Hot-Deck Imputation

Hot-Deck Imputation replaces missing data with comparable data from the same set. "Hot-deck imputation is a means of imputing data, using the data from other observations in the sample at hand." For example, suppose census officials were unable to count the number of people in a given house and decided to fill in the missing data using hot-deck imputation. They would use the data from a similar house in the same area, and substitute the number of people in that house for the missing data.

"Although imputation was used in the 1940 and 1950 censuses to determine characteristics of the population, it was not used to determine the actual population count for apportionment purposes until 1960."

Hot-Deck Imputation may be used in the 2010 census. It is controversial for two reasons. First, the Constitution requires Actual Enumeration. Second, this type of imputation could easily be used to gerrymander districts in a fashion which will favor Obama's reelection.

This paper from the U.S. Bureau of the Census describes the Hot-Deck method in detail: http://analytics.ncsu.edu/sesug/1999/075.pdf

In surveying adults on probation, the Census Bureau follows six requirements:

1. We impute age, race and gender independently.
2. For race, we first try to base imputation on other data (e.g., ethnicity) for the same person.
3. We impute all remaining missing values using only "good" unimputed) data for another person in the same group, or ctrlnum.
4. We use each "good" data value only once for imputation.
5. We work backwards over the ctrlnum; then, if necessary, we work forwards.
6. If no "good" data can be used from within the ctrlnum, we assign some type of "out of range" value.

Utah v. Evans

Utah v. Evans, 182 F. Supp. 2d 1165 (2001) is the leading court case about the use of Hot-Deck Imputation in the census. After the use of Hot-Deck techniques in the 2000 census, one of Utah's congressional seats was appointed to North Carolina. Utah challenged this, on the grounds that Hot-Deck Imputation is a form of sampling, and "violated various statutory provisions and the Constitution."

The District Court for the District of Utah, Central Division stated "We begin by noting that section 195 does not preclude the Census Bureau from the use of every type of statistical methodology in arriving at apportionment figures during a decennial census. Instead, it prohibits only "the use of the statistical method known as 'sampling.'"

"[H]ot deck imputation is not sampling. Sampling is the selection of a subset of units from a larger population in such a way that each unit of the population has a known chance of selection. Sampling is used where a scientifically selected set of units can be used to represent the entire population from which they are drawn."

The Court concluded "that the Constitution does not prohibit the use of narrowly tailored statistical methodologies, such as hot deck imputation, for the purpose of improving the accuracy of the decennial census and furthering "the constitutional goal of equal representation."

Problems with Hot-Deck Enumeration

Quoting Article I of the Constitution, the Utah v. Evans court said, "The final part of the sentence says that the “actual Enumeration” shall take place “in such Manner as” Congress itself “shall by Law direct,” thereby suggesting the breadth of congressional methodological authority, rather than its limitation." The text of the constitution and the courts interpretation of that text both state clearly that the census is the responsibility of Congress. But President Obama is having the White House run the 2010 census. This is an unconstitutional, dangerous violation of Separation of Powers.