Use and Interpretation of Spatial Autoregressive Probit Models

35 Pages Posted: 23 Aug 2013

See all articles by Donald J. Lacombe

Donald J. Lacombe

West Virginia University - Regional Research Institute

James P. LeSage

Texas State University - McCoy College of Business Administration

Date Written: August 21, 2013

Abstract

Applications of spatial probit regression models that have appeared in the literature have incorrectly interpreted estimates from these models. Spatially dependent choices frequently arise in various modeling scenarios, including situations involving analysis of regional voting behavior, decisions by states or cities to change tax rates relative to neighboring jurisdictions, decisions by households to move or stay in a particular location, and so on. We use county-level voting results from the 2004 Presidential Election as an illustrative example of some issues that arise when drawing inferences from spatial probit model estimates. Although the voting example holds particular intuitive appeal that allows us to focus on interpretive issues, there are numerous other situations where these same considerations come into play. Past work regarding Bayesian Markov Chain Monte Carlo estimation of spatial probit models from LeSage and Pace (2009) is used, as well as derivations from LeSage, Pace, Campanella, Lam and Liu (2011) regarding proper interpretation of the partial derivative impacts from changes in the explanatory variables on the probability of voting for a candidate. As in the case of conventional probit models, the effects arising from changes in the explanatory variables depend in a non-linear way on the levels of these variables. In non-spatial probit regressions a common way to explore the non-linearity in this relationship is to calculate `marginal effects' estimates using particular values of the explanatory variables (e.g., mean values or quintile intervals). The motivation for this practice is consideration of how the impact of changing explanatory variable values varies across the range of values encompassed by the sample data. Given the non-linear nature of the normal cumulative density function (CDF) transform on which the (non-spatial) probit model relies, we know that changes in explanatory variable values near the mean may have a very different impact on decision probabilities than changes in very low or high values. For spatial probit regression models the effects or impacts from changes in the explanatory variables are more highly non-linear. In addition, since spatial models rely on observations that each represent a location or region located on a map, the levels of the explanatory variables can be viewed as varying over space. We discuss important implications of this for proper interpretation of spatial probit regression models in the context of our election application.

Keywords: spatial spillovers, spatial autoregressive probit model, spatial Durbin probit model, interpreting effects estimates

Suggested Citation

Lacombe, Donald J. and LeSage, James P., Use and Interpretation of Spatial Autoregressive Probit Models (August 21, 2013). Available at SSRN: https://ssrn.com/abstract=2314127 or http://dx.doi.org/10.2139/ssrn.2314127

Donald J. Lacombe

West Virginia University - Regional Research Institute ( email )

P.O. Box 6825
Morgantown, WV 26506-6825
United States
1-304-293-8543 (Phone)
1-304-293-6699 (Fax)

HOME PAGE: http://community.wvu.edu/~djl041/

James P. LeSage (Contact Author)

Texas State University - McCoy College of Business Administration ( email )

Finanace and Economics Department
601 University Drive
San Marcos, TX 78666
United States
512-245-0256 (Phone)
512-245-3089 (Fax)

HOME PAGE: http://www.spatial-econometrics.com

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