Journal of Population Research

, Volume 31, Issue 4, pp 345–359 | Cite as

Spatial weighting improves accuracy in small-area demographic forecasts of urban census tract populations

  • Jack Baker
  • Adélamar Alcántara
  • Xiaomin Ruan
  • Kendra Watkins
  • Srini Vasan


Existing research in small-area demographic forecasting suffers from two important limitations: (1) a paucity of studies that quantify patterns of error in either total or age/sex-specific estimates and (2) limited methodological innovation aimed specifically at improving the accuracy of such forecasts. This paper attempts to fill, in part, these gaps in existing research by presenting a comparative evaluation of the accuracy of standard and spatially-weighted Hamilton–Perry forecasts for urbanized census tracts within incorporated New Mexico municipalities. These comparative forecasts are constructed for a 10-year horizon (base 1 April 2000 and target 1 April 2010), then compared to the results of the 2010 Census in an ex post facto evaluation. Results are presented for the standard Hamilton–Perry forecasts as well as two sets that incorporate two common variants of spatial weights to improve forecast accuracy. Findings are discussed in the context of what is currently known about error in small-area demographic forecasts and with an eye toward continued innovations.


Small-area estimation Demography Forecasts Urban Census tract 



This manuscript has been greatly improved by the suggestions made by two anonymous referees as well as Dr. Elin Charles-Edwards, Associate Editor for the Journal of Population Research. This research was supported by an annual appropriation to Geospatial and Population Studies by the Legislature of the State of New Mexico to support the Census Data Dissemination and Demographic Analysis project. While we wish to acknowledge these contributions, any errors or omissions in either logic or content remain the responsibility of the authors.


  1. Alba, R., Logan, J., & Stults, B. (2000). How segregated are middle-class African-Americans. Social Problems, 47(4), 543–558.CrossRefGoogle Scholar
  2. Armstrong, C. M., & Harris, M. (1949). A method of predicting school-age population. Albany: State University of New York, State Education Department.Google Scholar
  3. Baker, J., Alcantara, A., Ruan, X. M., Ruiz, D., & Crouse, N. (2014). Sub-county population estimates using administrative records: A municipal-level case study in New Mexico. In Nazrul Hoque & Lloyd Potter (Eds.), Emerging techniques in applied demography. New York: Springer.Google Scholar
  4. Baker, J., Alcantara, A., Ruan, X. M., & Watkins, K. (2012). The impact of incomplete geocoding on small area population estimates. Journal of Population Research, 29, 91–112.CrossRefGoogle Scholar
  5. Baker, J., Alcantara, A., Ruan, X. M., Watkins, K., & Vasan, S. (2013). A comparative evaluation of error and bias in census tract-level age/sex-specific population estimates: Component I (Net-migration) vs Component III (Hamilton–Perry). Population Research and Policy Review, 32, 919–942.CrossRefGoogle Scholar
  6. Baker, J., Ruan, X. M., Alcantara, A., Jones, T., Watkins, K., McDaniel, M., et al. (2008). Density-dependence in urban housing unit growth: An evaluation of the Pearl-Reed model for predicting housing unit stock at the census tract level. Journal of Economic and Social Measurement, 33, 155–163.Google Scholar
  7. Best, N., & Wakefield, J. (1999). Accounting for inaccuracies in population counts and case registration in cancer mapping studies. Journal of the Royal Statistical Society: Series A (Statistics in Society)., 162(3), 363–382.CrossRefGoogle Scholar
  8. Cai, Q. (2007). New techniques in small area population estimates by demographic characteristics. Population Research and Policy Review, 26, 203–218.CrossRefGoogle Scholar
  9. Cavanaugh, F. (1981). The Census Bureau’s 1980 Census Test of Population Estimates. In Small-area population estimatesmethods and their accuracy and new metropolitan area definitions and their impact on the private and public sector, Series GE-41, No. 7. Washington, DC: Government Planning Office.Google Scholar
  10. Centers for Disease Control (CDC). (1999). National Program of Cancer Registries cancer surveillance system rationale and approach. Atlanta.Google Scholar
  11. Chi, G., & Voss, P. (2011). Small-area population forecasting: Borrowing strength across space and time. Population, Space, and Place., 17, 505–520.Google Scholar
  12. Chi, G., & Zhu, J. (2008). Spatial regression models for demoraphic analysis. Population Research and Policy Review, 27, 17–42.CrossRefGoogle Scholar
  13. de Miguel, V., Garlappi, L., & Uppal, R. (2007). Optimal versus naive diversification: How inefficient is the 1/N portfolio strategy. Journal of Finance., 22(5), 1915–1953.Google Scholar
  14. Dietzel, C., & Clarke, K. (2007). Research article. Toward optimal calibration of the SLEUTH land use change model. Transactions in GIS, 11(1), 29–45.CrossRefGoogle Scholar
  15. Drummond, W. J. (1995). Address matching: GIS technology for mapping human activity patterns. Journal of the American Planning Association, 61(2), 240–251.CrossRefGoogle Scholar
  16. Duncan, O., & Duncan, B. (1955). A methodological analysis of segregation indexes. American Sociological Review, 20(2), 210–217.CrossRefGoogle Scholar
  17. Fabricant, R., & Weinman, J. (1972). Forecasting first grade public school enrollment by neighborhood. Demography, 9(4), 625–634.CrossRefGoogle Scholar
  18. Fellegi, I. P. (1968). Coverage Check of the 1961 Census of Population. Technical Memorandum (Census Evaluation Series). No. 2, Dominion Bureau of Statistics.Google Scholar
  19. Frotheringham, A., Brundson, C., & Charlton, M. (2002). Geographically weighted regression: The analysis of spatially-varyiugn relationships. West Sussex: Wiley.Google Scholar
  20. George, M. V. (2004). Population projections. In J. Siegel & D. Swanson (Eds.), The methods and materials of demography. New York: Springer.Google Scholar
  21. Getis, A. (2009). Spatial weight matrices. Geographical Analysis, 41(4), 404–410.CrossRefGoogle Scholar
  22. Getis, A., & Aldstadt, J. (2004). Constructing the spatial weights matrix using a local statistic. Geographical Analysis, 36(2), 90–104.CrossRefGoogle Scholar
  23. Gilboa, S. M. (2006). Comparison of residential geocoding methods in a population-based study of air quality and birth defects. Environmental Research, 101, 256–262.CrossRefGoogle Scholar
  24. Goldberg, D. W., Wilson, J. P., & Knoblock, C. A. (2007). From text to geographic coordinates: The current state of geocoding. URISA Journal, 19(1), 33–46.Google Scholar
  25. Haining, R. (2003). Spatial data analysis: Theory and practice. New York: Cambridge University Press.Google Scholar
  26. Hamilton, C., & Perry, J. (1962). A short method for projecting population by age from one decennial census to another. Social Forces, 41(2), 163–170.CrossRefGoogle Scholar
  27. Harris, R., Sleight, P., & Webber, R. (2005). Geodemographics, GIS, and neighborhood targeting. New York: Wiley.Google Scholar
  28. Herold, M., Goldstein, N., & Clark, K. C. (2003). The spatiotemporal form of urban growth: Measurement, analysis, and modeling. Remote Sensing of Environment, 86, 286–302.CrossRefGoogle Scholar
  29. Hogan, H. (1992). The 1990 post-enumeration survey: An overview. The American Statistician, 46(4), 261–269.Google Scholar
  30. Hogan, H. (1993). The 1990 post-enumeration survey: Operations and results. Journal of the American Statistical Association, 88, 1047–1060.CrossRefGoogle Scholar
  31. Hogan, J., & Tchernis, R. (2004). Bayesian factor analysis for spatially-correlated data, with application to summarizing area-level material deprivation from census data. Journal of the American Statistical Association, 99(466), 314–324.Google Scholar
  32. Hoque, N. (2010). An evaluation of small area population estimates produced by component method ii, ratio correlation, and housing unit methods for 1990. The Open Demography Journal, 3, 18–30.CrossRefGoogle Scholar
  33. Hund, L., Chen, J., Krieger, N., & Coull, B. (2012). A geostatistical approach to large-scale disease mapping with temporal misalignment. Biometrics, 68(3), 849–858.CrossRefGoogle Scholar
  34. Karimi, H. A., & Durcik, M. (2004). Evaluation of uncertainties associated with geocoding techniques. Computer-aided Civil and Infrastructural Engineering, 19, 170–185.CrossRefGoogle Scholar
  35. Keyfitz, N. (1981). The limits of population forecasting. Population and Development Review, 7(4), 579–593.CrossRefGoogle Scholar
  36. Kuldorff, M. (1997). A spatial scan statistic. Communication in Statistics: Theory and Methods, 26, 1481–1496.CrossRefGoogle Scholar
  37. Kuldorff, M. (1999). An isotonic spatial scan statistic for Geographical Disease Surveillance. Journal of the National Institute of Public Health., 48, 94–101.Google Scholar
  38. Landis, J., & Zhang, M. (1998). The second generation of the California urban futures model: Part 2, Specification and calibration results of the land use change submodel. Environment and Planning B., 25, 795–842.CrossRefGoogle Scholar
  39. Le Sage, J., & Pace, K. R. (2004). Models for spatially-dependent missing data. Journal of Real Estate Finance and Economics, 29(2), 233–254.CrossRefGoogle Scholar
  40. Leach, D. (1981). Re-evaluation of the logistic curve for human populations. Journal of the Royal Statistical Society, 144, 94–103.CrossRefGoogle Scholar
  41. Legare, J. (1972). Methods for measuring school performance through cohort analysis. Demography, 9(4), 617–624.CrossRefGoogle Scholar
  42. Long, J. (1995). Complexity, accuracy, and the utility of official population projections. Mathematical Population Studies, 5(3), 203–216.CrossRefGoogle Scholar
  43. Markowitz, H. M. (1952). Portfolio selection. Journal of Finance., 7, 77–91.Google Scholar
  44. Massey, D., & Denton, N. (1985). Spatial assimilation as a socioeconomic outcome. American Sociological Review, 50(1), 94–106.CrossRefGoogle Scholar
  45. McKibben, J. (1996). The impact of policy changes on forecasting for school districts. Population Research and Policy Review, 15(5–6), 527–536.Google Scholar
  46. Myers, J. K. (1954). Note on the homogeneity of census tracts: A methodological problem in urban ecological research. Social Forces, 32, 364–366.Google Scholar
  47. Oliver, M. N. (2005). Geographic bias related to geocoding in epidemiologic studies. International Journal of Health Geographics. 4(29): Online.Google Scholar
  48. Pace, K., & Gilly, O. R. (1997). Using the spatial configuration of data to improve estimation. The Journal of Real Estate Finance and Economics, 14(3), 330–340.CrossRefGoogle Scholar
  49. Patacchini, E., & Zenou, Y. (2007). Spatial dependence in local unemployment rates. Journal of Economic Geography, 7(2), 169–191.CrossRefGoogle Scholar
  50. Pflaumer, P. (1992). Forecasting US population totals with the Box-Jenkins approach. International Journal of Forecasting, 8, 329–338.CrossRefGoogle Scholar
  51. Schmid, C., & Shanley, F. (1952). Techniques of forecasting university enrollment. Tested empirically by deriving forecasts of enrollment for the University Of Washington. The Journal of Higher Education, 23(9), 483–488–502–503.CrossRefGoogle Scholar
  52. Schmitt, A., & Crosetti, A. (1954). Accuracy of the ratio-correlation method for estimating postcensal population. Land Economics, 30, 279–281.CrossRefGoogle Scholar
  53. se Can, A., & Megbolugbe, I. (1997). Spatial dependence in house price index construction. Journal of Real Estate Finance and Economics., 14(1–2), 203–222.CrossRefGoogle Scholar
  54. Smith, S. (1987). Tests of forecast accuracy and bias for county population projections. Journal of the American Statistical Association, 82(400), 991–1003.CrossRefGoogle Scholar
  55. Smith, S., & Shahidullah, M. (1995). An evaluation of projection errors for census tracts. Journal of the American Statistical Association, 90(429), 64–71.CrossRefGoogle Scholar
  56. Smith, S., & Sincich, T. (1992). The relationship between length of the base period and population forecast errors. Journal of the American Statistical Association, 85(410), 367–375.CrossRefGoogle Scholar
  57. Smith, S., Tayman, J., & Swanson, D. (2001). State and local population projections: Methodology and analysis. New York: Plenum.Google Scholar
  58. Stoto, M. (1983). The accuracy of population projections. Journal of the American Statistical Association, 78(381), 13–20.CrossRefGoogle Scholar
  59. Swanson, D., Schlottman, A., & Schmidt, B. (2010). Forecasting the population of census tracts by age and sex: An example of the Hamilton–Perry method in action. Population Research and Policy Review, 29(1), 47–63.CrossRefGoogle Scholar
  60. Swanson, D., & Tayman, J. (2012). Subnational population estimates. New York: Springer.CrossRefGoogle Scholar
  61. Tayman, J. (1999). On the validity of MAPE as a measure of forecast accuracy. Population Research and Policy Review, 18(4), 299–322.CrossRefGoogle Scholar
  62. Tayman, J., Schafer, E., & Carter, L. (1998). The role of population size in the determination and prediction of population forecast errors: An evaluation using confidence intervals for subcounty areas. Population Research and Policy Review, 17(1), 1–20.CrossRefGoogle Scholar
  63. Tobler, W. R. (1979). Smooth pycnophylactic interpolation for geographical regions. Journal of the American Statistical Association, 74, 519–530.CrossRefGoogle Scholar
  64. Vasan, S., Alcantara, A., Nefertari, N., Ruan, X. M., & Baker, J. (2014). Geography is destiny: Spatial correlations in poverty and educational attainment in a New Mexico School District. In Nazrul Hoque & Lloyd Potter (Eds.), Emerging techniques in applied demography. New York: Springer.Google Scholar
  65. Voss, P., & Kale, B. (1985). Refinements to small-area population projection models: Results of a test based on 128 Wisconsin communities. Presented at the Annual Meeting of the Population Association of America. 28–30 March.Google Scholar
  66. Voss, P. R., Long, D. D., & Hammer, R. B. (1999). When census geography doesn’t work: Using ancillary information to improve the spatial interpolation of demographic data. Center for Demography and Ecology, University of Wisconsin, Madison. Working Paper No. 99–26.Google Scholar
  67. Ward, D., Murray, A., & Phinn, S. (2000). A stochastically constrained cellular model of urban growth. Computers, Environment and Urban Systems, 24(6), 539–558.CrossRefGoogle Scholar
  68. White, H. R. (1954). Empirical study of selected methods of projecting state population. Journal of the American Statistical Association, 49, 480–498.Google Scholar
  69. Witmer, J. A., & Samuels, M. L. (1998). Statistics for the life sciences. New York: Sinauer.Google Scholar
  70. Zandbergen, P. (2009). Geocoding quality and implications for spatial analysis. Geography Compass, 3(2), 647–680.Google Scholar
  71. Zitter, M. (1954). Forecasting school enrollment for the United States and local areas. Journal of Teacher Education, 5(1), 53–63.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Jack Baker
    • 1
  • Adélamar Alcántara
    • 1
  • Xiaomin Ruan
    • 1
  • Kendra Watkins
    • 2
  • Srini Vasan
    • 1
  1. 1.Geospatial and Population Studies1 University of New MexicoAlbuquerqueUSA
  2. 2.Mid-Region Council of GovernmentsAlbuquerqueUSA

Personalised recommendations