# mice.impute.ds.norm: Imputation by Bayesian linear regression for DataSHIELD In stefvanbuuren/dsMiceClient: Distributed Multiple Imputations

## Description

Calculates imputations for univariate missing data by Bayesian linear regression, also known as the normal model.

## Usage

 1 mice.impute.ds.norm(y, ry, x, wy = 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. ... Other named arguments.

## Details

Imputation of y by the normal model by the method defined by Rubin (1987, p. 167). The procedure is as follows:

1. Calculate the cross-product matrix S=X_{obs}'X_{obs}.

2. Calculate V = (S+{diag}(S)κ)^{-1}, with some small ridge parameter κ.

3. Calculate regression weights \hatβ = VX_{obs}'y_{obs}.

4. Draw a random variable \dot g \sim χ^2_ν with ν=n_1 - q.

5. Calculate \dotσ^2 = (y_{obs} - X_{obs}\hatβ)'(y_{obs} - X_{obs}\hatβ)/\dot g.

6. Draw q independent N(0,1) variates in vector \dot z_1.

7. Calculate V^{1/2} by Cholesky decomposition.

8. Calculate \dotβ = \hatβ + \dotσ\dot z_1 V^{1/2}.

9. Draw n_0 independent N(0,1) variates in vector \dot z_2.

10. Calculate the n_0 values y_{imp} = X_{mis}\dotβ + \dot z_2\dotσ.

Using mice.impute.ds.norm for all columns emulates Schafer's NORM method (Schafer, 1997).

## Value

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

## Author(s)

Stef van Buuren, Karin Groothuis-Oudshoorn

## References

Rubin, D.B (1987). Multiple Imputation for Nonresponse in Surveys. New York: John Wiley & Sons.

Schafer, J.L. (1997). Analysis of incomplete multivariate data. London: Chapman & Hall.

## See Also

Other univariate imputation functions: mice.impute.ds.mean, mice.impute.ds.pmm

stefvanbuuren/dsMiceClient documentation built on June 27, 2019, 6:15 p.m.