Test Driving a Small-Area Population Forecasting Model:

Seeking Additional Horsepower through Updated Engineering and Non-Demographic Fuel Additives

Paul R. Voss and Guangqing ChiApplied Population Laboratory

Center for Demography and EcologyUniversity of Wisconsin – Madison

BSPS Annual Conference 2006

September 2006

The University of Southampton

Support provided by the Wisconsin Agricultural Experiment Station (Hatch project no. WIS04536)

Motivating Questions• What can be done to improve the abysmally atheoretical

nature of small-area population forecasts?• In particular, what about a regression approach?• Especially, what if we step outside our disciplinary confines

and incorporate variables from other fields that, at face value, must be predictors of population growth?

• nature of the land (ground cover, wetlands, hydrography, slope)• accessibility (transportation infrastructure, highways, airports, etc.)• developability (high/low growth potential)• desirability (natural and built amenities)• livibility (potential quality of living)

• And, surely, should we not begin immediately to adopt some of the spatial econometric approaches long effectively employed by quantitative geographers and regional scientists?

• Broaden our thinking regarding the relationships between population change and the host of factors influencing such change – some drawn from demography but many others from disciplines not normally involved in formal population forecasting efforts

• Categorize and integrate these factors in an effective way (construct indexes)

• Incorporate spatial process effects into the model• Carry out the forecasting at a sufficiently fine geogra

phic level that environmental and geophysical effects on population change can be better captured and modeled

Proposed Regression Approach

Strategy

• Assemble all necessary data for 1990 base year

• Forecast populations for 2000

• Compare 2000 forecasts with 2000 census results

Preview of Findings…

It didn’t work

Our Region1,837 minor civil divisions in state of Wisconsin, U.S.

Our Datacensus data

satellite imagery

other data from several federal and state statistical agencies

Population

Demographics

AccessibilityDevelopability

Livability Desirability

Temporal

Spatial

Population Change Conceptual framework

Population

Demographics

AccessibilityDevelopability

Livability Desirability

Temporal

Spatial

Population Change Conceptual frameworkLocal demographic characteristics----------------------------------------------Population densityAge: the young and the oldMinority: black and HispanicInstitutional population (college)Education attainment: HS and Bchl.Geographic mobilityPovertySeasonal housingSustenance organization: retail and agricultural industrial structure

Population

Demographics

AccessibilityDevelopability

Livability Desirability

Temporal

Spatial

Population Change Conceptual framework

Transportation infrastructure--------------------------------------Residential preferenceHighway infrastructureAccessibility to airportsAccessibility to highwaysAccessibility to workplaces

Population

Demographics

AccessibilityDevelopability

Livability Desirability

Temporal

Spatial

Population Change Conceptual framework

The potential for land conversion & development-----------------------------------WaterWetlandsSlopeTax-exempt (protected) landsBuilt-up lands

Population

Demographics

AccessibilityDevelopability

Livability Desirability

Temporal

Spatial

Population Change Conceptual framework

Natural & built amenities desirable for living--------------------------ForestsWaterLakeshore/riverbank/ coastlineGolf coursesslope

Population

Demographics

AccessibilityDevelopability

Livability Desirability

Temporal

Spatial

Population Change Conceptual framework

Urban conditions suitable for living---------------------------SafetySchool performancePublic transportationBusesPublic waterNew housingCounty seatIncomeReal estate valueEmployment rate

Using Principal Components Analysis, We Developed Indices of Each of These

Conceptual Areas

Mapping the Indexes Confirmed What We know about the Areas

And the Indexes all Revealed Fairly Strong Autocorrelation

Demographics

Moran’s I = 0.2878 Moran’s I = 0.4260

Moran’s I = 0.4639 Moran’s I = 0.4882

Accessibility

Moran’s I = 0.3565

Developability

Moran’s I = 0.4089

Desirability

Moran’s I = 0.7849 Moran’s I = 0.7860

Livability

We Ran Lots of Regressions

Whatever the Approach, We Always Ran a Standard Normal Linear

Regression and then Corrected this Specification by Incorporating Spatial Effects (spatial lag and spatial error)

OLS:

90

90

00 XP

PLn

SLM:

90

0090

90

00

P

PWLnX

P

PLn

SEM:

90

90

0090

90

00 WXP

PWLnX

P

PLn

Standard regression Spatial lag model Spatial error model Variables Coef. p-value Coef. p-value Coef. p-value Constant 0.055 0.000 0.048 0.002 0.054 0.000 Demographics 1990 0.018 0.000 0.018 0.000 0.018 0.000 Accessibility 1990 -0.014 0.000 -0.014 0.000 -0.014 0.000 Desirability 0.006 0.057 0.006 0.064 0.006 0.066 Livability 1990 0.011 0.000 0.011 0.000 0.011 0.000 Developability 0.064 0.002 0.064 0.002 0.065 0.001 Spatial parameter (λ ) / / 0.064 0.135 0.063 0.147 Measures of fit Log likelihood 899.45 900.55 901.58 AIC -1786.9 -1787.11 -1791.16

Regressions without Any Temporal Consideration

OLS:

90

80

90

90

00 XP

PLn

P

PLn

SLM:

90

0090

80

90

90

00

P

PWLnX

P

PLn

P

PLn

SEM:

90

80

90

90

0090

80

90

90

00 XP

PLnW

P

PWLnX

P

PLn

P

PLn

Regressions with Temporal Consideration of Population Change

Standard regression Spatial lag model Spatial error model Variables Coef. p-value Coef. p-value Coef. p-value Constant 0.061 0.000 0.056 0.000 0.060 0.000 Population change 1980-90 0.277 0.000 0.276 0.000 0.276 0.000 Demographics 1990 0.012 0.000 0.012 0.000 0.012 0.000 Accessibility 1990 -0.011 0.000 -0.011 0.000 -0.011 0.000 Desirability 0.006 0.057 0.006 0.062 0.006 0.062 Livability 1990 0.009 0.000 0.009 0.000 0.009 0.000 Developability 0.051 0.011 0.051 0.010 0.052 0.010 Spatial parameter (λ ) / / 0.049 0.252 0.036 0.417 Measures of fit Log likelihood 942.28 942.93 943.62 AIC -1870.56 -1869.86 -1873.23

Regressions with Temporal Considerations of Population Change and Indices

OLS:

8090

80

90

90

00 XXP

PLn

P

PLn

SLM:

90

008090

80

90

90

00

P

PWLnXX

P

PLn

P

PLn

SEM:

8090

80

90

90

008090

80

90

90

00 XXP

PLnW

P

PWLnXX

P

PLn

P

PLn

Standard regression Spatial lag model Spatial error model Variables Coef. p-value Coef. p-value Coef. p-value Constant 0.056 0.000 0.051 0.001 0.056 0.000 Population change 1980-90 0.275 0.000 0.274 0.000 0.273 0.000 Demographics 1990 0.004 0.387 0.004 0.397 0.004 0.408 Demographics 1980 0.008 0.067 0.008 0.065 0.008 0.062 Accessibility 1990 -0.021 0.121 -0.021 0.124 -0.021 0.123 Accessibility 1980 0.010 0.462 0.010 0.472 0.010 0.470 Desirability 0.007 0.025 0.007 0.027 0.007 0.027 Livability 1990 0.009 0.108 0.009 0.109 0.009 0.109 Livability 1980 0.001 0.873 0.001 0.871 0.001 0.845 Developability 0.057 0.005 0.057 0.005 0.058 0.005 Spatial parameter (λ ) / / 0.049 0.250 0.039 0.384 Measures of fit Log likelihood 944.21 944.86 945.60 AIC -1868.42 -1867.72 -1871.19

Extrapolation projection

Baseline projection

Standard regressionPartial spatio-temporalregression

Full spatio-temporalregression

Dependent variables: population change, population density, population density changeIndices generating methods: PCA, coefficients, coefficients and correlations

Projections using indices

Population forecast adjustments

Evaluation and comparison

Projection using individual variables

Select the best one

Select the better one

Regression projection

Forecasting and Evaluation

Model 1: Extrapolation projection

P P G2 0 0 0 9 0 1 0

GP P P P P P

9 0 8 0 9 0 7 0 9 0 6 0

1 0 2 0 3 03

Model 2: Standard regression

L nP

PL n

P

PX

9 0

8 0

8 0

7 08 0

L nP

PL n

P

PX

0 0

9 0

9 0

8 09 0

Model 3: partial spatio-temporal regression(incorporating spatial population effects)

L nP

PL n

P

PX W L n

P

P neighbor

90

80

80

7080

80

70

L nP

PL n

P

PX W L n

P

P neighbor

0 0

9 0

9 0

8 09 0

9 0

8 0

L nP

PL n

P

PX W L n

P

PW X

neighborneighbor

9 0

8 0

8 0

7 08 0 1

8 0

7 02 8 0

( )

L nP

PL n

P

PX W L n

P

PW X

neighborneighbor

0 0

9 0

9 0

8 09 0 1

9 0

8 02 9 0

( )

Model 4: full spatio-temporal regression(incorporating spatial population effects

and other neighbor characteristics)

Four Finalized Population Forecasting Models

So… How did it turn out with all this re-engineering and fancy fuel additives?

Not well

Without adjustments Model 1: extrapolation

projection

Model 2: standard

regression

Model 3: partial spatio-

temporal regression

Model 4: full spatio-

temporal regression

MPE -5.80% -4.86% -7.46% -10.05% MAPE 10.99% 10.45% 11.35% 12.86%

RMSPE 15.48% 14.56% 15.20% 16.03% MedPE -6.04% -4.76% -7.34% -8.84%

MedAPE 8.41% 7.89% 9.07% 10.06%

Population growth rate (% MCDs)

≤ -10% (5.28%) 22.71% 24.18% 20.15% 18.66% -10% < ≤ -5% (5.77%) 8.94% 9.17% 6.67% 6.41% -5% < < 0% (9.96%) 6.17% 5.77% 4.36% 4.76%

0% (0.44%) 14.46% 3.53% 2.93% 3.51% 0% < < 5% (15.41%) 5.94% 3.86% 4.34% 5.06% 5% ≤ <10% (16.28%) 7.38% 4.88% 6.75% 7.75%

≥10% (46.87%) 13.84% 14.22% 16.41% 17.82% Population size (% MCDs)

0≤ ≤ 250 (6.42%) 17.63% 15.37% 15.11% 14.98% 250< ≤ 2,000 (71.31%) 10.73% 10.08% 11.14% 11.58%

2,000< ≤ 20,000 (20.25%) 10.46% 10.78% 11.58% 13.67% >20,000 (2.02%) 4.65% 4.48% 4.66% 12.33% Metro/NonMetro (% MCDs) Metropolis, and major city

(4.68%) 6.83% 9.00% 8.44% 13.64%

Metropolis, not major city

(22.70%) 9.27% 10.73% 11.51% 12.96%

Non-Metropolis (72.62%) 9.93% 10.46% 11.49% 11.92%

Population projections to 2000 without adjustments at the MCD level

With adjustments Model 1: extrapolation

projection

Model 2: standard

regression

Model 3: partial spatio-

temporal regression

Model 4: full spatio-

temporal regression

MPE -3.65% -3.79% -3.87% -3.81% MAPE 9.63% 10.69% 10.71% 10.65%

RMSPE 13.56% 14.97% 14.93% 14.84% MedPE -3.70% -4.21% -4.29% -4.25%

MedAPE 7.11% 8.19% 8.17% 8.08%

Population growth rate (% MCDs)

≤ -10% (5.28%) 23.81% 25.78% 25.36% 25.26% -10% < ≤ -5% (5.77%) 9.47% 11.13% 10.98% 11.11% -5% < < 0% (9.96%) 5.87% 7.32% 7.31% 7.24%

0% (0.44%) 4.20% 4.32% 4.70% 4.45% 0% < < 5% (15.41%) 4.50% 4.38% 4.36% 4.45% 5% ≤ <10% (16.28%) 5.23% 4.99% 5.01% 5.00%

≥10% (46.87%) 12.13% 17.36% 13.87% 13.73% Population size (% MCDs)

0≤ ≤ 250 (6.42%) 16.16% 15.25% 15.04% 14.78% 250< ≤ 2,000 (71.31%) 9.41% 10.25% 10.30% 10.25%

2,000< ≤ 2 0,000 (20.25%) 8.84% 11.33% 11.29% 11.25% >20,000 (2.02%) 4.61% 5.35% 5.53% 5.76% Metro/NonMetro (% MCDs) Metropolis, and major city

(4.68%) 6.83% 10.22% 9.86% 9.24%

Metropolis, not major city

(22.70%) 9.27% 12.09% 12.11% 11.91%

Non-Metropolis (72.62%) 9.93% 10.28% 10.33% 10.35%

Population projections to 2000 with adjustments at the MCD level

Summary• Things just didn’t turn out as we hypothesized (and

hoped) they would• Our fancy spatio-temporal model outperformed

simple regression in the estimation stage of the analysis (but who cares?)

• But, to our dismay, in the forecasting stage, the a-theoretical, simple extrapolation model outperformed the regression models in all comparisons but one

• In only one set of MCDs did the fancy model outperform all others: MCDs of fewer than 250 people. We launched this project in the belief that non-demographic variables might perform best in very small areas, and this finding may suggest that we explore that possibility further

Thanks!