mice.impute.norm {mice}

Imputation by Bayesian linear regression

Description

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

Usage

mice.impute.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)\kappa)^{-1}, with some small ridge parameter \kappa.

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

4. Draw a random variable \dot g \sim \chi^2_\nu with \nu=n_1 - q.

5. Calculate \dot\sigma^2 = (y_{obs} - X_{obs}\hat\beta)'(y_{obs} - X_{obs}\hat\beta)/\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 \dot\beta = \hat\beta + \dot\sigma\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}\dot\beta + \dot z_2\dot\sigma.

Using mice.impute.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.cart(), mice.impute.lasso.logreg(), mice.impute.lasso.norm(), mice.impute.lasso.select.logreg(), mice.impute.lasso.select.norm(), mice.impute.lda(), mice.impute.logreg.boot(), mice.impute.logreg(), mice.impute.mean(), mice.impute.midastouch(), mice.impute.mnar.logreg(), mice.impute.mpmm(), 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()