Hostname: page-component-848d4c4894-x5gtn Total loading time: 0 Render date: 2024-05-14T21:25:07.064Z Has data issue: false hasContentIssue false

The 50 American States in Space and Time: Applying Conditionally Autoregressive Models

Published online by Cambridge University Press:  18 December 2018

Joshua L. Jackson
Affiliation:
School of Public and International Affairs, University of Georgia, Athens, GA, USA
James E. Monogan III*
Affiliation:
School of Public and International Affairs, University of Georgia, Athens, GA, USA
*
*Corresponding author. Email: monogan@uga.edu

Abstract

Spatial conditionally autoregressive (CAR) models in a hierarchical Bayesian framework can be informative for understanding state politics, or any similar population of border-defined observations. This article explains how a hierarchical CAR model is specified and estimated and then uses Monte Carlo analyses to show when the CAR model offers efficiency gains. We apply this model to data structures common to state politics: A cross-sectional example replicates Erikson, Wright and McIver’s (1993) Statehouse Democracy model and a multilevel panel model example replicates Margalit’s (2013) study of social welfare policy preferences. The CAR model fits better in each case and some inferences differ from models that ignore geographic correlation.

Type
Original Articles
Copyright
Copyright © The European Political Science Association, 2018.

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Previous versions of this paper were presented at the 2010 Annual Summer Meeting of the Society for Political Methodology in Iowa City, IA, the 2011 State Politics and Policy Conference in Hanover, NH, the 2011 Annual Meeting of the American Political Science Association in Seattle, the 2014 Southeast Methods Meeting in Columbia, SC, the Department of Politics and International Relations at the University of Warwick, the Department of Politics at the University of Exeter, the School of Social and Political Science at the University of Glasgow, and the Studying Politics in Time and Space Conference in College Station, TX. Complete replication information, which users are welcome to adapt to their own applications, is available at: http://dx.doi.org/10.7910/DVN/ADFBT7.

References

Banerjee, S, Carlin, BPandGelfand, AE (2004) Hierarchical Modeling and Analysis for Spatial Data. New York: Chapman & Hall/CRC.Google Scholar
Bernardinelli, L, Clayton, DandMontomoli, C (1995) Bayesian Estimates of Disease Maps: How Important are Priors? Statistics in Medicine 14, 24112431.CrossRefGoogle ScholarPubMed
Berry, FSandBerry, WD (1990) State Lottery Adoptions as Policy Innovations: An Event History Analysis. The American Political Science Review 84(2), 395415.CrossRefGoogle Scholar
Berry, FSandBerry, WD (2007) Innovation and Diffusion Models in Policy Research. In Paul A. Sabatier (ed., Theories of the Policy Process. Boulder, CO: Westview Press.Google Scholar
Besag, J, York, JandMollié, A (1991) Bayesian Image Restoration, with Two Applications in Spatial Statistics. Annals of the Institute of Statistical Mathematics 43(1), 120.CrossRefGoogle Scholar
Best, NG, Waller, LA, Thomas, A, Conlon, EMandArnold, RA (1999) Bayesian Models for Spatially Correlated Disease and Exposure Data. In J.M. Bernardo, J.O. Berger, A.P. Dawid and A.F.M. Smith ed. Bayesian Statistics 6. New York: Oxford University Press.Google Scholar
Brook, D (1964) On the Distinction between the Conditional Probability and the Joint Probability Approaches in the Specification of Nearest-Neighbour Systems. Biometrika 51, 481483.CrossRefGoogle Scholar
Darmofal, D (2009) Bayesian Spatial Survival Models for Political Event Processes. American Journal of Political Science 53, 241257.CrossRefGoogle Scholar
Erikson, RS, Wright, GCandMcIver, JP (1993) Statehouse Democracy: Public Opinion and Policy in the American States. New York: Cambridge University Press.Google Scholar
Franzese, RJ Jr.andHays, J (2007) Spatial Econometric Models of Cross-Sectional Interdependence in Political Science Panel and Time-Series-Cross-Section Data. Political Analysis 15(2), 140164.CrossRefGoogle Scholar
Gelman, AandRubin, DB (1992) Inference from Iterative Simulation Using Multiple Sequences. Statistical Science 7, 457511.CrossRefGoogle Scholar
Gill, J (2001) Whose Variance is it Anyway? Interpreting Empirical Models with State-Level Data. State Politics and Policy Quarterly 1(3), 318338.CrossRefGoogle Scholar
Gray, V (1973) Innovation in the States: A Diffusion Study. The American Political Science Review 67(4), 11741185.CrossRefGoogle Scholar
Lambert, DM, Brown, JPandFlorax, RJGM (2010) A Two-Step Estimator for a Spatial Lag Model of Counts: Theory, Small Sample Performance and an Application. Regional Science and Urban Economics 40(4), 241252.CrossRefGoogle Scholar
Leroux, BG (2000) Modelling Spatial Disease Rates Using Maximum Likelihood. Statistics in Medicine 19(17-18), 23212332.3.0.CO;2-#>CrossRefGoogle ScholarPubMed
LeSage, JP (1997) Bayesian Estimation of Spatial Autoregressive Models. International Regional Science Review 20(1 & 2), 113129.CrossRefGoogle Scholar
Margalit, Y (2013) Explaining Social Policy Preferences: Evidence from the Great Recession. American Political Science Review 107(1), 80103.CrossRefGoogle Scholar
McMillen, DP (1992) Probit with Spatial Autocorrelation. Journal of Regional Science 32(3), 335348.CrossRefGoogle Scholar
Monogan, JE III (2013a) Modeling Policy Adoption and Impact with Multilevel Methods. In Marc A. Scott,Jeffrey S. Simonoff and Brian D. Marx ed. The SAGE Handbook of Multilevel Modeling. Thousand Oaks, CA: Sage.Google Scholar
Monogan, JE III (2013b) The Politics of Immigrant Policy in the 50 U.S. States, 2005-2011. Journal of Public Policy 33(1), 3564.CrossRefGoogle Scholar
Stimson, JA (1985) Regression Models in Space and Time: A Statistical Essay. American Journal of Political Science 29, 914947.CrossRefGoogle Scholar
Wall, MM (2004) A Close Look at the Spatial Structure Implied by the CAR and SAR Models. Journal of Statistical Planning and Inference 121(2), 311324.CrossRefGoogle Scholar
Ward, MDandGleditsch, KS (2008) Spatial Regression Models. Thousand Oaks, CA: Sage.CrossRefGoogle Scholar
Supplementary material: Link

Jackson and Monogan dataset

Link
Supplementary material: PDF

Jackson and Monogan supplementary material

Online Appendix

Download Jackson and Monogan supplementary material(PDF)
PDF 333.2 KB