Index conversion function

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Index conversion function (ICF) is a variable describing how one index can be converted to another in a particular context. The variable is indexed by the two indices, and the values in cells represent the fraction of the total amount of substance (e.g., area, population) in the union determined by the two indices. For example, a country may be treated as a whole, or it may be divided into (i.e., indexed by) counties or municipalities. In this case, the three indices are "crisp" in the sense that a municipality belongs to exactly one county, and a county belongs to exactly one country. There can also be "overlapping" indices. For example, for a given population, a certain fraction of (not all) men or women belong to a particular age group. If the result domains of the two indices are not the same, the fraction of substance that goes beyond each index must be specified.

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Scope

What structure does an index conversion function have and how should it be used for index conversions within one dimension?

Definition

Input format

The data should contain the original data to be converted, the input index, the output index, and some kind of weighting scheme. If other information is needed, it is a disadvantage.

Output format

The output is the original data indexed by the output index (and no longer by the input index). The output must be consistent with the original data. I.e., if it is converted back to the original index, it must not be inconsistent with the original data.

Rationale

The procedure is based on Si_pi and Pi_si functions in the version 1.0.1 of the composite traffic model. The idea is further developed here.

NOTE! The ICF can also be operationalised in a way that instead of fractions, the values are given in substantive units (e.g. surface area for spatial indices, population size for populations). Then the value must be divided by the total sum of the variable to get proper fractions.

See also

• [[Using non-predetermined spatial disaggregation]
• Merging models with different grids