The next step in the weighting process is to assign weights to persons via a threedimensional rakingratio estimation procedure. This is done so that (1) the combined estimates of spouses and unmarried partners conform to the combined estimate of marriedcouple and unmarriedpartner households; (2) the estimate of householders conforms to the estimate of occupied housing units; and (3) the estimates for certain demographic groups are equal to their population estimates. Each person in an interviewed occupied HU is assigned an initial person weight equal to the HU weight after the HU poststratification factor is applied (
WHPF ). Next, there are three steps of ratio adjustment. The first step uses three cells to classify persons by spousal or unmarried partner relationship to the householder. The second step uses two cells to classify persons by householder and nonhouseholder. The third step uses up to 156 cells defined by race/Hispanic origin, sex, and age. The steps are defined as follows:
Step 1: Spouses and Unmarried Partners. All persons are placed into one of three cells:
1. Persons who are the primary person in a twopartner relationshipall householders in a marriedcouple or unmarriedpartner household.
2. Persons who are the secondary person in a twopartner relationshipall spouses or unmarried partners in those same households.
3. Balance of populationall persons not fitting into the first two cells.
The marginals for the first two cells are both equal to the estimate of marriedcouple plus unmarriedpartner households using the
WHPF weight. The marginal for the third cell is equal to the PEP total population estimate minus the sum of the marginals used for the other two cells. In this manner, the estimate of total population is controlled to the PEP total population estimate.
Step 2: Householders. The second step assigns all persons to one of two cells:
1.Householders
2.Nonhouseholders
The marginal for householders is the estimate of occupied HUs using the
WHPF weight. The marginal for nonhouseholders is equal to the PEP total population estimate minus the marginal used for the first cell in order to control for total population.
Step 3: RaceHispanic Origin/Sex/Age. The third step assigns all persons to one of up to 156 cells: six classifications of raceHispanic origin by sex by 13 age groups. The marginals for these rows at the weighting area level come from the PEP population estimates. Some weighting areas will not have sufficient sample to support all 156 cells and in these cases some collapsing is necessary. This collapsing is done prior to the raking and remains fixed for all iterations of the raking.
Race and Hispanic origin are combined to define six unique raceethnicity groups consistent with those used in weighting the Census 2000 long form. These groups are created by crossing "Non Hispanic" with the five major single race groups, plus the group of all Hispanics regardless of race. The raceethnicity groups are:
1. NonHispanic White
2. NonHispanic Black
3. NonHispanic American Indian and Alaska Native
4. NonHispanic Asian
5. NonHispanic Native Hawaiian or Pacific Islander
6. Hispanic
The assignment of a single major race to a person can be complicated because people can identify themselves as being of multiple races. People responding either with multiple races or "Other Race" are included in one of the six raceethnicity groups for estimation purposes only. Subsequent ACS tabulations are based on the full set of responses to the race question.
Initial estimates of population totals are obtained from the ACS sample for each of the weighting raceethnicity groups. These estimates are calculated based on the initial person weight of
WHPF . Estimates from the Census Bureau's PEP also are available for each weighting raceethnicity group. These total population estimates are used to control ACS total population estimates to be equal to the PEP by weighting area.
The initial sample and population estimates for each weighting raceethnicity group are tested against a set of criteria that require a minimum of 10 sample people and a ratio of the population control to the initial sample estimate that is between (1/3.5) and 3.5. This is done to reduce the effect of large weights on the variance of the estimates. If there are weighting raceethnicity groups that do not satisfy these requirements, they are collapsed until all groups satisfy the collapsing criteria. Collapsing decisions are made following a specified order in the following way (see Asiala, 2007, for further details):
1. If the requirements are not met when all nonHispanic race groups are combined, then all weighting raceethnicity groups are collapsed together and the collapsing is complete.
2. If the requirements are not met for Hispanics, the Hispanics are collapsed with the largest nonHispanic nonWhite group.
3. If the requirements are not met for any nonHispanic nonWhite group, it is collapsed with the largest (prior to collapsing) nonHispanic nonWhite group.
4. If the largest collapsed nonHispanic nonWhite group still does not meet the requirements, it is collapsed with the surviving nonHispanic nonWhite groups in the following order until the requirements are met: Black, American Indian and Alaska Native, Asian, and Native Hawaiian or Pacific Islander.
5. If all nonHispanic nonWhite groups have been collapsed together and the collapsed group still does not meet the requirements, it is collapsed with the nonHispanic White group.
6. If the requirements are not met for the nonHispanic White group, then it is collapsed with the largest nonHispanic nonWhite group.
Within each collapsed weighting raceethnicity group, the persons are placed in sexage cells formed by crossing sex by the following 13 age categories: 0−4, 5−14, 15−17, 18−19, 20−24, 25−29, 30−34, 35−44, 45−49, 50−54, 55−64, 65−74, and 75+ years. If necessary, these cells also are collapsed to meet the requirements of the same sample size and a ratio between (1/3.5) and 3.5. The goals of the collapsing scheme are to keep children age 0−17 together whenever possible by first collapsing across sex within the first three age categories. In addition, the collapsing rules keep men age 18−54, women age 18−54, and seniors 55+ in separate groups by collapsing across age.
The initial sample cell estimates are then scaled and rescaled via iterative proportional fitting, or raking, so that the sum in each row or column consecutively agrees with the row or column household estimate (Steps 1 & 2) or population estimate (Step 3). This procedure is iterated a fixed number of times, and final person weights are assigned by applying an adjustment factor to the initial weights.
The scaling and rescaling between rows and columns is referred to as an iteration of raking. An iteration of raking consists of the following three steps. (The weighting matrix is included to facilitate the discussion below.) The threestep process has been split out into two tables, Table 11.10 and Table 11.11, for clarity.
Table 11.10
Steps 1 and 2 of the Weighting Matrix

Step 2 
Step 1 Control 
Householder 
Nonhouseholder 
Step 1 
"Householder in two partner relationship" 


"Survey estimate of marriedcouple and unmarriedpartner households" 
"Spouse/unmarried partner in twopartner relationship" 
"Survey estimate of marriedcouple and unmarriedpartner households" 
Balance of population 
"PEP total population estimate minus the sum of the two controls above" 
Step 2 Control 
"Survey estimate of occupied housing units" 
"PEP total population estimate minus the control for householders" 

Table 11.11
Steps 2 and 3 of the Weighting Matrix

Step 2 
Step 3 Control 
Householder 
Nonhouseholder 
Step 3 
"NonHispanic White" 
04 Males 


"PEP population estimate for the collapsed cell by weighting area" 
04 Females 
… 
75+ Females 
NonHispanic AIAN 
… 
NonHispanic Asian 
… 
NonHispanic NHPI 
… 
Hispanic 
… 

Step 2 Control 

"Survey estimate of occupied housing units" 
"PEP total population estimate minus the control for householders" 

Step 1. At this step, the initial person weights are adjusted to make both the sum of the weights of householders in marriedcouple or unmarriedpartner households and the sum of the weights of their spouses or unmarried partners equal to the survey estimate of marriedcouple and unmarriedpartner households. This is done using the HU weight after the HU poststratification factor adjustment. The weights of all other persons are adjusted to make the sum of all weights equal to the PEP total population estimate.
Step 2. The Step 1 adjusted person weights are adjusted again to make the sum of the weights of all householders equal to the survey estimate of occupied HUs using the HU weight after the HU poststratification factor adjustment. The Step 1 adjusted weights of all other persons are adjusted to make the sum of all weights equal to the total population estimate.
Step 3. The Step 2 adjusted person weights are adjusted a third time by the ratio of the population estimates of raceHispanic origin/age/sex groups to the sum of the Step 2 weights for sample people in each of the demographic groups described previously.
The three steps of ratio adjustment are repeated in the order given above until the predefined stopping criterion is met. The stopping criterion is a function of the difference between Step 2 and Step 3 weights. The weights obtained from Step 3 of the final iteration are the final person weights.
A single factor, the person poststratification factor (
PPSF ), is calculated at the person level, which captures the entire adjustment accomplished by the ratioraking estimation. It is calculated as follows:
PPSF = final person weight ÷ initial person weight.
The factor is calculated and applied to each person, so that their weights become the product of their initial weights and the factor.
ACS singleyear estimates are produced for geographic areas with populations of at least 65,000, including incorporated places, for which population estimates also are published annually. Since population controls are applied at the weighting area level, occasionally the ACS estimate of total population for a large place within a weighting area may be far enough from its population estimate to cause confusion among data users. To avoid these anomalies, methodologies are being investigated to control person weights to total population for places with populations of at least 65,000 within weighting areas.