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Using a Regression Approach to Estimate Persons per Household and Vacancy Rates in the Production of Housing Unit-Based Population Estimates

Working Paper Number POP-WP085
Kirsten K. West, Bashir Ahmed, Antonio Bruce, and D.H. Judson


In 2007, the Population Division of the U.S. Census Bureau started a project to explore strategies for producing county level housing unit-based population estimates. The Housing Unit Method relies on the number of occupied housing units and the average number of persons per household (PPH) at a particular time. Research by Smith et al. (2002) confirmed that regression models based on symptomatic indicators of PPH change can produce more precise and less biased county PPH estimates than methods that rely on the most recent decennial census for estimation. Following their work, we tested different models and produced county level predicted PPH estimates for 2000 based on the regression results. The regression based PPH estimates were evaluated by comparisons to the PPH values in Census 2000 and PPH estimates based on alternative methods.

The regression approach looks promising for PPH estimation in postcensal years. The selected independent variables explained over 90 percent of the variation in some models for both 1990 and 2000. Measures such as the Mean Absolute Percent Error (MAPE) for the regression based PPH suggest that the error is less than 2 percent in these models. In comparison, were we to keep constant the 1990 PPH values throughout the decade, we would generate an error of 4.2 percent and introduce an upward bias close to 3.8 percent. If we kept constant the change observed in the previous decade, we would find the MAPE to be 3.4 percent and the predicted PPH in 2000 to be lower by 2.5 percent than the actual PPH. Finally, applying the change observed for a state for each county within that state yields a predicted PPH that is 1.4 percent higher than the actual PPH.

We were not successful in using the regression approach to estimate occupancy (percent vacant.)


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