Summary Statistics for Imputed Data from Zelig & Amelia

This blog post aims to provide a comprehensive guide on how to obtain summary statistics such as pooled means and standard deviations of imputed data using the Zelig and Amelia packages in R. While these packages are powerful tools for handling missing data, understanding their capabilities and limitations is crucial for accurate analysis.

Introduction

The Amelia package is a popular tool for multiple imputation in R, providing an efficient and robust way to handle missing data. The Zelig package extends this functionality by allowing users to perform various statistical analyses on the imputed data. This post will focus on how to obtain summary statistics such as pooled means and standard deviations of the imputed data using Amelia and Zelig.

Background

Before we dive into the details, let’s provide some background information on the Amelia and Zelig packages. The Amelia package uses a Bayesian approach to multiple imputation, which involves generating a set of imputed data sets based on a probabilistic model of the missing data. The Zelig package builds upon this by allowing users to perform various statistical analyses on the imputed data.

Setting Up the Data

To illustrate the process, we’ll create a sample dataset with some missing values.

# Load required libraries
library(Amelia)
library(Zelig)

# Create a sample dataset with missing values
n <- 100
x1 <- rnorm(n, 0, 1) # Random normal distribution
x2 <- .4 * x1 + rnorm(n, 0, sqrt(1 - .4)^2) # x2 is correlated with x1, r = .4
x1 <- ifelse(rbinom(n, 1, .2) == 1, NA, x1) # Randomly create missing values
d <- data.frame(cbind(x1, x2))

# Set the number of imputations (m)
m <- 5

# Impute the missing values using Amelia
d_imp <- amelia(d, m = m)

# View the summary statistics for the imputed data
summary(d_imp)

Obtaining Pooled Means and Standard Deviations

The original question asks how to obtain pooled means and standard deviations of the imputed data. To achieve this, we’ll use the lapply function to extract the means and standard deviations from each imputation and then pool them using Rubin’s rules.

First, let’s define a helper function foo that applies a given function to each column of the data.

# Define a helper function foo
foo <- function(x, fcn) {
  apply(x, 2, fcn)
}

# Extract the means and standard deviations from each imputation
q <- lapply(d_imp$imputations, foo, fcn = mean)
se <- lapply(d_imp$imputations, foo, fcn = sd)

# Pool the means using Rubin's rules
 pooled_means <- apply(q, 2, FUN = mean)

# Pool the standard deviations using Rubin's rules
pooled_sehat <- apply(se, 2, FUN = sqrt)

Editing and Combining Results

The original answer provides an edited version of the code that uses the mi.meld function from Zelig to combine the results. Let’s explore this further.

To pool the means and standard deviations using Rubin’s rules, we need to create a q matrix with the sample means from each imputation and an se matrix with the corresponding standard errors.

# Create a q matrix with the sample means from each imputation
q <- t(sapply(d_imp$imputations, foo, fcn = mean))

# Create a se matrix with the corresponding standard errors
se <- t(sapply(d_imp$imputations, foo, fcn = sd)) / sqrt(100)

# Pool the means using Rubin's rules
output <- mi.meld(q = q, se = se, byrow = TRUE)

Conclusion

In conclusion, obtaining summary statistics such as pooled means and standard deviations of imputed data using Amelia and Zelig involves several steps. By understanding how to extract the means and standard deviations from each imputation and then pooling them using Rubin’s rules, users can gain valuable insights into their data.

This post has provided a comprehensive guide on how to perform this task, covering the basics of multiple imputation with Amelia and Zelig as well as more advanced techniques for combining results. By following these steps, users can ensure accurate analysis and reliable conclusions when working with imputed data.

References

Amelia Package: https://www.amelia.impute.org/
Zelig Package: https://github.com/Amelia-Project/Zelig
Rubin’s Rules: https://en.wikipedia.org/wiki/Rubin%27s_rules

Last modified on 2024-01-23