For purposes of this document, the following definitions are provided:

• Building—a separate physical structure identified by the respondent containing one or more units.
• Property—one or more buildings owned by a single entity (person, group, leasing company, and so on). For example, an apartment complex may have several buildings, but they are owned as one property.

Target population: All rental housing properties in the United States, circa 2023.

Sampling frame: The RHFS sample frame is a single frame based on a subset of the 2021 American Housing Survey (AHS) sample units. The RHFS frame included all 2021 AHS sample units that were identified as:

1. Rented or occupied without payment of rent.
2. Units that are owner occupied and listed as “for sale or rent”.
3. Vacant units for rent, for rent or sale, or rented but not yet occupied.

By design, the RHFS sample frame excluded public housing and transient housing types (i.e. boat, RV, van, other). Public housing units are identified in the AHS through a match with the Department of Housing and Urban Development (HUD) administrative records.

The RHFS frame is derived from the AHS sample, which is itself composed of housing units derived from the Census Bureau Master Address File. The AHS sample frame excludes group quarters housing. Group quarters are places where people live or stay in a group living arrangement. Examples include dormitories, residential treatment centers, skilled nursing facilities, correctional facilities, military barracks, group homes, and maritime or military vessels. As such, all of these types of group quarters housing facilities are, by design, excluded from the RHFS.

In some cases, nursing homes are co-located with other non-group quarter housing unit types, such as “assisted living” or “independent living” housing units. Since these units are “in scope” in the AHS sample frame, they are deemed “in scope” for the RHFS sample frame. However, it can be difficult to separate the group quarters units from the housing units (i.e., non-group quarters) when reporting total units for the RHFS property.  Census Bureau field representatives do their best to ensure the property information collected in the RHFS reflects only the housing units portion of the property.  Moreover, due to the often complicated and unique financial structure of these type of properties, it makes little sense to attempt to administer the RHFS questionnaire to them. Properties identified as assisted living facilities are counted in the RHFS for purposes of total rental units, and are flagged as “assisted living”, but little information is collected about the property. The information collected for these properties included the following: number of units and buildings, year property acquired, year of oldest and newest buildings, how the property was acquired, type of ownership entity, percentage of units by bedroom type for property, and percentage of units by status (vacant-for-rent or other reason, occupied by property owner/personnel, vacancy rate and vacancy rate by bedroom unit type.

Finally, the 2024 RHFS sample was selected from the 2021 AHS, but surveyed in 2024. The 2021 AHS sample is selected in late calendar year 2020 and includes new housing units built and ready for occupancy as of late 2020. As such, the RHFS sample will not include any rental properties built between late 2020 and 2024. The total number of rental units in 2+ properties built in 2020 was 348,000, number built in 2021 was 348,000, and the number built in 2022 was 342,000^[1]. For more information on the 2021 AHS sample methodology please click here.

Sampling unit:  Buildings with at least one unit that is either rented or vacant-for rent.

Sample design: The 2024 RHFS was sampled from all rental units as identified in the 2021 AHS sample. AHS cases were stratified based on building size. Building size was based on the number of units in the building as reported by the AHS respondent. AHS respondents reporting single-family attached or detached were put in the single unit building strata. Multiunit buildings were further categorized into four pre-defined strata based on the number of units (2-4, 5-24, 25-49, 50 or more).

Within each stratum, eligible buildings were sorted by geographic variables, including census region, state, urban/rural status, county, and zip code to obtain a stratified systematic sample. The within-stratum sampling rates were determined to result in an expected coefficient of variation (CV)^[2] of 10 percent for the aggregated stratum estimates at the national level.

Table 1 below shows the frame size and the final sample sizes by stratum. The sample size incorporates an oversample of buildings that was based on the results from the 2021 iteration of this survey. This oversample was needed to account for non-response, ineligible properties, and sampled units that change strata after being selected from the frame. After data collection is completed, Table 1 will contain the number of completed interviews in both the original and final stratum. Units in the 25-49 units stratum were selected with certainty because the target sample size exceeded the number of units in the frame for this stratum. The owners and/or property managers of the sampled buildings were contacted and asked about specific financing and property-related characteristics.

Editing: Respondent data were reviewed for consistency across related items.

Nonresponse: Nonresponse is defined as the inability to obtain requested data from an eligible survey unit. Two types of nonresponse are often distinguished. Unit nonresponse is the inability to obtain any of the substantive measurements about a unit. In most cases of unit nonresponse, the Census Bureau was unable to obtain any information from the survey unit after several attempts to elicit a response.  Item nonresponse occurs either when a question is unanswered or unusable.

Nonresponse adjustment and imputation: A nonresponse adjustment factor, which is the ratio of the sample properties divided by the interviewed sample properties, is calculated and assigned to the interviewed sample properties.  Separate factors are computed for each stratum.

For details on the nonresponse adjustment factor, see the Estimation section.

Other macro-level adjustments: Weights of the sampled rental units are adjusted to create rental housing properties based on the respondents’ answers to a specific set of questions. For details on the weighting adjustments, see the Estimation section.

Tabulation unit: Rental housing properties and units within rental housing properties.

Estimation: Estimates of total rental housing properties were calculated using the final sample weights which include sampling, nonresponse, and population adjustments.

This final weight is the product of the following components:

• Basic Weight (SMPWGT)
• Sampling Adjustment Factor (PROP_ADJ)
• Nonresponse Adjustment Factor (NR_ADJ)
• Total Rental Units Control Factor, based on 2023 AHS (PS_ADJ)

The factors are successively multiplied by the sample weight to obtain the final weight. The completed responses receive a final weight greater than 0, and each ineligible sample unit receives a weight of 0.

Basic Weight (SMPWGT)

The basic weight is the inverse of the initial probability of selection of the address.  The sample address was selected from rental units identified in the 2021 AHS sample.  The sample weight (SMPWGT) is the product of the first stage weight (FWGT) and the second stage weight (SWGT) as described below:

First Stage Weight (FWGT)

The first stage (AHS sample rental units) of the RHFS design is the same as the 2021 AHS. In order to account for this stage in the sample, the AHS sample weight is used in the calculation of the basic weight for the sample.  The first stage sample weight for the sample AHS cases is the AHS basic weight provided at time of RHFS sample. The second stage weight (SWGT) of the RHFS sample design accounts for the within stratum sampling across the five building size strata shown in Table 1. It is the ratio of the number of units in each strata to the number of units sampled from each strata.

The sample weight is calculated as:  SMPWGT = FWGT * SWGT

Sampling Adjustment Factor (PROP_ADJ)

The sampling adjustment factor adjusts the sample weights so that the final weight is representative of the complete rental property instead of the originally selected sample AHS_ID, where AHS_ID refers to an AHS sample case. Calculating the correct probability of selection and subsequent weight requires the assumption that each part of the property is selected independently.  The probability of selection for the property is calculated as follows:

Where:

                  π_property         calculated probability of selection for the total property

                  π_i                       probability of selection for AHS_ID_i of the property

                  1- π_i                 probability of not selecting AHS_ID_i

                  Thus,

                        weight_property =                      1/ π_property           

For example, AHS_ID₁ was originally selected for interview. However, the property is made up of 3 more AHS_IDs (AHS_ID₂, AHS_ID₃, AHS_ID₄) and they each have an associated probability of selection (π₁₌ 0.5, π₂₌ 0.5, π₃₌ 0.26, π₄₌ 0.36). Using the above formula gives us π_i = 1-[(1-0.5)(1-0.5)(1-0.26)(1-0.36)] = 0.8816 and a new weight of 1.13. A property cannot have a π_i  greater than 1.

This approach is based on this concept: P(A or B or C or D selected) = 1- P(none of A or B or C or D are selected)

The adjustment factor is then calculated as

When this factor is applied to the SMPWGT we get the property weight (PROPWGT=SMPWGT* PROP_ADJ). This factor was calculated by looking at the respondent’s property definition, which includes the number of units per building.

Nonresponse Adjustment Factor (NR_ADJ)

The purpose of the nonresponse adjustment is to inflate the weights of responses to account for eligible nonresponses. There were 10,655 eligible sample cases out of the initial sample of 11,500.  Sampled cases were ineligible for several reasons, such as missing owner information, duplicates, public housing status or change in rental status. The calculations to compute the nonresponse adjustment are as follows:

Step 1. Assign both the complete response and the nonresponse cases to the appropriate cells as shown using region and sampling strata information.

• Weighted count of non-responses (WNR),

Step 4. Apply the calculated nonresponse adjustment factor to all complete responses in the appropriate cell.  This results in a non-response adjusted property weight (NR_PROPWGT).

NR_ADJ_i * PROPWGT = NR_PROPWGT

Total Rental Units Control Factor (PS_ADJ)

The 2024 RHFS sample was selected from the 2021 AHS rental units. HUD and the Census Bureau deemed it desirable to ensure consistency between RHFS and AHS rental unit estimates. To carry this out, a Total Rental Units Control Factor, otherwise known as AHS control totals, was applied to the 2024 RHFS rental unit estimates. 

The application of the Total Rental Units Control Factor proceeded in four steps. In the first step, estimates of “AHS rental units by building size” were derived from the 2023 AHS, since this is the most recent iteration of the AHS and aligns with the RHFS reference year (2023). This included occupied rental units, vacant rented and vacant for rent units. The estimates excluded public housing and transient housing. Table 2 shows the weighted number of AHS Units that are in scope for RHFS.

The adjustment factor (PS_ADJ) for each stratum is then calculated as the ratio of each stratum’s control total and the weighted sum of units for that stratum:

Sampling Error: The sampling error of an estimate based on a sample survey is the difference between the estimate and the result that would be obtained from a complete census conducted under the same survey conditions. This error occurs because characteristics differ among sampling units in the population and only a subset of the population is measured in a sample survey. The particular sample used in this survey is one of a large number of samples of the same size that could have been selected using the same design. Because each unit in the sampling frame had a known probability of being selected into the sample, it was possible to estimate the sampling variability of the survey estimates.

Common measures of the variability among these estimates are the sampling variance, the standard error, and the coefficient of variation (CV), which is also referred to as the relative standard error (RSE). The sampling variance is defined as the squared difference, averaged over all possible samples of the same size and design, between the estimator and its average value. The standard error is the square root of the sampling variance. The CV expresses the standard error as a percentage of the estimate to which it refers. For example, an estimate of 200 units that has an estimated standard error of 10 units has an estimated CV of 5 percent. The sampling variance, standard error, and CV of an estimate can be estimated from the selected sample because the sample was selected using probability sampling. Note that measures of sampling variability, such as the standard error and CV, are estimated from the sample and are also subject to sampling variability. It is also important to note that the standard error and CV only measure sampling variability. They do not measure any systematic biases in the estimates.

The Census Bureau recommends that individuals using these estimates incorporate sampling error information into their analyses, as this could affect the conclusions drawn from the estimates.

To estimate the variance of the 2024 RHFS survey estimates, a method of successive difference replication as outlined by Ash (2014)^[4] was adapted for use by RHFS. This method uses replicate weights to compare the variation in the sampled units by cycling through a pattern of replicate factors. This method of replication described by Ash (2014) [4] builds on the successive difference replication method developed by Fay and Train (1995)^[5]. The weighting procedure, including all adjustments, was repeated r = 1 to 100 times, once for each replicate, to produce 100 sets of replicate weights.   

Confidence Interval: The sample estimate and an estimate of its standard error allow us to construct interval estimates with prescribed confidence that the interval includes the average result of all possible samples with the same size and design. To illustrate, if all possible samples were surveyed under essentially the same conditions, and an estimate and its standard error were calculated from each sample:

1.  Approximately 68 percent of the intervals from one standard error below the estimate to one standard error above the estimate would include the average estimate derived from all possible samples.
2.  Approximately 90 percent of the intervals from 1.645 standard errors below the estimate to 1.645 standard errors above the estimate would include the average estimate derived from all possible samples.

In the example above, the margin of error (MOE) associated with the 90 percent confidence interval is the product of 1.645 and the estimated standard error.

An MOE is provided for each survey estimate displayed in the tables. The sample was designed to result in an expected coefficient of variation of 10% at the national level. The key estimates and MOEs are displayed below in Table 5.