Using Penalized Regression to Uncover Peer Effects in the Spatial Autoregressive Model

Undergraduate Honors Thesis

Citations

Citeable URL: https://scholar.colorado.edu/concern/undergraduate_honors_theses/wp988k39d

Abstract

We propose a technique for estimating the spatial weights matrix (SWM) of the spatial autoregressive model (SAR) using the least absolute shrinkage and selection operator (Lasso), first proposed by Tibshirani (1996). The SWM is typically assumed a priori as a known matrix of correlations among spatially correlated data, as it cannot be estimated using standard techniques due to overfitting. However, we use the Lasso to discover the most prominent spatial coefficients in the SWM and estimate them using feasible generalized least squares, while setting the relatively unimportant effects to zero. Furthermore, the Lasso solutions are optimized to minimize mean squared error over a grid of possible spatial lag parameters. Finally, we use the LARS-Lasso algorithm to compute an illustrative example of the technique.

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