StackImpute (version 0.1.0)

Louis_Information_Custom: Louis_Information_Custom

Description

This function takes a dataset with stacked multiple imputations and a score matrix and covariance matrix from stacked and weighted analysis as inputs to estimates the corresponding information matrix accounting for the imputation uncertainty.

Usage

Louis_Information_Custom(score, covariance_weighted, stack, M)

Arguments

score

n x p matrix containing the contribution to the outcome model score matrix for each subject (n rows) and each model parameter (p columns).

covariance_weighted

p x p matrix containing the estimated covariance matrix from fitting the desired model to the stacked and weighted multiple imputations. Note: For GLM models, use summary(fit)$cov.unscaled*StackImpute::glm.weighted.dispersion(fit) as the default dispersion parameter will be incorrect.

stack

data frame containing stacked dataset across multiple imputations. Could have 1 or M rows for each subject with complete data. Should have M rows for each subject with imputed data. Must contain the following named columns: (1) stack$.id, which correspond to a unique identifier for each subject. This column can be easily output from MICE. (2) stack$wt, which corresponds to weights assigned to each row. Standard analysis of stacked multiple imputations should set these weights to 1 over the number of times the subject appears in the stack.

M

number of multiple imputations

Value

Info, estimated information matrix accounting for within and between imputation variation

Details

This function uses the observed information matrix principle proposed in Louis (1982) and applied to imputations in Wei and Tanner (1990). This estimator is a further extension specifically designed for analyzing stacks of multiply imputed data as proposed in Beesley and Taylor (2019) https://arxiv.org/abs/1910.04625.

Examples

# NOT RUN {
data(stackExample)

fit = stackExample$fit
stack = stackExample$stack

covariates = as.matrix(cbind(1, stack$X, stack$B))
score = sweep(covariates, 1, stack$Y - covariates %*%
         matrix(coef(fit)), '*') / glm.weighted.dispersion(fit)
covariance_weighted = summary(fit)$cov.unscaled * glm.weighted.dispersion(fit)
Info = Louis_Information_Custom(score, covariance_weighted, stack, M = 50)
VARIANCE_custom = diag(solve(Info))

# }