.

...

Other named arguments.

Value

Vector with imputed data, same type as y, and of length sum(wy)

Details

Imputation of y by predictive mean matching, based on Rubin (1987, p. 168, formulas a and b) and Siddique and Belin 2008. The procedure is as follows:

1. Draw a bootstrap sample from the donor pool.

2. Estimate a beta matrix on the bootstrap sample by the leave one out principle.

3. Compute type II predicted values for yobs (nobs x 1) and ymis (nmis x nobs).

4. Calculate the distance between all yobs and the corresponding ymis.

5. Convert the distances in drawing probabilities.

6. For each recipient draw a donor from the entire pool while considering the probabilities from the model.

7. Take its observed value in y as the imputation.

References

Gaffert, P., Meinfelder, F., Bosch V. (2018) Towards an MI-proper Predictive Mean Matching, JSM 2018. Discussion Paper.

Little, R.J.A. (1988), Missing data adjustments in large surveys (with discussion), Journal of Business Economics and Statistics, 6, 287–301.

Parzen, M., Lipsitz, S. R., Fitzmaurice, G. M. (2005), A note on reducing the bias of the approximate Bayesian bootstrap imputation variance estimator. Biometrika 92, 4, 971–974.

Rubin, D.B. (1987), Multiple imputation for nonresponse in surveys. New York: Wiley.

Siddique, J., Belin, T.R. (2008), Multiple imputation using an iterative hot-deck with distance-based donor selection. Statistics in medicine, 27, 1, 83–102

Van Buuren, S., Brand, J.P.L., Groothuis-Oudshoorn C.G.M., Rubin, D.B. (2006), Fully conditional specification in multivariate imputation. Journal of Statistical Computation and Simulation, 76, 12, 1049–1064.

Van Buuren, S., Groothuis-Oudshoorn, K. (2011), mice: Multivariate Imputation by Chained Equations in R. Journal of Statistical Software, 45, 3, 1–67. doi:10.18637/jss.v045.i03

See also

Other univariate imputation functions: mice.impute.cart(), mice.impute.lasso.logreg(), mice.impute.lasso.norm(), mice.impute.lasso.select.logreg(), mice.impute.lasso.select.norm(), mice.impute.lda(), mice.impute.logreg(), mice.impute.logreg.boot(), mice.impute.mean(), mice.impute.mnar.logreg(), mice.impute.mpmm(), mice.impute.norm(), mice.impute.norm.boot(), mice.impute.norm.nob(), mice.impute.norm.predict(), mice.impute.pmm(), mice.impute.polr(), mice.impute.polyreg(), mice.impute.quadratic(), mice.impute.rf(), mice.impute.ri()

Author

Philipp Gaffert, Florian Meinfelder, Volker Bosch 2015

Examples

# do default multiple imputation on a numeric matrix
imp <- mice(nhanes, method = "midastouch")
#> 
#>  iter imp variable
#>   1   1  bmi  hyp  chl
#>   1   2  bmi  hyp  chl
#>   1   3  bmi  hyp  chl
#>   1   4  bmi  hyp  chl
#>   1   5  bmi  hyp  chl
#>   2   1  bmi  hyp  chl
#>   2   2  bmi  hyp  chl
#>   2   3  bmi  hyp  chl
#>   2   4  bmi  hyp  chl
#>   2   5  bmi  hyp  chl
#>   3   1  bmi  hyp  chl
#>   3   2  bmi  hyp  chl
#>   3   3  bmi  hyp  chl
#>   3   4  bmi  hyp  chl
#>   3   5  bmi  hyp  chl
#>   4   1  bmi  hyp  chl
#>   4   2  bmi  hyp  chl
#>   4   3  bmi  hyp  chl
#>   4   4  bmi  hyp  chl
#>   4   5  bmi  hyp  chl
#>   5   1  bmi  hyp  chl
#>   5   2  bmi  hyp  chl
#>   5   3  bmi  hyp  chl
#>   5   4  bmi  hyp  chl
#>   5   5  bmi  hyp  chl
imp
#> Class: mids
#> Number of multiple imputations:  5 
#> Imputation methods:
#>          age          bmi          hyp          chl 
#>           "" "midastouch" "midastouch" "midastouch" 
#> PredictorMatrix:
#>     age bmi hyp chl
#> age   0   1   1   1
#> bmi   1   0   1   1
#> hyp   1   1   0   1
#> chl   1   1   1   0

# list the actual imputations for BMI
imp$imp$bmi
#>       1    2    3    4    5
#> 1  30.1 35.3 22.5 22.5 26.3
#> 3  30.1 30.1 30.1 29.6 22.0
#> 4  21.7 27.2 21.7 20.4 25.5
#> 6  21.7 27.4 25.5 25.5 25.5
#> 10 27.2 22.7 22.7 24.9 27.4
#> 11 30.1 29.6 30.1 22.5 22.0
#> 12 35.3 26.3 25.5 24.9 27.4
#> 16 30.1 29.6 30.1 22.5 22.0
#> 21 30.1 22.5 30.1 22.5 22.0

# first completed data matrix
complete(imp)
#>    age  bmi hyp chl
#> 1    1 30.1   1 187
#> 2    2 22.7   1 187
#> 3    1 30.1   1 187
#> 4    3 21.7   2 186
#> 5    1 20.4   1 113
#> 6    3 21.7   1 184
#> 7    1 22.5   1 118
#> 8    1 30.1   1 187
#> 9    2 22.0   1 238
#> 10   2 27.2   1 186
#> 11   1 30.1   1 187
#> 12   2 35.3   1 229
#> 13   3 21.7   1 206
#> 14   2 28.7   2 204
#> 15   1 29.6   1 187
#> 16   1 30.1   1 187
#> 17   3 27.2   2 284
#> 18   2 26.3   2 199
#> 19   1 35.3   1 218
#> 20   3 25.5   2 206
#> 21   1 30.1   1 187
#> 22   1 33.2   1 229
#> 23   1 27.5   1 131
#> 24   3 24.9   1 284
#> 25   2 27.4   1 186

# imputation on mixed data with a different method per column
mice(nhanes2, method = c("sample", "midastouch", "logreg", "norm"))
#> 
#>  iter imp variable
#>   1   1  bmi  hyp  chl
#>   1   2  bmi  hyp  chl
#>   1   3  bmi  hyp  chl
#>   1   4  bmi  hyp  chl
#>   1   5  bmi  hyp  chl
#>   2   1  bmi  hyp  chl
#>   2   2  bmi  hyp  chl
#>   2   3  bmi  hyp  chl
#>   2   4  bmi  hyp  chl
#>   2   5  bmi  hyp  chl
#>   3   1  bmi  hyp  chl
#>   3   2  bmi  hyp  chl
#>   3   3  bmi  hyp  chl
#>   3   4  bmi  hyp  chl
#>   3   5  bmi  hyp  chl
#>   4   1  bmi  hyp  chl
#>   4   2  bmi  hyp  chl
#>   4   3  bmi  hyp  chl
#>   4   4  bmi  hyp  chl
#>   4   5  bmi  hyp  chl
#>   5   1  bmi  hyp  chl
#>   5   2  bmi  hyp  chl
#>   5   3  bmi  hyp  chl
#>   5   4  bmi  hyp  chl
#>   5   5  bmi  hyp  chl
#> Class: mids
#> Number of multiple imputations:  5 
#> Imputation methods:
#>          age          bmi          hyp          chl 
#>           "" "midastouch"     "logreg"       "norm" 
#> PredictorMatrix:
#>     age bmi hyp chl
#> age   0   1   1   1
#> bmi   1   0   1   1
#> hyp   1   1   0   1
#> chl   1   1   1   0