# impCoda: Imputation of missing values in compositional data In robCompositions: Compositional Data Analysis

## Description

This function offers different methods for the imputation of missing values in compositional data. Missing values are initialized with proper values. Then iterative algorithms try to find better estimations for the former missing values.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```impCoda( x, maxit = 10, eps = 0.5, method = "ltsReg", closed = FALSE, init = "KNN", k = 5, dl = rep(0.05, ncol(x)), noise = 0.1, bruteforce = FALSE ) ```

## Arguments

 `x` data frame or matrix `maxit` maximum number of iterations `eps` convergence criteria `method` imputation method `closed` imputation of transformed data (using ilr transformation) or in the original space (`closed` equals TRUE) `init` method for initializing missing values `k` number of nearest neighbors (if init \$==\$ “KNN”) `dl` detection limit(s), only important for the imputation of rounded zeros `noise` amount of adding random noise to predictors after convergency `bruteforce` if TRUE, imputations over dl are set to dl. If FALSE, truncated (Tobit) regression is applied.

## Details

eps: The algorithm is finished as soon as the imputed values stabilize, i.e. until the sum of Aitchison distances from the present and previous iteration changes only marginally (eps).\

method: Several different methods can be chosen, such as ‘ltsReg’: least trimmed squares regression is used within the iterative procedure. ‘lm’: least squares regression is used within the iterative procedure. ‘classical’: principal component analysis is used within the iterative procedure. ‘ltsReg2’: least trimmed squares regression is used within the iterative procedure. The imputated values are perturbed in the direction of the predictor by values drawn form a normal distribution with mean and standard deviation related to the corresponding residuals and multiplied by `noise`.

## Value

 `xOrig ` Original data frame or matrix `xImp ` Imputed data `criteria ` Sum of the Aitchison distances from the present and previous iteration `iter ` Number of iterations `maxit ` Maximum number of iterations `w ` Amount of imputed values ```wind ``` Index of the missing values in the data

## Author(s)

Matthias Templ, Karel Hron

## References

Hron, K., Templ, M., Filzmoser, P. (2010) Imputation of missing values for compositional data using classical and robust methods Computational Statistics and Data Analysis, 54 (12), 3095-3107.

`impKNNa`, `pivotCoord`
 ```1 2 3 4 5 6 7 8 9``` ```data(expenditures) x <- expenditures x[1,3] x[1,3] <- NA xi <- impCoda(x)\$xImp xi[1,3] s1 <- sum(x[1,-3]) impS <- sum(xi[1,-3]) xi[,3] * s1/impS ```