AN APPLICATION OF BAYESIAN METHODS TO SMALL AREA ESTIMATES OF POVERTY RATES

Joey CampbellCorey SparksThe University of Texas at San AntonioDepartment of Demography

INTRODUCTION

Estimates of various socio-demographic variables for small geographical areas are proving difficult with the replacement of the Census long form with the American Community Survey (ACS).

Sub-national demographic processes have generally relied on Census 2000 long form data products in order to answer research questions.

INTRODUCTION

ACS data products promise to begin providing up-to-date profiles of the nation's population and economy

Unit and item level non-response in the ACS have left gaps in sub-national coverage

The result is unstable estimates for basic demographic measures.

PURPOSE

Borrowing information from neighboring areas with a spatial smoothing process based on Bayesian statistical methods

Generate more stable estimates of rates for geographic areas not initially represented in the ACS.

A spatial smoothing process grounded in Bayesian statistics, is used to derive estimates of poverty rates at the county level for the United States.

Data come from two sources US Census 2000 Summary File 3 American Community Survey

2001 – 2005 1-year estimates 2005 – 2007, 2006 – 2008 3-year estimates 2005 – 2009 5-year estimates

U.S. Counties N=3,141 (Continental) 2000 Census is missing poverty rates for 0 counties ACS is missing poverty rates for up to 3,123 counties for

some years Primarily due to small population sizes of counties

ESTIMATING COUNTY-LEVEL RATES

Bayesian Statistics Combines observed data with prior

information to “strengthen” estimates for parameters of interest

Allows posterior estimation of these parameters using likelihood and prior information

METHODS: BAYESIAN HIERARCHICAL MODEL

Bayesian Statistics Uses Prior information for estimation of parameters of

interest Allows for posterior estimation of these parameters using the

combination of the information in the likelihood and the prior

Hierarchical Modeling Bayesian Hierarchical Model Allows for a spatially and temporally smoothed estimate of

rates Draws “strength” from neighboring observations Estimated with WinBUGS via Markov–Chain Monte Carlo

methods 100,000 simulations with 20,000 burn in period

THE MODELS yi ~ bin(pi, ni) logit(pi) = μ0 + Ai + Bj + Cij

THE MODELS yi ~ bin(pi, ni) logit(pi) = μ0 + Ai + Bj + Cij

Overall rate

The spati

al grou

p

THE MODELS yi ~ bin(pi, ni) logit(pi) = μ0 + Ai + Bj + Cij

Overall rate

The time grou

p

The spati

al grou

p

THE MODELS yi ~ bin(pi, ni) logit(pi) = μ0 + Ai + Bj + Cij

Overall rate

The spati

al grou

p

The space -

time grou

p

The time grou

p

THE MODELS yi ~ bin(pi, ni) logit(pi) = μ0 + Ai + Bj + Cij

Overall rate

THE MODELS

yi ~ bin(pi, ni) logit(pi) = μ0 + Ai + Bj + Cij

Summary of Model Specification

Spatial Terms

Temporal Terms

Space-time

Terms

Model Ai Bj Cij

1 vi + ui βtj 0

2 vi + ui tj 0

3 vi + ui tj + ξj 0

4 vi + ui tj ψij

5 vi + ui tj + ξj ψij

6 vi + ui tj ψijEach model was evaluated with respect to how it recreated the overall poverty rate, the known time trend, and the known spatial distribution

RESULTS: OVERALL POVERTY RATE

The overall estimate of U.S. poverty in 2001 according to SAIPE = 13.74 percent. Model 1 = 13.97 percent Model 2 = Model 3 =13.96 percent Model 4 = Model 5 = 14.15 percent, and Model 6 = 14.17 percent.

Overall, the Bayesian models produce similar rates of those estimated by more traditional methods.

RESULTS: ERROR RATES

Mean Absolute Percent Error (MAPE) Rates for Bayesian Estimates of US County Poverty Rates compared to SAIPE

Model 2001 2002 2003 2004 2005 2006 2007 2008 2009 Total

1 11% 10.6%

10.8%

11.2% 8.8% 9.3% 9.8% 10.9

%13.1%

11.5%

2 10.5% 10% 10.4

%11.1% 8.2% 9.1% 9.8% 11% 13% 10.3

%

3 10.5% 10.4% 10.4% 11.1% 8.2% 9.1% 9.8% 11.0% 13.0% 10.3%

4 10.6% 11.8% 12.0% 13.1% 10.3% 11.0% 10.6% 11.1% 11.7% 11.3%

5 10.6% 11.8% 12.0% 13.1% 10.3% 11.0% 10.6% 11.1% 11.7% 11.3%

6 10.7% 11.9% 12.2% 13.2% 10.3% 11.0% 10.5% 10.8% 11.8% 11.3%

DISCUSSION

Although the estimates of various socio-demographic variables in the ACS have improved over time, progress is not as fast as expected

Local level efforts have been advocated to help combat various outcomes associated with poverty.

Consequently, reliable estimates for small areas are necessary for these efforts to move forward

DISCUSSION

The Bayesian approach has been demonstrated to produce reliable and dependable estimates by borrowing information both across time and from neighboring counties

Hopefully these estimates (and this method) can be employed to effectively understand how socio-demographic variables vary at the local level

Additionally, models may be formulated that incorporate ACS errors directly (Bayesian SEM)