Dear Bipin,

Yes, spatial autocorrelation and spatial non-stationarity are different concepts.

SPATIAL AUTOCORRELATION

If you measure something over space, for example the household income, it is likely that two observations that are close to each other in space are also similar in measurement. This assumption is also known as the First Law of Geography: "everything is related to everything else, but near things are more related than distant things" (Tobler, 1970). In this sense, Spatial Autocorrelation is a measure of similarity (correlation) between nearby observations. It describes the degree two which observations (values) at spatial locations (whether they are points, areas, or raster cells), are similar to each other. A commonly used statistic that describes spatial autocorrelation is Moran’s I, Geary’s C and, for binary data, the join-count index.

SPATIAL NON-STATIONARITY

Spatial nonstationarity is a condition in which a simple “global” model cannot explain the relationships between some sets of variables. The nature of the model must alter over space to reflect the structure within the data (Brundson et al., 1996). For example, you are trying to model the relationship between two variables, number of cars per person and income, in a given city. Using a global linear regression, you find that neighborhoods with higher incomes have more cars per person. However, in some neighborhoods where public transport is better this relationship changes, and even with a high average income, people tend to use public transportation. Thus, the relationship you are modeling is non-stationary throughout space. The Geographically weighted regression (GWR) is a technique mainly intended to indicate where non-stationarity is taking place on the map, that is where locally weighted regression coefficients move away from their global values.

Tobler W., (1970) "A computer movie simulating urban growth in the Detroit region". Economic Geography, 46(Supplement): 234-240.

Article Geographically Weighted Regression: A Method for Exploring S...

Best,

Sacha

Dear Bipin,

By spatial non-stationarity we basically refer to a statistical relationship between variables, the coefficients of which are spatially varying. For instance, if we assume that you build a model by which you predict y (y=ax+b), a global model that is static throughout your domain keeps the elements a and b static and hence, does not take into account non-stationarity. You could address such an issue by adjusting your model parameters to certain values for subregions in your original domain, in which you can assume that the attributes of your model do not change significantly with respect to your variable in concern.

By spatial autocorrelation we refer to the correlation that a variable exhibits over a region. For instance, if you are interested in temperature and you measure temperature at locations x1, x2 and x3, the autocorrelation is the correlation of temperature measurements at x1 and x2, x1 and x3. The interesting thing is to see what are the distances separating locations x1, x2 and x3 and further see how this autocorrelation is affected by distance. Spatial autocorrelation is based on the 1st Law of Geography (or Tobler's Law) and is basically treated by geostatistics and the construction of variograms. For your question about non-stationarity you might find interesting the directional variograms which are purposed to investigate just that.

See also:

1) http://onlinelibrary.wiley.com/doi/10.1111/j.1538-4632.1996.tb00936.x/epdf

2) http://onlinelibrary.wiley.com/doi/10.1002/9781118786352.wbieg1159/abstract?userIsAuthenticated=false&deniedAccessCustomisedMessage=

https://libraries.mit.edu/files/gis/spatial_auto_exercise_iap2013.pdf

http://jenniferalentz.info/Teaching/StudyGuides/SpatialAutocorrelation.pdf

http://www.sih.m.u-tokyo.ac.jp/english/seminar/pdf/GIS/Spatial%20Analysis%202%20-%20Point%20Pattern%20Analysis%20and%20Spatial%20Autocorrelation.pdf

Dear Bipin,

Just to complement the already well-answered question.

This is a reasonable question because the same phenomenon can be analyzed employed both the spatial autocorrelation and the spatial non-stationarity concepts/methodology. Perhaps this is one of the reasons for the confusion.

Cheers!