The data for monthly housing costs are developed from a distribution of "Selected Monthly Owner Costs" for owner-occupied units and "Gross Rent" for renter-occupied units. The owner-occupied categories are further separated into those with a mortgage and those without a mortgage. See the sections on "Selected Monthly Owner Costs" and "Gross Rent"" for more details.

This measure divides the monthly housing costs distribution into two equal parts: one-half of the cases falling below the median monthly housing costs and one-half above the median. Medians are shown separately for units "with a mortgage" and for units "not mortgaged." Median monthly housing costs are computed on the basis of a standard distribution. (See the "Standard Distributions" section under Derived Measures.") Median monthly housing costs are rounded to the nearest whole dollar.

The first step is to compute the basic sampling weight for the HU based on the inverse of the probability of selection. This sampling weight is computed as a multiplication of the base weight ( BW ) and a computer-assisted personal interviewing (CAPI) subsampling factor ( SSF ). The BW for an HU is calculated as the inverse of the final overall first-phase sampling rate as given in Chapter 4, Table 4.2. HUs sent to CAPI are eligible to be subsampled (second-phase sampling) at one of the rates described in Table 4.4. Those selected for the CAPI subsample, and for which no late mail return is received in the CAPI month, are assigned a CAPI SSF equal to the inverse of their (second-phase) subsampling rate. Those not selected for the CAPI subsample receive a factor of 0.0. HUs for which a completed mail return is received, regardless if it was eligible for CAPI, or a computer-assisted telephone interviewing (CATI) interview is completed receive a CAPI SSF of 1.0. The CAPI SSF is then used to calculate a new weight for every HU, the weight after CAPI subsampling factor ( WSSF ). It is equal to the base weight times the CAPI subsampling factor. After each of the subsequent weighting steps, with one exception that will be noted, a new weight is calculated as the product of the new factor and the weight following the previous step. For additional details about the weighting steps discussed in this and the following section, see Asiala (2004).

Table 11.4 Computation of the Weight After CAPI Subsampling Factor ( WSSF )

Weighting step	Sample disposition
	Mail respondent	CATI respondendent	CAPI sampled units	CAPI nonsampled units	CAPI eligible, but then becomes mail respondent
Base Weight (BW)	1 ÷ (overall sampling rate)	1 ÷ overall sampling rate)	1 ÷ (overall sampling rate)	1 ÷ (overall sampling rate)	1 ÷ (overall sampling rate)
CAPI subsampling factor (SSF)	1	1	1 ÷ (CAPI sub- sampling rate)	0	1
Weight after subsampling factor (WSSF)= BW × SSF	1 ÷ (overall sampling rate)	1 ÷ (overall sampling rate)	1 ÷ (overall sampling rate) × 1 ÷ (CAPI sub- sampling rate)	0	1 ÷ (overall sampling rate)

Note: Table summarizes computation of the WSSF by the weighting step and the sample dispostion.

The goal of ACS estimation is to represent the characteristics of a geographic area across the specified period. For single-year estimates, this period is 12 months, and for 3- and 5-year estimates, it is 36 and 60 months, respectively. The annual sample is allocated into 12 monthly samples. The monthly sample becomes a basis for the operations of the ACS data collection, preparation, and processing, including weighting and estimation.

The data for HUs assigned to any sample month can be collected at any time during a 3-month period. For example, the households in the January sample month can have their data collected in January, February, or March. Each HU in a sample belongs to a tabulation month (the month the interview is completed). This is either the month the processing center checked in the completed mail questionnaire or the month the interview is completed by CATI or CAPI.

Because of seasonal variations in response patterns, the number of HUs in tabulation months may vary, thereby over-representing some months and under-representing other months in the single and multiyear estimates. For this reason, an even distribution of HU weights by month is desirable. To smooth out the total weight for all sample months, a variation in monthly response factor ( VMS ) is calculated for each month as:



This adjustment factor is computed within each of the 2,005 ACS weighting areas (either a county or a group of less populous counties). The index for weighting area is suppressed in this and all other formulas for weighting adjustment factors.

Table 11.5 illustrates the computation of the VMS adjustment factor within a particular county. In this example, the total base weight ( BW ) for each month is 100 (as shown on line 1 of this table). The total weight ( WSSF ) across modes within each month varies from 90 to 115 (as shown on line 5). The VMS factors are then computed by month as the ratio of the total BW to the total WSSF (as shown on line 6).

Table 11.5 Example of Computation of VMS

Line	Month
	March	April	May	June	July
Line 1: Total base weight (BW) across released samples Total weight after CAPI subsampling (WSSF)by mode:	100	100	100	100	100
Line 2: (a) Mail	55 (Mar sample)	45 (Apr sample)	40 (May sample)	45 (Jun sample)	50 (Jul sample)
Line 3: (b) CATI	30 (Feb sample)	25 (Mar sample)	30 (Apr sample)	30 (May sample)	25 (Jun sample)
Line 4: (c) CAPI	30 (Jan sample)	25 (Feb sample)	20 (Mar sample)	25 (Apr sample)	30 (May Sample)
Line 5: Total weight WSSF across modes (a+b+c)	115	95	90	100	105
Line 6: VMS adjustment factor	100 ÷ 115	100 ÷ 95	100 ÷ 90	100 ÷ 100	100 ÷ 105

The adjusted weights after the variation of monthly response adjustment ( WVMS ) are a product of the weights after CAPI subsampling factor ( WSSF ) and the variation of monthly response factor ( VMS ). When the VMS factor is applied, the total VMS weights ( WVMS ) across all HUs tabulated in a sample month will be equal to the total base weight of all HUs selected in that months sample. The result is that each month contributes approximately 1/12 to the total single-year estimates. In other words, the single-year estimates of ACS characteristics are a 12-month average without over- or under-representing any single month due to variation in monthly response. Analogously, each month contributes approximately 1/36 and 1/60 to the 3- and 5-year estimates, respectively.

Since 1996, the American Community Survey questions have been the same.

In this step, all HUs are placed into adjustment cells based on the cross-classification of building type (single- versus multiunit structures) and census tract. If a cell contains fewer than 10 interviewed HUs, it is collapsed with an adjoining tract until the collapsed cell meets the minimum size of 10.² Cells with no noninterviews are not collapsed, regardless of size, unless they are forced to collapse with a neighboring cell that fails the size criterion. The first noninterview adjustment factor ( NIF1 ) for each eligible cell is:


Footnote:

²Data are sorted by the weighting area, building type, and tract. Within a building type, a tract that has 10 or more responses is put in its own tract. A tract that has no nonresponses and some responses (even though the total is fewer than 10) is put in its own tract. A tract that has nonresponses and fewer than 10 responses is collapsed with the next tract. If the final tract needs to be collapsed, it is collapsed with the previous tract.

where
WVMS ij = Adjusted HU weight after the variation in monthly response adjustment for the j th HU within the i th adjustment cell.

All occupied and temporarily occupied interviewed HUs are adjusted by this first noninterview factor. Vacant and deleted HUs are assigned a factor of 1.0, and noninterviews are assigned a factor of 0.0. The computation of the weight after the first noninterview adjustment factor is summarized in Table 11.6.

Table 11.6 Computation of the Weight After the First
Noninterview Adjustment Factor ( WNIF1 )

Interview status	WNIF1ij
Occupied or temporarily occupied HU	WVMSij × NIF1i
Vacant or deleted HU	WVMSij
Noninterviewed HU	0

Since 1996, the American Community Survey questions have been the same.

One element not accounted for by the two noninterview factors above is the systematic differences that exist between characteristics of households that return census mail forms and those that do not (Weidman et al., 1995). The same element has been observed in the ACS across response modes. Virtually all noninterviews occur among the CAPI sample, and people in these HUs may have characteristics that are more similar to CAPI respondents than to mail and CATI respondents. Since the noninterview factors ( NIF1 and NIF2 ) are applied to all HUs interviewed by any mode, compensation may be needed for possible mode-related noninterview bias. The mode bias factor ensures that the total weights in the cells defined by a cross-classification of selected characteristics are the same as if the weight of noninterview HUs had been assigned only to CAPI HUs, but the factor distributes the weight across all respondents (within the cells) to reduce the effect on the variance of the resulting estimates.

The first step in the calculation of the mode bias noninterview factor ( MBF ) is to calculate an intermediate factor, referred to as the mode noninterview factor ( NIFM ). The NIFM is not used directly to compute an adjusted weight; instead, it is used as a factor applied to the WVMS weight to allow the calculation of the MBF . The cross-classification cells are defined for building type by tabulation month. Only HUs interviewed by CAPI and noninterviews are placed in the cells. If a cell contains fewer than 10 interviewed HUs, it is collapsed with an adjoining month. Cells with no noninterviews are never collapsed unless they are forced to collapse with a neighboring cell that fails the size criterion. The NIFM for a cell is:



This mode noninterview factor is assigned to all CAPI-interviewed occupied and temporarily occupied HUs. HUs for which interviews are completed by mail or CATI, vacant HUs, and deleted HUs are given a factor of 1.0. Noninterviews are given a factor of 0.0. The NIFM factor is used in the next step only. Note that the NIFM adjustment is applied to the WVMS weight rather than the HU weight after the first and second noninterview adjustments ( WNIF1 and WNIF2 ). The computation of the weight after the mode noninterview adjustment factor is summarized in Table 11.8.

Table 11.8 Computation of the Weight After the Mode
Noninterview Adjustment Factor ( WNIFM )

Interview status	WNIFMij
Occupied or temporarily occupied HU	WVMS 1 ij × NIFMi
Vacant or deleted HU	WVMSij
Noninterviewed HU	0

where
WNIFMij = Adjusted HU weight after the mode noninterview adjustment for the j th HU within the i th adjustment cell.

Next, a cross-classification table is defined for tenure (three categories: HU owned, rented, or temporarily occupied), tabulation month (12 categories), and marital status of the householder (three categories: married/widowed, single, or unit is temporarily occupied). All occupied and temporarily occupied interviewed HUs are placed in their cells. If a cell has fewer than 10 interviewed HUs, the cells with the same tenure and month are collapsed across all marital statuses. If there are still fewer than 10 interviewed HUs, the cells with the same tenure are collapsed across all months. The mode bias factor ( MBF ) for each cell is then calculated as:



All interviewed occupied and temporarily occupied HUs are adjusted by this mode bias factor, and the remaining HUs receive the factor 1.0. These adjustments are applied to the WNIF2 weights. The computation of the weight after the mode bias factor is summarized in Table 11.9 below.

Table 11.9 Computation of the Weight After the Mode
Bias Factor ( WMBF )

Interview status	WMBFij
Occupied or temporarily occupied HU	WNIF 2ij x MBFi
Vacant, deleted or noninterviewed HU	WNIF 2ij

where
WMBFij = Adjusted HU weight after the mode bias factor adjustment for the j th HU within the i th adjustment cell.