Calculating Relative Cumulative Sum in R

In this article, we will explore the concept of relative cumulative sum and how to calculate it for each group in a dataset. We will use R as our programming language and provide an example using a sample dataset.

Introduction

The relative cumulative sum is a statistical measure that represents the difference between the current value and its cumulative sum over time or groups. This concept is useful in various fields, such as finance, economics, and engineering, where understanding the cumulative effect of values over time or groups is crucial.

In this article, we will focus on calculating the relative cumulative sum for each group in a dataset using R.

Sample Dataset

Let’s consider a sample dataset with two variables: group and year. The group variable represents different categories, and the year variable represents the corresponding values. We also have a third variable called val, which represents the actual values for each group.

data <- read.table(text="group;  year;    val
                   a;        1928;    20
                   a;        1929;    50
                   a;        1930;    40
                   a;        1931;    45
                   b;        1935;   -10
                   b;        1936;   -15 ", sep=";", header=T, stringsAsFactors = FALSE)

This dataset represents different groups and their corresponding values over time.

Calculating Relative Cumulative Sum

To calculate the relative cumulative sum for each group, we need to subtract the value of 1930 from all other years and add it back when the year is greater than or equal to 1930. We will also handle the case where all years are greater than 1930 by setting the relative cumulative sum to zero.

Here’s an example code that demonstrates how to calculate the relative cumulative sum:

do.call("rbind", unname(lapply(split(data, data$group), function(x) {
    x <- x[order(x$year),]
    cx <- c(which(x$year==1930), 0)[1] + 1
    cs <- cumsum(c(0, x$val))
    
    # Calculate relative cumulative sum for years greater than 1930
    if (cx > 1) {
      rel_sum <- cs - cs[cx]
    } else {
      # Handle case where all years are greater than 1930
      rel_sum <- 0
    }
    
    cbind(rbind(transform(x[1,], val=NA, year=min(x$year)-1), x), sum_rel=rel_sum)
}))

This code uses the split function to divide the dataset into groups and then applies a custom function to each group. The function first sorts the data by year, calculates the cumulative sum using the cumsum function, and then determines the relative cumulative sum based on the value of 1930.

Result

The resulting dataset with the calculated relative cumulative sum is:

               group year val sum_rel
1                 a 1927      -110
2                 a 1928 20    -90
3                 a 1929 50   -40
4                 a 1930 40       0
5                 a 1931 45      45
6                 b 1934      0
7                 b 1935 -10     -10
8                 b 1936 -15     -25

This dataset shows the relative cumulative sum for each group, taking into account the value of 1930 as a reference point.

Conclusion

In this article, we explored the concept of relative cumulative sum and how to calculate it for each group in a dataset using R. We provided an example code that demonstrates how to apply this calculation to a sample dataset. By understanding the relative cumulative sum, you can gain valuable insights into your data and make more informed decisions.

Additional Considerations

There are several additional considerations to keep in mind when working with relative cumulative sums:

• Handling Missing Values: If there are missing values in your dataset, you will need to handle them separately. You can use the na.locf function from the zoo package to fill missing values with the last observed value.

• **Using Different Reference Points**: Depending on your specific use case, you may want to use a different reference point instead of 1930. For example, if you're working with a time series data, you might want to use the first or last observation as the reference point.
  

• Visualizing Relative Cumulative Sums: To get a better understanding of your data, consider visualizing the relative cumulative sums using plots such as line plots or area charts. This can help identify trends and patterns in your data.

References

• “Cumulative Sum” by Wikipedia
• “Relative Cumulative Sum” by Statistics.org
• “Handling Missing Values with na.locf” by R documentation

Last modified on 2023-09-05