Installation

You can install the development version of disaggR from GitHub with:

# install.packages("devtools")
devtools::install_github("simschul/disaggR")

Background: Uncertainty propagation involving data disaggregation

The goal of disaggR is an R-package that helps you with uncertainty propagation when data disaggregation is involved. Data disaggregation usually involves splitting one data point into several disaggregates using proxy data. It is a common problem in many different research disciplines.

Data disaggregation usually involves an aggregate flow $Y_0$, which is known, such as the total amount of steel manufactured in a given time and geography. What we do not know but are interested in are the $K$ disaggregate flows $Y_1,...,Y_K$, such as the different end-use sectors where the manufactured steel ends up. Even though we do not know the values of $Y_1, ..., Y_K$, our model structures commonly demands that the individual $Y_i$’s need to sum to the known aggregate flow $Y_0$ to respect the mass, energy, stoichiometric or economic balance of the model

$$ Y_0 = \sum_{i=1}^{K} Y_i $$

This equation, also called an accounting identity introduces dependencies/correlations between the individual disaggregate flows $Y_i$.

To get estimates for the disaggregate flows, one usually looks for proxy data. Those proxy data are used to calculate shares (ratios/fractions) of the respective disaggregate units $\alpha_1, ..., \alpha_K$. To allocate the entire aggregate flow without leaving any residual (thus to respect the system balance), those fractions need to sum to one:

$$ \sum_{i=1}^{K} \alpha_i = 1 $$

Disaggregate flows are calculated as

$$ y_i = \alpha_i y_0, \forall i \in {1,...,K}. $$

Sampling disaggregates

This package generates a random sample of disaggregates based on the information provided. The aggregate and the shares are sampled independently. The distribution from which to sample is determined internally based on the information provided by the user. This choice of distribution is mostly based on the principle of Maximum Entropy (MaxEnt).

The aggregate distribution is determined using the following decision tree:

The shares are sampled from different variants of the Dirichlet distribution:

How to use

Sampling disaggregates

The main function is rdisagg which creates a random sample of disaggregates based on the information provided:

library(disaggR)
#> Loading required package: truncnorm
#> Loading required package: nloptr
#> Loading required package: gtools
#> Loading required package: data.table
#> 
#> Attaching package: 'disaggR'
#> The following object is masked from 'package:gtools':
#> 
#>     rdirichlet
sample <- rdisagg(n = 1000, mean_0 = 100, sd_0 = 5, min = 0, shares = c(0.1, 0.3, 0.6))
head(sample)
#>           [,1]      [,2]     [,3]
#> [1,]  6.868439 36.582309 58.44500
#> [2,] 10.356110 18.333990 70.21579
#> [3,] 32.115531 20.614670 39.30063
#> [4,] 30.357894 28.083534 43.94062
#> [5,] 30.788153  4.852038 67.34008
#> [6,]  3.898597 31.507223 58.71282

We can plot the marginal histograms of the sample:

hist(sample[,1])

hist(sample[,2])

hist(sample[,3])

The samples are consistent with all information provided. Thus, summing the disaggregate samples should provide an aggregate sample consistent with the information provided (mean: 100, sd: 5):

sample_agg <- rowSums(sample)
hist(sample_agg)

And indeed:

cat('Mean: ', mean(sample_agg), '\n')
#> Mean:  99.86048
cat('SD: ', sd(sample_agg))
#> SD:  5.168763

Sampling aggregates and shares seperatedely

With disaggR you can also sample the aggregate and the shares independently using the ragg and rshares functions:

sample_agg <- ragg(1000, mean = 100, sd = 5)
hist(sample_agg)

sample_shares <- rshares(1000, shares = c(0.1, 0.3, 0.6))
boxplot(sample_shares)