Structural Similarity in OD Matrices – Further Investigations
Tom Van Vuren, Mott MacDonald Ltd, Tim Pollard, Mott MacDonald Ltd
The paper provides more detailed testing of a new comparator index MSSIM, introduced in an ETC paper in 2013, used to compare OD matrices structurally on similarity rather than relying on assignment results or more general statistical tests.
In 2013 we presented a paper at the European Transport Conference on the use and value of the Mean Structural Similarity Index (MSSIM) in comparing OD matrices. Why is comparing OD matrices important:
- data collection is expensive, and being able to determine whether further expenditure on observing travel patterns is necessary makes sense in an era of austerity;
- novel data sources are being investigated and comparing matrices derived from these with matrices derived from traditional methods gives confidence in Big Data
- guidance requires that pre and post estimation matrices should not be too dissimilar, and existing indicators such as the R-squared statistic may not capture structural similarities well
In the paper we described our early experiences with the Mean Structural Similarity Index; a measure first described in this context by Djukovic et al. (2013). We identified that the MSSIM indicator provides additional and different insights into the similarity between OD matrices compared to either the R-squared measure recommended in WebTAG, or the results from matrix assignments, such as the GEH statistic. In particular:
- MSSIM shows structural similarities where R-squared statistic cannot detect these
- assignment-based analytics hide dissimilarities that MSSIM can identify
We compare the GPS derived input matrix for the PRISM West Midlands model with other observed data sources, and compare the OD matrices pre and post matrix estimation from counts.
However, the paper also identified practical issues that affect the value and stability of the indicator, which are explored further in this follow-up paper. In particular:
- The size of the window covering (part of) the matrix;
- The order in which to analyse groups of OD pairs;
- Possible aggregation of matrix values in bands or buckets;
- Selecting appropriate parameter values within the MSSIM calculations;
leading to preliminary advice on the use of the MSSIM indicator in practical applications elsewhere.
Association for European Transport