# Imputation by direct use of lasso linear regression

Source:`R/mice.impute.lasso.norm.R`

`mice.impute.lasso.norm.Rd`

Imputes univariate missing normal data using lasso linear regression with bootstrap.

## 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.- nfolds
The number of folds for the cross-validation of the lasso penalty. The default is 10.

- ...
Other named arguments.

## Details

The method consists of the following steps:

For a given y variable under imputation, draw a bootstrap version y* with replacement from the observed cases

`y[ry]`

, and stores in x* the corresponding values from`x[ry, ]`

.Fit a regularised (lasso) linear regression with y* as the outcome, and x* as predictors. A vector of regression coefficients bhat is obtained. All of these coefficients are considered random draws from the imputation model parameters posterior distribution. Same of these coefficients will be shrunken to 0.

Draw the imputed values from the predictive distribution defined by the original (non-bootstrap) data, bhat, and estimated error variance.

The method is based on the Direct Use of Regularized Regression (DURR) proposed by Zhao & Long (2016) and Deng et al (2016).

## References

Deng, Y., Chang, C., Ido, M. S., & Long, Q. (2016). Multiple imputation for general missing data patterns in the presence of high-dimensional data. Scientific reports, 6(1), 1-10.

Zhao, Y., & Long, Q. (2016). Multiple imputation in the presence of high-dimensional data. Statistical Methods in Medical Research, 25(5), 2021-2035.

## See also

Other univariate imputation functions:
`mice.impute.cart()`

,
`mice.impute.lasso.logreg()`

,
`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.midastouch()`

,
`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()`