Module 11 - Special Topics in GIS - Multivariate Regression, Diagnostics and Regression in ArcGIS

This week's lab was very interesting and very challenging, as we learned more about statistical analysis of data, this time in ArcGIS, and about multivariate analysis.

We can use several tools in the Spatial Statistics toolbox in ArcMap to analyze our spatial data and determine what sorts of relationships exist among variables, and whether the relationships are statistically significant.  One of the tools is called Ordinary Least Squares, or OLS.  One dependent variable is loaded into the tool, along with one or more explanatory or independent variables.  The resulting report shows many different statistics about the strength and type of effect the independent variables have on the dependent variable, and how likely those statistics are to be significant.  We can also examine the distribution of residuals on a map.  Residuals are the degree to which the explanatory variables actually fail to explain the dependent variable.  We can also check for autocorrelation, which is the degree to which data points that are spatially close to each other on a map have similar values.  There are 6 criteria to check the results from the ArcGIS OLS, by examination of the various statistics.  They include how well the variables help the model, whether any of the variables are redundant, whether the model is biased, either spatially across the study area or by magnitude of values, whether the relationships between explanatory and dependent variables are as we expected them, and if we have all necessary explanatory variables.  We can run an additional analysis called Exploratory Regression, that quickly looks at all possible combinations of as many and whichever of our explanatory variables as we want, and give us the statistics we need to decide which explanatory variables create the best model.  The key statistics are R-squared (adjusted), which tells us what percentage of the dependent variable is explained by the independent variables, and the AIC (Akaike's Information Criterion) is a relative factor that we use to compare several models to find the best-fitting one.