As we continue to process 2020 Census responses, people have asked what happens when we don’t get a response from an address. In this blog, I’ll describe the statistical techniques we turn to when we do not get a response.

To get a complete and accurate census, we need to know certain information about every household address in the census:

• Whether it is a real and livable residence.
• If so, whether it is vacant or occupied.
• If it's occupied, how many people live there.
• Demographic characteristics about the people who live there, such as age, sex and race.

At the end of data collection, we had the information required to address the first three bullets on almost every address in the country. For the remaining small fraction of addresses, we apply a technique called count imputation to resolve whether they were occupied and how many people lived there.

During data processing, we also use another type of imputation — characteristic imputation — to fill in missing characteristics for people in the census.

In what follows, we distinguish between addresses for housing units and group quarters. We must answer similar questions about group quarters, but we treat the two differently in our data collection and in how we handle missing responses.

Below, I'll describe how we:

• Collect census data when we can't reach someone in the household.
• Use count imputation for the remaining housing units.
• Apply a different type of count imputation for group quarters.
• Apply characteristic imputation to handle missing demographic characteristics for housing units and group quarters. 

Our research has shown that the best information about a household comes from the household itself. However, some households didn’t respond even after the outreach efforts of nearly 400,000 partners across the country, a multilingual communications campaign, as well as a number of mailings and visits from census takers.

When we can’t get a response directly from an address, we look to three widely used statistical methods to fill the gaps:

• Administrative records. First, if a census taker can’t get a response from a household, administrative records enable us to count the household with information they have already provided to the government, such as through a response to a previous census or survey, to the IRS through a tax return, or to one of several other government programs. We only use records when we have confidence in their quality for the household. We talked more about how we use this existing information in the recent Administrative Records and the 2020 Census blog.
• Proxy responses. If high-quality administrative records aren’t available for an address after an initial visit, census takers continue to visit the address. If they still can’t get a response after three visits, they try to get information about the address from a neighbor, landlord or building manager. We refer to these as “proxy responses.” We also rely on these types of proxies to help us verify housing units that appear vacant or cannot be located.
• Imputation. As a last resort, we use a statistical technique called “imputation” to fill the gaps in a dataset. It makes the overall dataset — or census in this case — more accurate than leaving the gaps blank. By using imputation, we fill in what we don’t know, using information we do know.

We will provide metrics related to our use of each of these three techniques on the same day we release the first census results later this month. More information about these upcoming metrics is available in the recent Introduction to Quality Indicators: Operational Metrics blog.

One type of imputation we use is called “count imputation.” This type helps us fill in the information that leads to the count of people living in a household — the first three items in the list I mentioned above.

For example, we use imputation to fill in whether an address is occupied and the number of people who live there by copying information from the nearest, similar neighbor. Here’s how that works:

• To fill in missing information, we start by grouping every address based on what we’ve learned about it throughout the census process — information from our address list, data our census takers have gathered in the field, and other sources.
• For addresses that are missing information, we copy data from its nearest neighbor in the same group.

We use this approach because it works well where vacant housing and houses of a similar size are clustered geographically. As a result, we can insert missing information about an address’s occupancy status and population size more accurately.

If we were to leave the count for an address blank after all attempts to obtain a response failed, it would be like assigning a count of 0. This would be less accurate overall than imputing a number statistically, since we often have information that people are living there.

It is important to note that count imputation for households has been used to complete the census count going back to the 1960 Census. Using this statistical method was challenged in the courts following the censuses of 1980 and 2000. Each time the courts upheld the use of count imputation.  

After we finish processing 2020 Census responses, we will report what percentage of the count comes from count imputation.

• In each of the last five censuses, count imputation made up less than half of 1 percent of the total population count.
• In 2010, 0.4 percent of the population count was imputed.
• This decade, we expect a similarly small percentage of addresses will need count imputation because they were not accounted for during our data collection operations.
• However, in the 2020 Census, the overall rate of count imputation will increase relative to 2010 for a different reason.

During our recent post-processing activities, we incorporated a new operation that removed a large number of people duplicated in the 2020 Census. (We’ll discuss this more in an upcoming blog.) This operation left a small set of household addresses unresolved and in need of count imputation.

As a result, when we report later this month on the percentage of addresses and people imputed, we will also report its two components:

• The percentage unresolved after data collection.
• The percentage unresolved because of unduplication.

Group quarters are residences where typically a number of unrelated people live, such as a college dormitory, a nursing home or a state prison.

As described in more detail in the 2020 Census Group Quarters blog, we had to adapt and delay some of the ways we counted group quarters because of the COVID-19 pandemic.

After the end of data collection, when we began processing census data from group quarters, we realized that many of them were occupied on April 1, 2020 (the reference day for the census), but didn't provide a population count. 

For example, when we enumerated them in midsummer, some group quarters said they were vacant but they were actually occupied on April 1. If not corrected, such cases could lead to an undercount. If the corrections were not properly coordinated with our procedures to remove duplicated people, they could contribute to an overcount. 

To address these issues, the Census Bureau reached out in a special telephone operation to contact many of the group quarters that provided us incomplete data. Simultaneously, we assembled a team to correct responses when possible and to apply a new count imputation procedure when more specific information was not available.

For some group quarters, we still didn't have response data to determine precisely how many people should be assigned to an occupied facility. For these cases, we devised business rules to determine which group quarters needed count imputation. We then developed, tested and applied imputation procedures to the appropriate cases. 

Unlike the count imputation procedure for housing unit addresses, the procedure for group quarters doesn't draw information from the nearest, similar neighbor.

Instead, we use imputation procedures that are more like those we use in economic surveys and censuses. To impute a count, this approach generally uses information already available on the group quarters under consideration — such as the expected count or the maximum capacity the group quarters reported during the advance contact. 

The Census Bureau had never before conducted count imputation on unresolved group quarters. In the coming months, we will provide metrics on the use of imputation for the group quarters population. For those individuals, we will also impute all their characteristics, as I describe below.

For housing units and group quarters, we use another type of imputation, “characteristic imputation,” to help us fill in a household’s missing characteristics, such as age or race. (Although the concept is similar for housing units and group quarters, our application differs slightly between the two.)

With this type of imputation, we look at a combination of sources to fill in the missing information — other information from the individual’s or household’s 2020 Census response, their responses from another census or survey, other existing records, or information from similar nearby neighbors.

For example:

• If a person reported their date of birth, we can fill in their missing age. If date of birth is missing too, we can often use what they reported on another census or survey.
• If race is reported for a parent, we could use that information to fill in their child’s missing race. If no information is available within the household, we would impute the information using data from similar nearby households.
• If all of the characteristics are missing for every person in a household, we would look to prior survey or census responses and other existing records. If those are unusable, we would impute the information by copying data from similar nearby households.

As with count imputation, we plan to provide rates on characteristic imputation after we finish processing 2020 Census responses. (We apply this type of imputation during the next phase of data processing — creating the Census Edited File — so these rates will not be available yet when we release the count imputation rates toward the end of April.)

We emphasize that count imputation and characteristic imputation are only implemented long after all data collection has ended. They follow after all attempts to obtain a response — a self-response from the household or group quarters, an interview with a census taker, information from a proxy, or administrative records of high quality — have been exhausted.

We recognize that using information from these three techniques — imputation, using administrative records, and proxies — may not always match the reality of an address’s occupancy status or the characteristics of the people who live there. However, these techniques are widely used in statistics because they have been proven to be more accurate than leaving the information blank.

Ultimately, we know the best information about a household comes directly from the household or the people at the group quarters. When they don’t respond, these techniques help us deliver a more complete and accurate count.