Statistical Methods: Traditional Regression Analysis

The term traditional regression analysis implies any multivariate linear regression models in the form of Y = Xb + e, where bold letters are used because they represent matrices or vectors (a special type of matrix). When dealing with a categorical dependent variable, binary (or multinomial) logistic regression is our choice (e.g., An et al. 2002, Liu et al accepted). When applying these models on a CHES (e.g., often spatially explicit) basis, special care has been paid to potential spatial autocorrelation among data records: knowing data at one record (location) would automatically shed light upon knowledge about data at nearby or adjacent records or locations. This is a violation of a key assumption in regard to independence among data records in regression analysis.

One way to handle this problem is to subsample the data such that the selected records or data points are less or minimally subject to spatial autocorrelation. We conduct this subsampling process through two primary ways of 1) random sampling or 2) selecting data points that are apart from one another at a distance that is not less than the range of the corresponding semivariogram. More recent efforts have been devoted to the spatial filtering approach in terms of the Getis filtering or eigenvector spatial filtering methods. Below are several CHES-related papers that use traditional regression analysis to understand human or landscape processes and a few books that introduce the basics of regression analysis.

Readings and References:

An, L., F. Lupi, J. Liu, M. Linderman, and J. Huang (2002). Modeling the choice to switch from fuelwood to electricity: Implications for giant panda habitat conservation. Ecological Economics 42(3):445-457.

An, L., J. Liu, Z. Ouyang, M. Linderman, S. Zhou, and H. Zhang (2001). Simulating demographic and socioeconomic processes on household level and implications for giant panda habitats. Ecological Modelling 140:31-49.

Clark, W.A.V., and P.L. Hosking (1986). Statistical Methods for Geographers. John Wiley & Sons: New York.

Liu, Y., Dai, J., S. Yang, R. Bilsborrow, M. Wang, and L. An (accepted). Measuring neighborhood impacts on out-migration from Fanjingshan National Nature Reserve, China. Spatial Demography.

Sullivan, A., A.M. York, L. An, S.T. Yabiku, and S.J. Hall (2017). How does perception at multiple levels influence collective action in the commons? The case of Mikania micrantha in Chitwan, Nepal. Forest Policy and Economics 80:1-10.

Wang, N., D.G. Brown, L. An, S. Yang, and A. Ligmann-Zielinska (2013). Comparative performance of logistic regression and survival analysis for detecting spatial predictors of land-use change. International Journal of Geographic Information Science 27(10):1960-1982.

Wong, D.W.S., and J. Lee (2005). Statistical Analysis of Geographic Information with ArcView and ArcGIS. Wiley: Hoboken, NJ.

Yost, A., L. An, R. Bilsborrow, L. Shi, X. Chen, and W. Zhang (2020). Linking concurrent payments for ecosystem services in a Chinese nature reserve. Ecological Economics 169, 106509.

Examples, Models, and/or Documents:

Syllabus of regression analysis