Simulate Missing Values with MNAR Method in R

Introduction

Missing data can be a challenging problem in statistical analysis and machine learning. In many cases, data may contain missing values due to various reasons such as non-response, errors during collection or processing, or inherent characteristics of the data itself. When dealing with missing data, it is essential to understand the pattern of missingness and its implications on the analysis.

One common approach to handle missing data is by imputing values using different methods. One popular method is the Missing Not At Random (MNAR) method, which assumes that the probability of missingness depends on some underlying variable. In this article, we will explore how to simulate missing values with the MNAR method in R.

Background

The Missing Not At Random (MNAR) method assumes that the probability of missingness is independent of the observed data. This means that the probability of missing a value does not depend on any other variable or the actual value itself.

In statistical terms, the MNAR assumption can be expressed as follows:

p_{ij} = p_i (i = 1, …, n; j = 1, …, m)

where p_{ij} is the probability that the i-th observation has a missing value in the j-th variable, and p_i is the probability of missingness for the i-th observation.

One popular algorithm used to impute values using MNAR assumption is the Multiple Imputation by Chained Equations (MICE) method. The MICE algorithm iteratively applies different imputation models to each variable until convergence.

Simulating Missing Values with MNAR Method in R

To simulate missing values using the MNAR method, we can use a combination of R’s built-in functions and dplyr package.

Step 1: Load Required Libraries

First, we need to load the required libraries. We will use the dplyr package for data manipulation and the rbinom function from base R to simulate missing values.

# Load required libraries
library(dplyr)

Step 2: Simulate Data

Next, we will simulate a dataset with two variables: x1 and x2. We will use rbinom to generate binary data for x1 and rnorm to generate normal data for x2.

# Simulate data
set.seed(123)
n <- 100
x1 <- rbinom(n, 0, 0.5) # Binary variable x1 with p = 0.5
x2 <- rnorm(n, 0, 1)   # Normal variable x2 with mean 0 and standard deviation 1
df <- data.frame(x1, x2)

Step 3: Impute Missing Values

Now, we will use the dplyr package to impute missing values using the MNAR method. We will create a new column x2_mcar that contains the imputed values of x2.

# Impute missing values
df %>% 
  mutate(
    x2_mcar = if_else(x1 == 1 & runif(n()) < 0.1, NA_real_, x2)
  )

In this code snippet, we use the mutate function from dplyr to create a new column x2_mcar. We then use the if_else function to check if x1 equals 1 and if a random value generated by runif is less than 0.1. If both conditions are true, we set the value of x2 to NA. Otherwise, we keep the original value of x2.

Step 4: Verify Imputation

To verify that the imputation method works correctly, we can use the summary function from R to print the summary statistics of the imputed values.

# Print summary statistics
summary(df$x2_mcar)

This code snippet will print the mean, median, standard deviation, and other summary statistics for the imputed values of x2.

Conclusion

In this article, we explored how to simulate missing values using the MNAR method in R. We discussed the assumptions underlying the MNAR method and provided a step-by-step guide on how to implement it using dplyr package.

We hope that this article has been helpful in understanding the concept of MNAR method and its application in data imputation. If you have any questions or need further clarification, please feel free to ask!

Last modified on 2023-09-10