# GIS and Stratified Heterogeneity

Mark Altaweel

Updated:

A method to measure uneven distribution of landscape or population features in a given space is stratified heterogeneity. The method allows one to determine how different given regions or spaces are, allowing the method to determine how patchy or heterogeneous a single strata or different layers are. Variations in a given location within a layer or a group are defined as local heterogeneity, while variations between layers or groups is spatial stratified heterogeneity. The approach is commonly used to determine species, biological, and land cover variations.[1]

## Methods of Determining Stratified Heterogeneity in GIS

Within this approach, various methods are used to determine heterogeneity. One method is the application of spatial beta binomial distribution, where randomness is assessed as part of a Bayesian approach to seeing if given differences in a strata are evident that differ from expected probability.[2] Other methods include using a q-statistic method that measures heterogeneity in layers in a ratio from 0 to 1, where 1 represents perfect heterogeneity and 0 is no significant heterogeneity.[3] Techniques also combine the so-called sandwich method when null or weak values within layers might be present. In this case, stratification is created based on variance within a layer that is minimized while variation between layers is maximized. Common values are then estimated for each layer. The stratification uses units that report variation where measurements are then made to show how heterogeneous layers are based on the minimizing and maximizing approach within and between layers respectively. In effect, this is a way to classify and then measure given data to address having null or weak values present within datasets.[4]

## Applications of Stratified Heterogeneity in GIS

Examples of applications have included classifying land use systems around the globe. A common problem is that spatial variation is evident at different scales, creating problems of sampling in order to determine variety within and between strata. Additionally, adding time-dependent data can make it difficult to see how variation occurs based on time since often land use relationships are evident in one instant but not in other temporal resolution due to data collection and other issues. One way around this problem is to applying sampling techniques of land cover at a given spatial and temporal scales and then using interpolative modeling so that the remainder of a given land cover distribution can be determined from available samples at a given time.[5] Marine environments and water quality can also be monitored using stratified heterogeneity methods, where water quality affected by phosphates and pollutants is likely to have differential effects on marine and other aquatic-related measures for water quality.[6] While most methods apply spatial heterogeneity to landscape or biological-based examples, some have attempted to apply the approach to the social sciences. For instance, to understand disability employment in China, different regions were assessed for their qualities, including employment and population. The analysis showed biases in employment of disabled people, where such results could be used to guide policy makers in determining where resources should be spent or laws more strictly applied.[7]

Overall, stratified heterogeneity is not a widely used method as of yet. However, it has shown potential and utility in determining patchiness within and between layers using common statistical techniques. This provides analysis with a useful way to determine the degree of spatially variation within datasets.

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References

[1] For more on general aspects of stratified heterogeneity, see:  Wang, J.-F., Jiang, C.-S., Hu, M.-G., Cao, Z.-D., et al. (2013) Design-based spatial sampling: Theory and implementation. Environmental Modelling & Software. [Online] 40280–288. Available from: doi:10.1016/j.envsoft.2012.09.015.

[2] For more on spatial beta binomial distributions, see:  Song, B., Huang, D., Wang, R., Masae, S., et al. (2008) A measure for spatial heterogeneity of vegetation in the Center of Inner Mongolia. Progress in Natural Science. [Online] 18 (3), 289–295. Available from: doi:10.1016/j.pnsc.2007.07.015.

[3] For more on the q-statistic technique, see:  Wang, J.-F., Zhang, T.-L. & Fu, B.-J. (2016) A measure of spatial stratified heterogeneity. Ecological Indicators. [Online] 67250–256. Available from: doi:10.1016/j.ecolind.2016.02.052.

[4] For more on the so-called sandwich method, see:  Wang, J. (2015) Sandwich mapping of diseases with a small sample in a stratified heterogeneous domain. Annals of GIS. [Online] 21 (2), 169–173. Available from: doi:10.1080/19475683.2015.1031176.

[5] For a review on techniques on stratified heterogeneity, see:  Wang, J.-F., Stein, A., Gao, B.-B. & Ge, Y. (2012) A review of spatial sampling. Spatial Statistics. [Online] 21–14. Available from: doi:10.1016/j.spasta.2012.08.001.

[6] For more information on how stratified heterogeneity can be used in monitoring marine environments and water quality, see:  Fan, H., Gao, B., Xu, R. & Wang, J. (2017) Optimization of Shanghai marine environment monitoring sites by integrating spatial correlation and stratified heterogeneity. Acta Oceanologica Sinica. [Online] 36 (2), 111–121. Available from: doi:10.1007/s13131-017-0969-3.

[7] For more on stratified heterogeneity on understanding disability employment and as an example in its use in the social sciences, see:  Liao, Y., Wang, J., Du, W., Gao, B., et al. (2016) Using spatial analysis to understand the spatial heterogeneity of disability employment in China: Spatial heterogeneity of disability employment in China. Transactions in GIS. [Online] Available from: doi:10.1111/tgis.12217 [Accessed: 11 April 2017].