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sDNA recommend use NQPD to measure closeness rather than inverse SAD/SMD/SCD/MAD/MMD/MCD. (Please refer the 3.b Closeness centrality sDNA measure description documentation )

In my understanding, their computation are as the following(for example with angular):
- NQPDA: sum of (each link 1/distance)
- Inverse SAD: 1 / (sum of each link distance)
- Inverse MAD: link_count / (sum of each link distance)

The major difference between them are get the inverse first or get the sum first.
But why the NQPD is better? Is there any explanation about this? maybe from mathematics?

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    You should label your second and third bullet points "inverse SAD" and "inverse MAD" to be correct – Sideshow Bob May 31 '17 at 10:50
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Closeness should be a measure of accessibility. Accessibility, intuitively, means either more stuff (network, destinations, whatever) or easier access to the stuff. So we see that there are two components to accessibility, quantity and quality; also these could be measured on multiple scales, so really accessibility is a multi dimensional phenomenon. Still, if we are willing to accept compromise we can try to summarize it in a single variable.

The original formulation of closeness (and also some Space Syntax formulations of what they call Integration, near enough the same thing) defined it as 1/(sum of distance). This works for global measurements on a network of fixed size. However if network size varies, or analysis is conducted on local network buffers (which is more usual in spatial analysis nowadays), is suffers the problem that it decreases with more stuff but increases with easier access. So, an increase in 1/(sum of distance) could mean either more or less accessibility - not a useful measure!

Closeness was soon revised to 1/(mean distance). This measures quality but not quantity. In real urban networks, 1/(mean distance) has a highly skewed distribution, while mean distance (or -(mean distance)) tends to have a more normal one, so the latter is usually recommended for statistical modelling unless there is a strong structural reason to use the inverse form.

While Mean Distance measures only quality, NQPD measures both quantity and quality. The actual thing computed in sDNA is SUM (weight^nqpdn / distance^nqpdd ) so the user can specify relative importance of quantity and quality by setting constants nqpdn and nqpdd. Really this was a response to those who wanted to measure quantity and quality together using 1/(sum of distance), but do it better.

The alternative to measuring quantity and quality together is to explicitly use two separate variables: Links, Length or Weight for quantity, and Mean Distance (MAD, MED, MCD etc) for quality. To make something comparable to NQPD you could then divide them e.g. quantity^x/distance^y.

Intuitively I think NQPD is somehow more accurate than the latter approach as it pairs each link quantity (which may be weighted) with its corresponding quality before summing; like a micro model rather than an aggregate one. But sDNA's Mean Distances are also weighted measures, so if there is e.g. a highly weighted link near the origin this will be reflected in MAD anyway. Perhaps it doesn't matter much. I don't have a mathematical proof.

On the other hand, using separate variables for quantity/quality is easier to calibrate to any outcome variable using linear regression, while NQPD would be very expensive to calibrate. A gravity model can easily be built from your quantity and quality variables and fitted with translog regression and poisson link function.

A final approach as I mentioned on your other question is using hybrid radius to make a multivariate model of network quantity at multiple radius. Switch on banded radius and compute network quantity e.g. Links accessible within different distance bands (which can be angular distance if you like, e.g. 0-90, 90-180, 180-360, ... etc). You can then calibrate a non-parametric distance decay curve using multivariate regression; use something which can handle correlated predictors e.g. ridge regression which is available in sDNA Learn. So, instead of measuring quantity and quality separately, we have measured the quantity of links for each different band of quality.

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  • Thanks very much for the detailed answering! NQPD measures both quantity and quality! That's it! – Jie Jun 1 '17 at 7:50

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