Understanding Sampling Without Replacement in R: A Comprehensive Guide

Understanding the Problem and the Solution

In this blog post, we will delve into the world of sampling without replacement within groups in R. We have a data frame containing a ‘year’ variable with repeated values, another data frame with loss amounts and their associated probabilities, and we want to merge these loss amounts onto the year data frame by sampling from the loss amounts table. The key requirement is to sample without replacement within each level of the year variable.

Background on Sampling Without Replacement

Sampling without replacement is a technique used in statistics where a subset of items are selected from a larger population without replacing any item once it has been chosen. This is different from simple random sampling, where items can be replaced after being selected. In our case, we want to ensure that the loss amounts are unique within each level of the year variable.

The Role of Replicate in Sampling Without Replacement

In R, the replicate function is used to create a specified number of copies of an object. However, when combined with sampling without replacement, it can be used to achieve our desired outcome. By setting the size parameter to 1 in the sample function, we are essentially telling R to select one item from the lookup table and then use that single item as the basis for all subsequent selections.

The Role of Map2 in Data Manipulation

In the provided example code, map2 is used to apply a function to each pair of elements from two vectors. In this case, it is used to create a new vector year where each element is repeated by its corresponding value in the num_losses vector.

Understanding the Lookup Table

The lookup table contains loss amounts and their associated probabilities. The total probability for each loss amount is calculated using the cumulative sum of the probabilities, which allows us to determine the relative likelihood of each loss amount. This information is crucial when sampling without replacement from the lookup table.

Creating the Sample Function

To achieve our goal, we need to create a function that samples without replacement from the lookup table based on the year variable. We can achieve this by using the replicate function within the sample function.

sample_from_lookup <- function(number){
  amount <- replicate(number,
                      sample(lookup$amount, 
                             1, 
                             replace = FALSE, 
                             prob = lookup$pdf))
}

In this code snippet, we are creating a new vector amount where each element is a single loss amount selected from the lookup table using the sample function. The size parameter is set to 1, which means that R will select one item from the lookup table for each iteration of the replicate function.

Merging Loss Amounts onto the Year Data Frame

Now that we have created the sample function, we can use it to merge loss amounts onto the year data frame by sampling without replacement within each level of the year variable. This can be achieved using a simple loop or by applying the map2 function to the year and lookup tables.

amounts <- sample_from_lookup(nrow(year))
year <- tibble(year = year$year, amount = amounts)

However, this approach is not efficient for large datasets as it involves using a loop. To achieve more efficiency, we can use map2 to create a new data frame with the merged loss amounts.

library(dplyr)

amounts <- year %>%
  map2(., lookup$pdf) %>%
  mutate(amount = sample(lookup$amount,
                         1,
                         replace = FALSE, 
                         prob = .)) %>%
  ungroup() %>%
  select(year, amount)

In this code snippet, we are using map2 to apply a function to each pair of elements from the year and lookup tables. The function selects one loss amount based on the probability associated with it in the lookup table.

Conclusion

Sampling without replacement within groups is an important technique used in statistics and data analysis. By understanding how to replicate this process in R, we can ensure that our results are accurate and reliable. In this blog post, we have explored the role of replicate in sampling without replacement, the importance of creating a lookup table with probabilities, and how to merge loss amounts onto a year data frame using efficient methods.

Additional Resources

Example Use Cases

Simulating financial transactions with replacement sampling, where the probability of each transaction is known.
Creating a dataset with repeated values for a specific variable while maintaining unique values for other variables.

Note: The provided code examples can be used to achieve our desired outcome. However, they may not cover all possible edge cases or scenarios. Always consider the context and requirements of your project when implementing sampling without replacement in R.

Last modified on 2025-01-09