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7. Exponential Transformation
In the current SIMD methodology, domain scores are ranked and transformed to be exponentially distributed, before being combined as a weighted sum to form the SIMD score. The objective of exponential transformation is to standardise the distribution of each domain score, and to prevent canceling out of a high level of deprivation on one domain by a low level of deprivation on another, as can occur if domain scores are standardised by transformation to a symmetrical distribution. Ranking is used as part of the standardisation process to prevent an extreme level of deprivation on a single domain dominating the final SIMD score.
We shall explore the effects of the two-stage transformation on each domain score. We shall examine the effects of changing this transformation step to a simple standardisation (by subtracting the mean and dividing by the standard deviation for each domain score) through application to the observed indicator data and the simulated indicator datasets. We shall also select transformations of the domain scores that have similar overall effects to the current two-stage transformation, but do not involve ranking, and will therefore preserve differences between data zones. These transformations, followed by simple standardisation, will also be assessed by application to the observed indicator data and the simulated indicator datasets.
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