The package **modi** provides several functions for
multivariate outlier detection and imputation. They may be used when
analysing multivariate quantitative survey data. The distribution of
such data is often not multivariate normal. Futhermore, the data is
often skewed and exhibits features of a semi-continuous distribution.
Finally, missing values and non-response is common. The functions
provided in **modi** address those problems.

The following outlier detection and imputation functions are provided
in **modi**:

`BEM()`

is an implementation of the BACON-EEM algorithm to detect outliers under the assumption of a multivariate normal distribution.`TRC()`

is an implementation of the transformed rank correlation (TRC) algorithm to detect outliers.`EAdet()`

is an outlier detection method based on the epidemic algorithm (EA).`EAimp()`

is an imputation method based on the epidemic algorithm (EA).`GIMCD()`

is an outlier detection method based on non-robust Gaussian imputation (GI) and the highly robust minimum covariance determinant (MCD) algorithm.`POEM()`

is a nearest neighbor imputation method for outliers and missing values.`winsimp()`

is an imputation method for outliers and missing values based on winsorization and Gaussian imputation.`ER()`

is a robust multivariate outlier detection algorithm that can cope with missing values.

You can install modi from github by runing the following line of code in R:

```
# install.packages("devtools")
::install_github("martinSter/modi") devtools
```

The following simple example shows how the BACON-EEM algorithm can be applied to detect outliers in the Bushfire dataset:

```
# Bushfire data set with 20% of observations missing completely at random (MCAR)
library(modi)
# load the data containing missing values and the corresponding weights
data(bushfirem, bushfire.weights)
# run BEM algorithm to detect multivariate outliers
<- BEM(bushfirem, bushfire.weights, alpha = (1 - 0.01 / nrow(bushfirem)))
bem.res #> alpha should be less than 0.5:
#> alpha set to 1 - alpha
#> 0.9997368
#> BEM has detected 15 outlier(s) in 0.11 seconds.
# show the outliers as detected by BEM
$outind, ]
bushfirem[bem.res#> X1 X2 X3 X4 X5
#> 7 92 110 46 165 NA
#> 8 94 95 29 113 190
#> 9 94 94 29 110 188
#> 10 100 104 21 133 208
#> 11 108 115 17 144 NA
#> 12 134 156 10 163 233
#> 15 81 137 426 NA 306
#> 31 136 155 NA 246 301
#> 32 103 97 552 NA 364
#> 33 NA 66 576 340 377
#> 34 79 66 572 340 376
#> 35 79 66 577 341 379
#> 36 78 NA 574 342 377
#> 37 78 66 571 343 379
#> 38 NA 66 NA 344 380
# show mean per column as computed in BEM
print(bem.res$output$center)
#> NULL
```

The implementation of this R package was supported by the Hasler foundation.