# impute_lm

##### (Robust) Linear Regression Imputation

Regression imputation methods including linear regression, robust linear regression with \(M\)-estimators, regularized regression with lasso/elasticnet/ridge regression.

##### Usage

```
impute_lm(dat, formula, add_residual = c("none", "observed", "normal"),
na_action = na.omit, ...)
```impute_rlm(dat, formula, add_residual = c("none", "observed", "normal"),
na_action = na.omit, ...)

impute_en(dat, formula, add_residual = c("none", "observed", "normal"),
na_action = na.omit, family = c("gaussian", "poisson"), s = 0.01, ...)

##### Arguments

- dat
`[data.frame]`

, with variables to be imputed and their predictors.- formula
`[formula]`

imputation model description (See Model description)- add_residual
`[character]`

Type of residual to add.`"normal"`

means that the imputed value is drawn from`N(mu,sd)`

where`mu`

and`sd`

are estimated from the model's residuals (`mu`

should equal zero in most cases). If`add_residual = "observed"`

, residuals are drawn (with replacement) from the model's residuals. Ignored for non-numeric predicted variables.- na_action
`[function]`

what to do with missings in training data. By default cases with missing values in predicted or predictors are omitted (see `Missings in training data').- ...
- further arguments passed to
- family
- Response type for elasticnet / lasso regression. For
`family="gaussian"`

the imputed variables are general numeric variables. For`family="poisson"`

the imputed variables are nonnegative counts. See`glmnet`

for details. - s
- The value of \(\lambda\) to use when computing predictions for
lasso/elasticnet regression (parameter
`s`of`predict.glmnet`

). For`impute\_en`

the (optional) parameter`lambda`is passed to`glmnet`

when estimating the model (which is advised against).

##### Value

`dat`

, but imputed where possible.

##### Model specification

Formulas are of the form

`IMPUTED_VARIABLES ~ MODEL_SPECIFICATION [ | GROUPING_VARIABLES ] `

The left-hand-side of the formula object lists the variable or variables to
be imputed. The right-hand side excluding the optional `GROUPING_VARIABLES`

model specification for the underlying predictor.

If grouping variables are specified, the data set is split according to the values of those variables, and model estimation and imputation occur independently for each group.

Grouping using `dplyr::group_by`

is also supported. If groups are
defined in both the formula and using `dplyr::group_by`

, the data is
grouped by the union of grouping variables. Any missing value in one of the
grouping variables results in an error.

Grouping is ignored for `impute_const`

.

##### Methodology

**Linear regression model imputation** with `impute_lm`

can be used
to impute numerical variables based on numerical and/or categorical
predictors. Several common imputation methods, including ratio and (group)
mean imputation can be expressed this way. See `lm`

for
details on possible model specification.

**Robust linear regression through M-estimation** with
`impute_rlm`

can be used to impute numerical variables employing
numerical and/or categorical predictors. In \(M\)-estimation, the
minimization of the squares of residuals is replaced with an alternative
convex function of the residuals. A concise online description
of \(M\)-estimation can be found
http://research.microsoft.com/en-us/um/people/zhang/INRIA/Publis/Tutorial-Estim/node24.html#SECTION000104000000000000000.
Also see e.g. Huber (1981).

**Lasso/elastic net/ridge regression imputation** with `impute_en`

can be used to impute numerical variables employing numerical and/or
categorical predictors. For this method, the regression coefficients are
found by minimizing the least sum of squares of residuals augmented with a
penalty term depending on the size of the coefficients. For lasso regression
(Tibshirani, 1996), the penalty term is the sum of squares of the
coefficients. For ridge regression (Hoerl and Kennard, 1970), the penalty
term is the sum of absolute values of the coefficients. Elasticnet regression
(Zou and Hastie, 2010) allows switching from lasso to ridge by penalizing by
a weighted sum of the sum-of-squares and sum of absolute values term.

##### References

Huber, P.J., 2011. Robust statistics (pp. 1248-1251). Springer Berlin Heidelberg.

Hoerl, A.E. and Kennard, R.W., 1970. Ridge regression: Biased estimation for nonorthogonal problems. Technometrics, 12(1), pp.55-67.

Tibshirani, R., 1996. Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society. Series B (Methodological), pp.267-288.

Zou, H. and Hastie, T., 2005. Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 67(2), pp.301-320.

##### See Also

Other imputation: `impute_cart`

,
`impute_hotdeck`

, `impute`

##### Examples

```
data(iris)
irisNA <- iris
irisNA[1:4, "Sepal.Length"] <- NA
irisNA[3:7, "Sepal.Width"] <- NA
# impute a single variable (Sepal.Length)
i1 <- impute_lm(irisNA, Sepal.Length ~ Sepal.Width + Species)
# impute both Sepal.Length and Sepal.Width, using robust linear regression
i2 <- impute_rlm(irisNA, Sepal.Length + Sepal.Width ~ Species + Petal.Length)
```

*Documentation reproduced from package simputation, version 0.2.2, License: GPL-3*