About Aspatial Regression
Regression methods are a set of tools for assessing variation in one variable (the dependent variable, y) at set levels of another variable or variables (independent, or x variables). A simple regression line is included in scatter plots (when you have the Graph Statistics option selected) to aid in data exploration --here we discuss a more formalized approach to applying regression techniques to your data. Unlike measures of correlation, like those that also accompany the scatter plots in SpaceStat, these tools assume that there is a functional dependence of values of the dependent variable on the level of the independent variable or variables. Aspatial regression can be used to predict a dependent variable in terms of continuous and/or categorical independent variables, and to determine the relative importance of various independent variables in predicting y, including the importance of squared and interaction terms. Note that for SpaceStat to recognize a dataset as categorical, it must be a string (alphanumeric) dataset type.
Comparison with geographically weighted regression
"Aspatial" forms of regression are applied to all of the data within your dataset. In other words, they give you a measure of the global rather than local relationships between variables. If the relationship across space between the independent variable(s) and dependent variables does not change, the aspatial methods described here will give you results that are very similar to the results from the suite of methods that do allow you to generate local estimates, referred to as geographically weighted regression (GWR) techniques. We have implemented aspatial and geographically weighted regression using a unified approach, so you can run a GWR with equal weighting across space, and achieve the same results as you would have gotten from aspatial regression. To facilitate comparison, the dialog box in SpaceStat' task manager is shared between aspatial and GWR methods so that the same regression model can be used with both without having to retype the model structure. Remember that GWR is currently only available for point geographies, so if you want to be able to go back and forth between aspatial and GWR analyses for a polygon geography, perform your aspatial analyses on the polygon centroids.
As implied above, an important limitation of aspatial regression is that it ignores the spatial coordinates of the observations in the analysis. Aspatial regression methods are included in SpaceStat because they are commonly used, and because they provide a comparison with results obtained from GWR.
Choosing the form of the regression model
Regression methods are thoroughly discussed in many general statistical texts (e.g., Remington and Schork 1985, Zar 1999, Devore 2003) and in advanced, regression-focused texts (e.g., Kutner et al. 2004 ) and have been used to analyze data from a wide range of fields.
Three items will control the form of the regression model:
1. The nature of the dependent variable y:
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Continuous (linear or Gaussian model)
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Positive integer counts and rates (Poisson model)
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Binary variables (logistic model)
2. The nature of the explanatory, or "x" variable or variables:
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Continuous
3. The number of independent variables:
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Single variable (simple form)
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Multiple variables (multivariate form).
The help topics on regression are divided into sections on the three forms of aspatial regression that are included in SpaceStat: traditional linear models, Poisson models, and logistic models.
When you perform aspatial regression in SpaceStat, you can also choose between running the exact model that you define ("Full model"), or you can choose to do exploratory model building with one of the model selection tools.