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ESTIMATION PROCEDURE

Estimates from the census sample were obtained from an iterative ratio estimation procedure (iterative proportional fitting) resulting in the assignment of a weight to each sample person or housing unit record. For any given tabulation area, a characteristic total was estimated by summing the weights assigned to the persons or housing units processing the characteristic in the tabulation area.

Estimates of family or household characteristics were based on the weight assigned to the person designated as householder. Each sample person or housing unit record was assigned exactly one weight to be used to produce estimates of all characteristics. For example, if the weight given to a sample person or housing unit had the value 6, all characteristics of that person or housing unit would be tabulated with the weight of 6. The estimation procedure, however, did assign weights varying from person to person or housing unit to housing unit. The estimation procedure used to assign the weight was performed in geographically defined "weighting areas". Weighting areas were generally formed of contiguous portions of geography which closely agreed with census tabulation areas within counties.

Weighting areas were never allowed to cross state or county boundaries. In small counties with a sample unit below 400 persons, the minimum required sample condition was relaxed to permit the entire county to become a weighting area.

Within a weighting area, the ratio estimation procedure for persons was performed in four stages. For persons, the first stage applied 17 household-type groups. The second stage used two groups: sampling rate of 1-in-2 and sampling rate below 1-in-2. The third stage used the dichotomy householder/nonhouseholders. The fourth stage applied 180 aggregate age/sex/Hispanic origin/race categories.

The stages were as follows:

   Stage I:  Type of Household

   Group
   Persons in Housing Units With a Family With Own Children Under 18
      1     2 persons in housing unit
      2     3 persons in housing unit
      3     4 persons in housing unit
      4     5 to 7 persons in housing unit
      5     8 or more in housing unit

   Persons in Housing Units With a Family Without Own Children Under 18

    6-10    2 through 8 or more persons in housing unit

   Persons in All Other Housing Units

      11    1 person in housing unit
   12-16    2 through 8 or more persons in housing unit

   Persons in Group Quarters

      17    Persons in Group Quarters

     Stage II: Sampling Rates

        1    Sampling rate of 1-in-2
        2    Sampling rate less than 1-in-2

     Stage III:  Householder/Nonhouseholder

        1    Householder
        2    Nonhouseholder

     Stage IV:  Age/Sex/Hispanic origin/Race

             White
             Persons of Hispanic origin
               Male
         1     0 to  4 years of age
         2     5 to 14 years of age
         3    15 to 19 years of age
         4    20 to 24 years of age
         5    25 to 34 years of age
         6    35 to 54 years of age
         7    55 to 64 years of age
         8    65 to 74 years of age
         9    75 years of age or older

               Female
     10-18     Same age categories as groups 1 through 9.

               Persons Not of Hispanic origin
     19-36     Same age and sex categories as groups 1 through 18.

               Black
     37-72     Same age/sex/Hispanic origin categories as groups
          through 36

               Asian or Pacific Islander
    73-108     Same age/sex/Hispanic origin categories as groups 1 
               through 36
 
               American Indian, Eskimo or Aleut
109-144    Same age/sex/Hispanic origin categories as groups 1 
               through 36
               
               Other Race (includes those races not listed above)
145-180 Same age/sex/Hispanic origin categories as groups 1
            through 36

Within a weighting area, the first step in the estimation procedure was to assign an initial weight to each sample person record. This weight was approximately equal to the inverse of the probability of selecting a person for the census sample.

The next step in the estimation procedure, prior to iterative proportional fitting, was to combine categories in each of the four estimation stages, when needed, to increase the reliability of the ratio estimation procedure. For each stage, any group that did not meet certain criteria for the unweighted sample count or for the ratio of the 100 percent to the initially weighted sample count, was combined, or collapsed, with another group in the same stage according to a specified collapsing pattern. At the forth stage, an additional criterion concerning the number of 100-percent persons in each race/Hispanic origin category was applied.

As the final step, the initial weights underwent four stages of ratio adjustment applying the grouping procedures described above. At the first stage, the ratio of the 100- percent to the sum of the initial weights for each sample person was computed for each stage I group. The initial weight assigned to each person in a group was then multiplied by the stage I group ratio to produce an adjusted weight.
In stage II, the stage I adjusted weights were again adjusted by the ratio of the 100-percent to the sum of the stage I weights for sample persons in each stage II group. Next, at stage III, the stage II weights were adjusted by the ratio of the 100-percent to the sum of the stage II weights for sample persons in each stage III group.

Finally, at stage IV, the stage III weights were adjusted by the ratio of the 100-percent to the sum of the stage III weights for sample persons in each stage IV group. The four stages of ratio adjustment were performed two times (two iterations) in the order given above. The weights obtained from the second iteration for stage IV were assigned to the sample person records. However, to avoid complications in rounding for tabulated data, only whole number weights were assigned. For example, if the final weight of the persons in a particular group was 7.25 then 1/4 of the sample persons in this group were randomly assigned a weight of 8, while the remaining 3/4 received a weight of 7.

The ratio estimation procedure for housing units was essentially the same as that for persons, except that vacant units were treated differently. The occupied housing unit ratio estimation procedure was done in four stages, and the vacant housing unit ratio estimation procedure was done in a single stage. The first stage for occupied housing units applied 16 household type categories, while the second stage used the two sampling categories described above for persons. The third stage applied three units-in-building categories, i.e. single units, multiunit less than 10 and multiunit 10 or more.

The fourth stage could potentially use 200 tenure/race/Hispanic origin/rent value groups. The stages for ratio estimation for housing units were as follows:

   OCCUPIED HOUSING UNITS

   Stage I:  Type of Household

   Group
   Housing Units With a Family With Own Children Under 18.

   1       2 persons in housing unit
   2       3 persons in housing unit
   3       4 persons in housing unit
   4       5 to 7 persons in housing unit
   5       9 or more persons in housing unit

   Housing Units With a Family Without Own Children Under 18.
   6-10    2 through 8 or more persons in housing unit

   All Other Housing Units

   11      1 person in housing unit
12-16 2 persons in housing unit through 8 or more persons in
          housing unit

   Stage II: Sampling Rate Category

   1       Sampling rate of 1-in-2
   2       Sampling rate less than 1-in-2

   Stage III: Units in Building

   1       Single unit structure
   2       Multiunit consisting of fewer than 10 individual units
   3       Multiunit consisting of 10 or more individual units

   Stage IV: Tenure/Race and origin of Householder/
           Value of Rent

   Group   Owner

     
      White Householder
   Hispanic origin (Householder)
   Value of Housing Unit
 1               Less than $20,000
 2               $20,000 to $39,999
 3               $40,000 to $59,999
 4               $60,000 to $79,999
 5               $80,000 to $99,999
 6               $100,000 to $149,999
 7               $150,000 to $249,999
 8               $250,000 to $299,999
 9               $300,000+
10              Other

   Householder Not of Hispanic origin

     11-20    Same value categories as groups 1 through 10

   Black Householder
21-40 Same Hispanic origin/value categories as groups 1 through
         20

   Asian or Pacific Islander Householder
     41-60    Same Hispanic origin/value categories as groups
              1 through 20

   American Indian, Eskimo, or Aleut Householder

     61-80    Same Hispanic origin/value categories as groups
              1 through 20

   Other Race Householder

     81-100   Same Hispanic origin/value categories as groups
              1 through 20

               Renter
               White Householder
               Householder of Hispanic origin

   Group           Rent categories

101             Less than $100
102             $100 to $199
103             $200 to $299
104             $300 to $399
105             $400 to $499
106             $500 to $599
107             $600 to $749
108             $750 to $999
109             $1000+
110             No cash rent

   Householder Not of Hispanic origin

     111-120  Same rent categories as groups 101 through 112

   Black Householder
121-140 Same Hispanic origin/rent categories as groups 101 
through 120

   Asian or Pacific Islander Householder
     141-160  Same Hispanic origin/rent origin
              categories as groups 101 through 120

   American Indian, Eskimo, or Aleut Householder

     161-180  Same Hispanic origin/rent categories
              as groups 101 through 120

   Other Race Householder
     181-200  Same Hispanic origin/rent categories
              as groups 101 through 120

VACANT HOUSING UNIT

   Group
 1         Vacant for Rent
 2         Vacant for Sale
 3         Other Vacant

The estimates produced by this procedure realize some of the gains in sampling efficiency that would have resulted if the population had been stratified into the ratio- estimation group before sampling, and the sampling rate had been applied independently to each group. The net effect is a reduction in both the standard error and the possible bias of most estimated characteristic to levels below what would have resulted from simply using the initial (unadjusted) weight. A by- product of this estimation procedure is that the estimates from the sample will for the most part be consistent with the 100-percent figures for the population and housing unit groups used in the estimation procedure.

Pages 4-2 through 4-5 from:

Census of Population and Housing, 1990: Public Use Microdata Sample U.S. Technical Documentation / prepared b the Bureau of the Census. Washington: The Bureau, 1992.

Text version of this document was prepared by ICPSR.

Html markup was done at the Population Studies Center, University of Michigan