I am constructing an index composed of around 100 indicators aggregated in sub-index and these in an Index, among the indicators different types can be found: categorical, ordinal, interval and ratio.
- Categorical indicator are normalized with a categorical approach (i.e. assign numbers to values).
- Ordinal, Interval and ratio are normalized by Min-Max approach.
The scale of the index, will be 0-1 and the weights for indicators will be determined by "expert opinion" approach (i.e. theoretical).
The indicators of the index and its classification in sub-indexes have been developed to represent a theoretical model, and in a next step Confirmatory Factorial analysis would be applied for proving the theoretical model with the empirical data.
The final objective of the index is not only to rank the units of analysis (communities), but to reflect the distance between them. It also aims to be reproducible and applicable to different contexts (countries), allowing to compare unit of analysis across the contexts.
During the normalization of the indicator was observed that indicators referred to % over total population (e.g. % of children and % of elders) did not vary among the different units of analysis.
Though the indicators are already normalized on a scale 0-1, as being %, if taken the raw % each unit of analysis (e.g. communities within a country) obtain a very similar value (e.g. A=0.2; B=0.21; C=0.19), thus not contributing to the variability of the index (moving across the whole range 0-1) when aggregated.
I started then a process of standardization of the obtained % (basic Z-score) aiming at bringing it again in a scale 0-1 with the max-min rescaling over the Z-score, so its variability increased, as it is relative to the sample distribution.
Could anyone suggest if this is a reasonable approach or if other approaches would be recommended?. Bibliography references are always welcome.
PS: I refer to normalize when all indicators are in the same scale of measurement; I refer to standardization, when I speak about the formula (X-MEAN/SD) also know as Z-scoring.