aggregate aggregates the set of elementary indicators through the selected
method and computes the composite according to the specified set of weights.
Arguments
- data
data matrix with the set of normalised elementary indicators (without missing values).
- method
aggregation method. Possible choices:
"linear"(default) and"non-linear". See Details.- w
vector of weights, as returned by
get_weights().
Details
The choice of the aggregation method heavily depends on the degree of compensability or substitutability of the elementary indicators. A compensatory approach requires the use of linear functions (e.g., a linear combination of the elementary indicators), while a partially compensatory (or non-compensatory) approach involves non-linear functions (e.g., a multiplicative approach).
In the first case, which corresponds to set method = "linear", the composite indicator
for target unit \(c\) is obtained as weighted (according to w) arithmetic mean of the \(Q\)
elementary (and normalised) indicators \(I_{qc}\):
$$CI_c = \sum_{q=1}^Q w_q I_{qc}$$
In the second case, using method = "non-linear", the resulting composite indicator is obtained
as weighted geometric mean of the elementary indicators:
$$CI_c = \prod_{q=1}^Q I_{qc}^{w_q}$$