Calculating Sum of Squared Deviations in Large Datasets using Base R

Introduction

In this article, we will discuss a common problem when working with large datasets in R: calculating the sum of squared deviations for each combination of variables. We will explore different approaches to achieve this efficiently, focusing on base R functions and avoiding loops.

Problem Statement

The question arises from trying to store the results of sum of squared deviations in a specific way for a large dataset. The provided example uses two variables: sample.nr and lot.name, with 18 data points each. However, as the dataset grows in size (thousands of sample.nr and lot.name), the computational time increases significantly.

Current Implementation

The current implementation relies on nested for loops to iterate over all combinations of lot.name and sample.nr. This approach is inefficient for large datasets due to its high time complexity.

# save results
output <- setNames(data.frame(matrix(ncol=length(lot.id), nrow=length(sample.id))), 
                    c("L01", "L02", "L03"))

for (i in 1:length(sample.id)){
  
  for (j in 1:length(lot.id)){
    
      dtA <- dtf[dtf$lot.name == lot.id[j] & dtf$sample.nr == sample.id[i], ]
      
      css <- sum((dtA[,3] - mean(dtA[,3])) ^2)
      
      output[i,j] <- css
  }
}

Alternative Approach using Aggregate

The aggregate function can be used to calculate the sum of squared deviations for each combination of lot.name and sample.nr. This approach avoids the need for nested loops, making it more efficient.

css.func <- function(x) {
  sum((x - mean(x)) ^2)
}

res <- aggregate(concentration~sample.nr + lot.name, dtf, css.func)

# print result
print(res)

The aggregate function takes the formula to be applied, the dataset, and a function as arguments. In this case, we use the formula concentration ~ sample.nr + lot.name, indicating that the calculation should be performed for each combination of sample.nr and lot.name. The css.func function is applied to each group.

Reshaping the Result

The resulting data frame res has a long format, with one row per combination of sample.nr and lot.name. To convert this to a wide format, where each variable is in its own column, we can use the reshape function from the reshape2 package.

library(reshape2)
reshape(res, idvar = "sample(nr)", timevar = "lot.name", direction = "wide")

# print result
print(newname1)

The resulting data frame has a wide format with one row per combination of sample.nr and lot.name, and each variable in its own column.

Conclusion

Calculating the sum of squared deviations for large datasets can be efficiently achieved using base R functions, such as aggregate. This approach avoids the need for nested loops, making it more suitable for large datasets. By reshaping the result from a long format to a wide format, we can easily access and manipulate the data.

Further Optimization

While the aggregate function provides an efficient way to calculate sum of squared deviations, further optimization may be possible depending on the specific use case. For example:

• Using dplyr package: The dplyr package provides a more modern and efficient way to perform calculations using data manipulation languages (DMLs).
• Vectorization: Some operations can be vectorized, allowing for faster performance.
• Parallel processing: If the dataset is extremely large, parallel processing techniques can be used to speed up the calculation.

Additional Tips

• Use set.seed() to ensure reproducibility of results.
• Check the documentation for each function and package to understand their arguments, usage, and limitations.
• Consider using a more efficient data structure, such as a matrix or array, if working with large datasets.

Last modified on 2023-09-09