The Bicentennial Census: New Directions for Methodology in 1990: 30th Anniversary Edition (2015)

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Census Methodology: Prior Practice and Current Test Plans

The panel believes it is important to consider proposed changes in the methodology of the decennial census in the context of past experience. Changes that depart greatly from recent methodology need careful consideration of their costs and benefits. Review of practices in previous U.S. censuses and in the censuses of other Western nations can also suggest ideas that may be worth adopting for future censuses in the United States. The purpose of this chapter is to provide background for the discussion and recommendations in subsequent chapters on proposed changes in methodology. The chapter first describes the methodology followed in taking the 1980 decennial census. The description is not meant as a comprehensive account but as an overview to acquaint readers new to the decennial census process with the basic procedures and their chronology. Next, the discussion briefly references alternative procedures that were followed in previous U.S. censuses and related procedures used in other Western nations.

The remainder of the chapter provides an overview of the Census Bureau’s research and testing plans for the 1990 census as currently formulated. The panel offers a general assessment of these plans and makes recommendations directed to strategies for selecting priority projects. Subsequent chapters provide detailed recommendations on pretest and research plans in specific areas.

1980 CENSUS METHODOLOGY

It is convenient for descriptive purposes to divide the process for the 1980 census into eight components. These are (roughly in chronological order):

1. Development of a master address list of residential housing;
2. Development of lists of special places, for example, institutions;
3. Checking of address list prior to the census;
4. Enumeration;
5. Follow-up;
6. Coverage improvement;
7. Data processing; and
8. Post-census evaluation.

These eight headings give a quick overview of how the census was taken with the methodology of 1980: (1) a master address list of housing units was constructed from a variety of sources; (2) other kinds of group housing were added in; (3) these addresses were checked for completeness and accuracy; (4) forms were then delivered and collected by mail and by enumerators; (5) complete responses were sought for incomplete questionnaires, including forms that were completely blank, and for questionnaires that were not returned; (6) alternative enumeration methods were used to obtain responses from hard-to-count elements of the population; (7) the questionnaire data were converted into computer-readable form, incomplete or inconsistent information was imputed, and final census products (counts, cross-tabulations, and sample public use microdata files) were created; and as a last step, (8) the accuracy of the final set of records was evaluated to inform users of the quality of the data presented and to help design the next decennial census. The following sections more fully describe each of these eight components. The discussion draws heavily on Bureau of the Census (1982b, 1983b), Bounpane (1983), and National Research Council (1978).

Development of Master Address List of Residential Housing

Building on the experience of previous censuses, the Census Bureau made the fundamental decision for 1980 to enumerate the vast majority of the population—about 95 percent of the total—using mailout-mailback procedures. Use of the mails required construction of a comprehensive address list. For purposes of this step in 1980, the Census Bureau divided the United States into three types of areas: (1) mail areas for which the Census Bureau purchased commercial mailing lists; (2) mail areas for which Census Bureau staff developed the mailing list; and (3) conventional (non-mailout) areas.

Mail Areas for Which Commercial Mailing Lists Were Used

For urban areas that met certain requirements—(1) the Census Bureau had a computerized geographic coding file for the area, (2) the area was

located within the Postal Service city delivery boundaries, and (3) computerized commercial mailing lists were available for the area—the Census Bureau purchased several of the more complete and accurate commercial lists and used them to develop a master tape address register (TAR). In New York City, Philadelphia, and Chicago, the Census Bureau merged the 1970 census master address list with the commercial mailing lists obtained and in New York City also merged the 1978 census dress rehearsal list into the master TAR list. Elsewhere the 1970 lists were not used. This procedure represented an extension of the 1970 process wherein the Census Bureau purchased only one mailing list. The 1980 TAR areas accounted for over 50 percent of all residences.

Mail Areas for Which Commercial Mailing Lists Were Not Used

For the remaining mail areas, which accounted for over 40 percent of all residences, Census Bureau personnel “prelisted” each area, that is, compiled a list of addresses in the field. In 1980, field staff were instructed to “knock on every door with no callbacks,” that is, conduct a physical canvass of all potential residences, including an attempted contact, to help determine whether the address was indeed a residence and was occupied. Where the canvassers could not make personal contact with occupants during this stage, they obtained information on occupancy status from neighbors, landlords, etc.

Conventional (non-mailout) Areas

There were some areas of the United States for which the Census Bureau felt it was more cost-effective to enumerate by conventional means, that is, by sending out an enumerator to obtain a completed questionnaire instead of asking residents to mail back a form. The enumerators compiled the address list at the time of enumeration in these areas, which contained about 5 percent of the total residences of the United States and were mostly thinly populated.

Development of Lists of Special Places

For the 1980 census, the Census Bureau compiled from a variety of sources lists of so-called special places in which people live in nonresidential settings, including college dormitories, military bases, naval vessels, hotels, motels, and shelters, and institutions such as hospitals, nursing homes, and penitentiaries. The population residing in special places is not insignificant—about 3 percent of the total in 1980 (Bureau of the Census, 1982c:53)—and such places can pose special problems for obtaining a complete and accurate enumeration.

Checking of the Master Address List Prior to the Census

After compilation of the master address list, the next step was to implement several checks for accuracy and completeness. In the TAR areas (urban areas for which the Census Bureau purchased computerized commercial mailing lists), U.S. Postal Service staff conducted three checking operations and Census Bureau enumerators conducted yet a fourth.

The Postal Service carried out an advance post office check (APOC) in summer 1979—mail carriers checked address cards for completion and accuracy while following their regular routes. Census enumerators made a second check of the master address list in early 1980, the precanvass, to verify that every address still existed and was assigned to the correct geographic area. The enumerators also added missed or newly built residential units to the list. The Postal Service carried out the third and fourth checks in the TAR areas just prior to Census Day, April 1. In the casing check, 3 weeks prior to enumeration, mail carriers received addressed census questionnaires with instructions to note any addresses to which they deliver mail for which they did not receive a questionnaire. Finally, during the actual delivery of the census questionnaires, mail carriers again noted addresses for which they did not have questionnaires—the time of delivery (TOD) check. In the prelist mail areas where census enumerators had developed the address list, only the casing and time of delivery checks were performed. The various address check programs represented an expansion of similar programs that were conducted in 1970.

Enumeration

Enumeration—what is generally thought of when one hears the word census—was the next step. In the mailout areas of the country, mail carriers delivered the census questionnaires two or three days prior to Census Day, April 1, 1980. Each questionnaire included instructions for the respondents to fill out and mail back the completed form to the local district office. For most questions, respondents were to blacken circles that could be read by the Census Bureau’s computerized data input system (FOSDIC), while other questions required handwritten entries. In the 1970 mail census areas, questionnaires went out in the mail to 60 percent of residential addresses and were received back in the mail from 86 percent of the occupied residences. In 1980, 95 percent of addresses got questionnaires in the mail and 83 percent of occupied households mailed them back. In most areas in 1980, five of every six households received short-form questionnaires containing a limited set of population and housing items; every sixth household received the long-form questionnaire containing the items asked of every household plus additional items asked just of the one-sixth sample. In places of under

2,500 population, one in two households received the long form. Overall, about 20 percent of households received the long form.

As one of several experiments conducted as part of the 1980 census in selected district offices, the Census Bureau tested the use of a somewhat different procedure for delivering the questionnaires, called update list/leave. In this procedure, enumerators instead of mail carriers delivered the questionnaires, and at the same time updated the address list (see Chapter 5 for some results of this experiment).

In the conventional areas, the Postal Service delivered unaddressed short-form questionnaires to all households several days before April 1. Householders were instructed to fill out their form and wait for an enumerator. Beginning on Census Day, enumerators visited each household and picked up a completed form or helped the residents complete the form, at the same time compiling a list of addresses. At designated households, enumerators helped the residents complete the long-form questionnaire.

In both mailout-mailback and conventional areas, specialized procedures were used to obtain questionnaires (individual census reports) containing just the population items from persons living in various types of group quarters, such as military bases, naval vessels, college dormitories, prisons, and hospital chronic wards. At places offering transient residence, such as hotels, motels, and missions, Census Bureau staff enumerated travelers who had no one at their usual home to count them and other persons with no usual place of residence.

Follow-up

In the 1980 census mail areas, the first stage of follow-up began 2 weeks after Census Day. This stage concentrated on obtaining questionnaires that had not been sent back to one of the 375 district offices (unit nonresponse). Enumerators were instructed to return, a total of four times if needed, to residences that did not mail back a questionnaire. At the end of this process, enumerators as a last resort asked neighbors and landlords for any information that they might have about the residents and completed basic demographic and housing items on the questionnaire. Census office staff also followed up over the telephone households that mailed back an incomplete questionnaire to obtain the missing information (item nonresponse). In several district offices, on an experimental basis, Census Bureau office staff followed up nonresponding households over the telephone using directories ordered by address (see discussion of this experiment in Chapter 6).

A second stage of personal follow-up in the mail census areas began 2 to 3 months after Census Day. In this stage, census enumerators implemented several specific coverage improvement procedures, described in the next section, followed up the very small percentage of nonresponding

households (estimated at about 2 percent) for which not even “last resort” information was obtained in the first stage, and also followed up for missing items on otherwise complete questionnaires for which the earlier telephone follow-up was not successful. Follow-up operations conducted by the 37 district offices in conventional areas were similar to the second stage of follow-up in mail areas. Chapter 6 describes the 1980 census follow-up experience in more detail. District offices, on average, completed all follow-up operations about 5 to 6 months after Census Day in mail census areas and 4 to 5 months in conventional areas. For a small percentage of housing units (less than 0.5 percent of the total) from which questionnaires were not obtained by the end of follow-up, the district office “closed out” the case. For some of these units, the office knew the household size, but for others there was no knowledge of whether the unit was occupied.

Coverage Improvement

Coverage improvement is a term encompassing several different approaches to the collection of information from households that were missed by the master address list, or from individuals within otherwise-enumerated households who were missed or elected not to respond. The various address checks carried out prior to Census Day were part of the coverage improvement effort for the 1980 census. In addition, Census Bureau staff implemented several post-Census Day coverage improvement programs—primarily in mail areas during the second stage of follow-up:

1. Checks Based on Responses to Coverage Questions; Whole Household Usual Home Elsewhere Check. Enumerators visited addresses at which a respondent in a small apartment building (less than 10 units) reported more housing units than listed for the structure on the master address list, households that reported more residents on the front of the questionnaire than on the inside pages (the dependent roster check), households whose respondents indicated some uncertainty about who was considered a household member, and households with persons listed as having their usual place of residence elsewhere to make sure all households and persons were properly counted. Whole households reporting usual residence elsewhere were checked to be sure that the occupants were counted only once at their usual residence.
2. Vacant/Delete Check. In 1980 a second independent enumerator revisited every unit classified as vacant in the first stage of follow-up (or at the time of enumeration in conventional areas) to determine if the unit had actually been occupied on Census Day and also to try to identify and enumerate persons who moved into the unit

after Census Day who had not been enumerated at their former residence. The Census Bureau implemented this check in response to findings from the 1970 census indicating that a nontrivial proportion of housing units enumerated in the census as vacant was actually occupied. In 1970, however, in contrast to the complete recheck of vacancy status carried out in 1980, Census Bureau staff rechecked only a sample of units initially declared vacant and used the results to carry out a computer imputation for other units.

3. Nonhousehold Sources Program. For areas with large minority populations, the Census Bureau district office staff clerically performed a cross-match between census records and lists of names and addresses from outside sources, including driver’s license lists, records of the Immigration and Naturalization Service, and, in New York City, welfare records. Enumerators visited addresses at which persons were identified from the match who might have been omitted from the count.
4. Prelist Recanvass. In mailout-mailback areas for which Census Bureau staff developed the address list and only two of the pre-Census Day address checks were performed, the field staff rechecked the list for completeness during the second stage of follow-up.
5. Post-Enumeration Post Office Check (PEPOC). In all conventional areas, mail carriers noted addresses that did not appear to be on the address list; these addresses were followed up by Census Bureau personnel. This program was previously implemented in the 1970 census on a sample basis in rural areas of the South.
6. Casual Count. In major urban areas, Census Bureau field personnel visited places where persons who had no fixed address or who were missed at their residence might be found, such as skid row districts, pool halls, employment offices, etc.
7. Were You Counted? The Census Bureau had special forms printed in news media inviting persons who believed that they were missed by the census to complete the forms and send them in. The district office staff checked their records to see if persons sending in these forms were already included.
8. Local Review. The Census Bureau provided preliminary housing unit and population counts to local officials after completion of the first stage of follow-up. Officials reviewed the counts and indicated possible problem areas that were field checked and corrections made as needed.

The coverage improvement efforts for the 1980 census represented a considerable expansion in number and scope over the 1970 effort. In addition to the procedures described above for identifying missed persons and

households, programs aimed at increasing public cooperation, particularly among hard-to-count groups, were greatly expanded. The latter included special publicity efforts, assistance centers that the public could call or visit for help in filling out census forms, and the availability of foreign-language questionnaires. Chapter 5 describes the experience with coverage improvement in 1970 and 1980 and provides program-by-program estimates of both cost and yield, or net additions to the count of population and housing units.

Data Processing

The next step in the decennial census process was to take the raw data collected from the enumeration, follow-up, and coverage improvement stages, create computerized household and person records, and edit these data records prior to producing and distributing the final census counts, cross-tabulations, and sample microdata files. The reader should note that no names or addresses were retained on the computerized files. In 1980 computer editing of the raw data involved four steps: (1) imputation for unit nonresponse, (2) imputation for item nonresponse (see Appendix 3.1 for definition and description of the sequential hot-deck imputation method used), (3) weighting the records containing long-form data collected from about 20 percent of the households by iterative proportional fitting (see Appendix 3.2 for definition and description), and (4) implementing various suppression routines on the cross-tabulations and sample microdata records to protect the confidentiality of individual respondents’ answers. In addition, clerks manually coded handwritten responses to long-form questions on occupation, industry, place of work, and other items, a step that preceded computer processing of the long-form information.

As mentioned above, for less than 0.5 percent of all addresses, census enumerators were not able to obtain even last-resort information. For these close-out cases, the Census Bureau, where necessary, first imputed the occupancy status of the unit and then, for units designated as occupied, “substituted,” that is, imputed using sequential hot-deck imputation (see Appendix 3.1) a filled-out questionnaire from a randomly selected neighbor. Of the total population count in 1980, 0.3 percent represents persons who were imputed in this manner (Bounpane, 1983:31). In addition, the Census Bureau made substitutions for persons and housing units for which the last-resort information obtained in the second stage of follow-up was inadequate and, in a very few instances (0.1 percent of the total), for which a questionnaire was inadvertently damaged during processing. The total of substituted persons including close-out and last-resort cases was 1.5 percent of the final 1980 population count (Bureau of the Census, 1983d:Table B-4).

For questionnaires with missing or inconsistent information, computer programs allocated or assigned, again using sequential hot-deck imputa-

tion, the responses of a geographically nearby respondent with similar characteristics as determined from the completed portion of the census questionnaire. Some consistency edits did not require hot-deck imputation but were made on the basis of other information within the same data record. About 10 percent of the total households in 1980 had one or more short-form items imputed, and almost 45 percent of people receiving the long-form questionnaire had one or more items imputed (Bureau of the Census, 1983d:Table B-4, 1983f:Table C-1; see also Citro, 1984).

As mentioned before, about 80 percent of households received the short form, while a sample of about 20 percent received the long form. (The sample was selected systematically rather than randomly; that is, every sixth address, or, in places under 2,500 population, every other address, was designated for the sample.) Both types of forms included a common set of basic demographic and housing questions. Publications and data tapes containing just the short-form items were produced from the entire set of census records (complete count), but data products that cross-tabulated these items with the other items asked on the long form were produced in a second pass of only the sample records. Without adjusting sample weights, the marginal tabulations of basic characteristics contained in the complete count and sample data products would agree only within bounds of sampling error. The Census Bureau forced these marginals to agree closely through reweighting the sampled cases using a technique called iterative proportional fitting (see Appendix 3.2). Forcing agreement promoted consistency in the census tabulations, reduced the variance of the estimates, and also probably reduced any biases that may have occurred in the sample selection.

Finally, prior to release of tabulations and data files to the public, the Census Bureau implemented computer programs to suppress information that might permit identification of individual respondents. For example, characteristics of minority populations in areas that had fewer than 15 such persons were not released (Bureau of the Census, 1982b:103-106).

Post-Census Evaluation

The Census Bureau implemented a variety of programs to attempt to evaluate the quality of the census in 1980. Programs to evaluate the completeness of census coverage of the population—that is, the completeness of the count—included the Post-Enumeration Program (PEP) and demographic analysis. Other programs evaluated the quality of responses for particular content items. Chapter 4 describes coverage evaluation programs carried out in 1980 and prior censuses.

The reader should not gain the impression from the above description that every step in the decennial census process flowed smoothly or was conducted exactly as planned. Each stage experienced problems, some of

design and some of implementation. A major goal of the research and testing program that has begun for the 1990 census is to identify modifications to census methodology that promise to facilitate the census process and enhance the quality of census data. Before turning to a review of the Census Bureau’s current research plans, the two sections that follow briefly review the highlights of methodologies used in previous U.S. censuses and in other Western nations to indicate the range of possibilities.

METHODOLOGY USED IN PREVOUS CENSUSES

It is natural to begin this discussion with the 1950 census, which was the first population census in the United States to have comprehensive programs for evaluation of completeness of coverage. The 1950 census (see Bureau of the Census, 1955) relied exclusively on personal enumeration to obtain responses to census questions. Enumerators went door-to-door with sheets (line schedules) that had room to list 30 persons on the front—one person to a line—and up to 12 housing units on the back. Enumerators asked every fifth person an additional set of questions and every thirtieth person a few more questions, generating sampling rates of 100 percent, 20 percent, and 3.3 percent. There was no prior compilation of an address list, although the Census Bureau estimated total housing unit counts by block for most cities of 50,000 or more population to use as a check on the completeness of the enumeration. On an experimental basis in 1950, the Census Bureau tested the use of a list/leave self-enumeration procedure whereby enumerators listed addresses and left questionnaires for households to fill in and mail back to census district offices. The Census Bureau also tested the use of household instead of line schedules.

The 1960 census (see Bureau of the Census, 1966) used a combination of mail and personal interview enumeration techniques. In areas covering roughly 82 percent of the population, enumeration involved a two-stage list/leave procedure. In these areas, several days before April 1 the Postal Service dropped off household questionnaires called advance census reports (ACRs) that contained the 100 percent items. Residents were asked to fill in the answers and wait to give the ACR to an enumerator. Enumerators came to all households and transcribed the 100 percent items to computer-readable forms. If the household had not answered the questions, the enumerator obtained answers at that time. The best estimate is that 60 percent of households had the forms filled out and waiting before the enumerator arrived. At every fourth household, the enumerator left a long-form questionnaire, which the household was to fill in and mail back to census district offices. A different set of enumerators followed up for sample questionnaires that were not returned—about 20 percent of the sample—and for vacant units in the sample. In the remaining areas of the country covering

about 18 percent of the population, the enumeration involved a single-stage approach. The Postal Service delivered unaddressed questionnaires. Enumerators visited each household and obtained answers to the 100 percent items and also to the sample items for designated households.

The 1970 census (see Bureau of the Census, 1976a) foreshadowed in most respects the methodology adopted for 1980. This census extended the use of the mails in conducting the enumeration. In areas of the country encompassing roughly 60 percent of the population, the Postal Service delivered questionnaires to all households several days prior to Census Day with instructions to the residents to complete and mail back the forms. Four-fifths of the households received the short-form questionnaire, while the other fifth received one of two versions of the long form (one version was sent to 15 percent and the other was sent to 5 percent of households). In the remaining areas of the country covering roughly 40 percent of the population, the Census Bureau used conventional enumeration procedures similar to the single-stage procedure used in rural areas in 1960. In one change from 1960, the unaddressed short forms sent to households in the conventional areas were already in computer readable format. On an experimental basis in 1970, the Census Bureau tested use of mailout-mailback procedures in selected areas that would otherwise have been enumerated conventionally. The success of this experiment led to the decision to expand the mailout-mailback procedure to over 95 percent of households in 1980.

The 1970 census was the first to implement specific programs designed to improve coverage, including both checks of the master address list prior to Census Day and programs, such as a recheck of units classified as vacant, conducted after the first stage of follow-up. For 1980 the Census Bureau greatly expanded the number and scope of coverage improvement programs. Unlike 1970, for which two of the programs—the National Vacancy Check and the Post-Enumeration Post Office Check—were implemented on a sample basis, an early decision was made to carry out all coverage improvement programs on a 100 percent basis in 1980.

METHODOLOGY USED IN OTHER WESTERN COUNTRIES

There is a wide range of methodologies used to carry out periodic censuses in other Western nations. The following text very briefly highlights major features of census methodology in eight countries—Australia, Canada, Great Britain, France, the Federal Republic of Germany, the Netherlands, Sweden, and Denmark. (For the last six countries, the discussion draws heavily on Redfern, 1983.) Obviously, procedures that work well in one country may not be applicable to another for many reasons, such as different public perceptions and attitudes or differences in population size and consequent scale of census operations. Nonetheless, it is useful

in reviewing census methodology in the United States to be aware of what is being done elsewhere.

Australia currently conducts a census every 5 years using a list/leave/pickup procedure. Enumerators deliver questionnaires, while at the same time compiling an address register. Several days later, enumerators revisit each household to pick up the completed questionnaires. Field operations generally close out within 2 weeks of Census Day. Australia uses post-enumeration survey techniques to evaluate the completeness of the count and, based on the results, produces adjusted population totals for states, which are used for reapportionment of the legislature and fund allocation. Characteristics data, however, are not adjusted (see Doyle, 1980).

Canada conducts a quinquennial census using a list/leave/mailback procedure (see Fellegi, 1980a). Beginning on Census Day, enumerators canvass their assigned areas, compile an address register, and leave questionnaires at each address with instructions for householders to fill them in. As in the United States, 80 percent of the households receive a short form and 20 percent a long form. In all areas of significant population concentration, householders are asked to mail back their census forms, while, in sparsely populated areas, enumerators call back to pick them up. In both types of areas, enumerators follow up for unit and item nonresponse. Enumerators are held entirely responsible for conducting a complete and accurate census in their districts—the same person in each area performs the initial list/leave and follow-up operations. Enumerators’ work is subject to quality control. Most field work ends in about 3 weeks.

Great Britain conducts decennial censuses using list/leave/pickup techniques. Enumerators, who are recruited, trained, and paid by the central government rather than local agencies—in contrast to the practice in most countries of continental Europe—deliver and retrieve questionnaires in their areas. The enumerators for the most recent 1981 census completed field operations within about 2 months of Census Day. The questionnaire in 1981 included relatively few items—16 questions for each person and five questions on housing and cars. No questions were asked on income, ethnicity, marital history, or childbearing history. Sampling was not used in the field, but responses to questions that required manual coding, such as occupation, were processed on a 10 percent sample basis.

The recent 1982 census in France used conventional enumeration techniques as well. The enumerator staff, who were recruited and supervised by the local administrations, collected data using three main forms: one for each individual, for each housing unit, and for each building. Questions asked of each individual were relatively few in number compared with the United States; for example, questions were not asked on ethnicity, language, income, or journey to work. There was a relatively large number of questions on housing. Most items, although obtained from 100 percent of the

population, were processed on a 25 percent sample basis. The French are considering a system of mailout-mailback of a short form to every three in four households and using enumerators to obtain responses to a long form at the remaining one in four addresses.

The Federal Republic of Germany last conducted a census of buildings and houses in 1968 and a census of population in 1970 with conventional enumeration techniques. The 1970 census used two forms: a long form administered in 10 percent of the enumeration districts and a short form administered in the remaining 90 percent of districts. The local communities played a major role in the field work, recruiting and training enumerators, checking the census returns against the local population registers, and correcting one or the other set as necessary. The federal government planned a combined population and housing census for 1983, with a single form containing a shorter list of questions than the 1970 long form. However, public opposition to the census forced the government to postpone it indefinitely. The opposition stemmed from considerations of privacy and confidentiality and specifically objection to the practice in the 1961 and 1970 censuses of using individually identifiable census information to correct the local population registers (see Butz, 1984, for a description of the controversy).

The Netherlands most recently carried out a census of population in 1971 administered by the municipalities, which generated an initial address list from the local population registers, recruited, trained, and paid the enumerators, and used the census returns to update the registers. The census operations were completed and data published, but about 2.3 percent of the population failed to cooperate as a consequence of public debate about computers and privacy. The 1971 census had a separate form for each person, and the questionnaire for heads of households included about 60 items. The plans for the 1981 census specified important design changes, including: (1) abandoning the practice of using census returns to update the local registers (on the basis of results from the 1971 census showing the registers to be very complete); (2) obtaining demographic information from the registers; and (3) administering a short form to four in five addresses asking solely for the number of housing units, households, and residents in each household, and a long form to the remaining 20 percent of addresses similar in length to the 1971 questionnaire. However, public concern about confidentiality of the data and disappointing response to a pretest in 1979 led the Central Commission on Statistics to recommend that the 1981 census be cancelled. In its place, the commission acted to increase the size of the Labor Force Survey from about 2.5 to 5 percent in spring 1981, to carry out a 1 percent housing survey in fall 1981, and to obtain basic demographic information from the population registers.

Sweden currently conducts a quinquennial census using mailout-mailback techniques. For the most recent census in 1980, forms were mailed to

each person age 16 or older and to each married couple with names and personal reference numbers preprinted from the local population registers. The form asked only for a list of adults permanently living in the home and for details of the person’s labor force activity. The mail return rate in both 1975 and 1980 was about 97 percent. The statistics office linked the returns to the population registers to obtain demographic data including age, sex, marital status, and citizenship and obtained data on housing from returns made by owners of real estate for tax assessment purposes. The Swedish government is actively pursuing the concept of a completely register-based census but is encountering considerable public concern.

Denmark has been the pioneer of a census based completely on administrative registers rather than enumeration. Denmark instituted local population registers beginning in 1924 and in 1968 created an automated central population register with a unique reference number for each person. The 1970 census in Denmark was the last conducted using enumeration techniques. In 1976, Denmark used the central population register to obtain a set of demographic data for all persons for statistical purposes. In 1977, the national government created a central register of buildings and dwellings, based on declarations made by property owners for tax assessment purposes, and made various other improvements in relevant administrative records systems. The government used the following registers to carry out a completely register-based census in 1981:

• Central population register;
• Central register of buildings and dwellings;
• Registers of wages and salaries paid to each employee as reported by employers to the tax office;
• Registers of income as returned by individuals to the tax office;
• Registers of employment insurance and unemployment benefits;
• Central register of enterprises and establishments;
• Register of educational achievements; and
• Geographic address coding files.

Problems posed by this census methodology in Denmark are numerous: (1) the central population register is generally believed to be of high quality but contains records for persons who have emigrated; (2) some data items, such as means of travel to work, are not available; (3) other items, notably occupation, have serious reporting problems; and (4) there have been delays in obtaining data from some registers, notably the tax office records. Chief arguments made in its favor, compared with traditional enumeration techniques, are that costs and burden on the public are greatly reduced and that data are available for items, such as income, that were never included in conventional census questionnaires. There has been very little public

objection in Denmark to the large-scale linkage of records involved in a register-based census. No evaluation information exists on the completeness and accuracy of the 1981 Denmark census.

Government and academic statisticians in the United States have suggested modifications in this nation’s census methodology that would incorporate concepts and procedures used elsewhere. The Census Bureau, as previously described, tested use of a variant of the list/leave/mailback technique in the 1980 census update list/leave experiment. More extensive use of administrative records has been proposed for purposes ranging from address list construction to improvement of coverage and selected content items (see Brown, 1984). Alvey and Scheuren (1982) have advocated research on the concept of an administrative records census and developed a preliminary assessment of the coverage and subject detail that could be expected from existing administrative records systems, such as Internal Revenue Service and Social Security Administration records. Other proposed modifications to census methodology in this country include the use of sampling for obtaining the count and adjustment of field counts for incompleteness of coverage. The next section describes the Census Bureau’s current plans for research and testing directed to the choice of methodology for the 1990 census.

CENSUS BUREAU RESEARCH PLANS FOR 1990

The Census Bureau staff has been actively working since 1983 to design and implement a research and testing program for the 1990 census. The staff prepared detailed research plans in late 1983 and early 1984 on the following topics, each of which relates to an area of interest to the Panel on Decennial Census Methodology (the most recent version is cited in each case):

• “Uses of Sampling for the Census Count” (Miskura et al., 1984) proposes research on several applications of sampling for obtaining the count, including: replacing the census with a large sample survey, following up only a sample of households that fail to mail back their questionnaires, and implementing coverage improvement and content verification programs on a sample basis.
• “Research Plan on Adjustment” (Hogan, 1984b) describes an ambitious and wide-ranging research program directed toward improvement in methods for evaluating census coverage and development of methods for adjustment of census counts and investigation of their implications for census data uses and users.
• “Record Linkage Research Plan” (Jaro, 1984a) discusses plans to develop automated procedures for matching records for use in coverage evaluation programs and other aspects of census methodology. This research plan is directed toward a critical problem

area for most methods of coverage evaluation—determining in an accurate and timely manner which persons captured in an independent survey or set of administrative records were or were not enumerated in the census.

• “Research Plan on the Uses of Administrative Records for the 1990 Census” (Brown, 1984) discusses possible uses of administrative records for coverage and content improvement and evaluation, content collection, special place enumeration, and as a replacement for the census.
• “Residence Rules for the 1990 Decennial Census” (Herriot and Speaker, 1984) reviews the rules of residence that are used in the census to determine who should be counted and to assign persons to geographic areas.

The first field activities directed toward the 1990 census involved tests of alternative methods of compiling address lists in urban and rural areas that were conducted in several localities in spring 1984 (Bureau of the Census, 1984b). Concurrently, the Census Bureau staff developed specific plans for the first full-scale pretests to be carried out in spring 1985 (Bureau of the Census, 1984b). In this round of tests, the Census Bureau experimented with various automated procedures to improve census operations in Tampa, Florida. In addition to testing use of these automated procedures in a second location, Jersey City, New Jersey, the Census Bureau conducted a test of a two-stage census operation in the latter city.

The two-stage procedure involved collecting only short-form information from all housing units in the first stage and later contacting a sample of housing units during an administratively separate second stage for long-form information. Households in the second-stage sample were asked to respond to all the short-form items once again, in contrast to the procedure used in 1960, wherein respondents were asked to repeat only name and relationship for each household member.

In conjunction with the Tampa pretest, the Census Bureau is conducting a post-enumeration survey of a sample of blocks as part of its research and testing program on coverage evaluation methods. The test will include an administrative records match for two typically hard-to-count groups, minority males ages 18-40 and minority children under age 10.

In summer and fall 1984, Census Bureau staff began to develop goals for a much more extensive pretest program to be carried out in spring 1986 (see Matchett, 1984; Johnson, 1984). The 1986 pretest objectives incorporated some of the ideas outlined in the research plans cited earlier and omitted others. Subsequently, some changes were made to the pretest plans (see Bureau of the Census, 1985b), but most of the objectives initially identified were retained. The process for planning the 1990 census pretests is actively

ongoing; the description that follows summarizes the main features of the pretest objectives for 1986 as they were defined in spring 1985.

Effort is to be directed in 1986 toward tests of specific methods and procedures in the following areas:

• Feasibility of adjustment-related operations. This area includes tests of coverage evaluation based on pre-enumeration and post-enumeration surveys of samples of blocks in an urban test site and a post-enumeration survey in a rural site. The plans include using the results from the urban post-enumeration survey to simulate all operational aspects of carrying out a full-scale adjustment of the census figures for the urban site by the end of 1986. (See Chapters 7 and 8 for additional description.)
• Automation. The Census Bureau proposes to test two major processing alternatives: (1) a system of separate collection and processing offices for use in urban areas and (2) a system of local offices that combine collection and processing for possible use in rural and selected suburban areas. The urban test will include experiments with different data entry techniques. In all instances, the intent is to develop automated processing systems that provide greater management control of the questionnaires and of the address list and that permit entry of responses into computer-readable form on a flow basis. In contrast, the 1980 census local district offices relied exclusively on clerical staff to manually check-in and review questionnaires, update the address list, and perform other operations. Questionnaires were sent in batches to one of three centers for data entry and computer processing.
• Native American enumeration techniques and procedures. The Census Bureau proposes to test various methods to improve coverage and accuracy of enumeration on American Indian reservations, including obtaining tribal rolls and designating tribal liaisons, modifying the training procedures for indigenous enumerators, and advancing travel expenses for enumerators.
• Rural area techniques and procedures. This area includes testing alternative methods of improving questionnaire delivery and coverage in rural areas that were conventionally enumerated in 1980 and also in prelist areas for which Census Bureau staff developed the mailing list in 1980 rather than working with commercial lists. (See Chapter 5 for further description.)
• Coverage improvement. This area includes tests to improve the effectiveness of at least a dozen coverage improvement procedures that were used in 1980, such as address checks, a program to recheck the status of units originally classified as vacant, a program

to check administrative records against census returns to identify possibly uncounted persons, local review of preliminary census counts, and others (see Chapter 5).

• Enumeration methods for multiunit structures with mail delivery problems. Procedures proposed for testing include refining the various checks that are conducted of the mailing list to identify likely problem addresses (e.g., buildings with a central mail drop) and to use an update list/leave procedure for multiunit structures with delivery problems, for which census enumerators rather than Postal Service staff deliver the questionnaires and update the mailing list at the same time. (See Chapter 5 for further description. The update list/leave test may be deferred until 1987.)
• Follow-up procedures. Included in this area are proposed tests to use telephone follow-up for households that do not mail back questionnaires and to use computer-assisted telephone interviewing of households whose questionnaires fail one or more edits. (A proposal originally included to test the use of sampling for follow-up of households that do not mail back questionnaires was dropped; see Chapter 6.)
• Geographic support system. Various tests are proposed of aspects of the geographic support system, including the address control files, maps, and geocoding files that assign addresses to pieces of census geography.
• Outreach. The Census Bureau proposes to test a number of ideas for improved outreach and advertising for the decennial census.
• Questionnaire design and content. This area, like coverage improvement, includes a large number of ideas and procedures for testing, such as: a general-purpose follow-on survey of short-form households about 2 months after Census Day; alternative race and ethnicity questions; questions about noncash income; questions about second residences to help minimize both overcounting and undercounting; and the use of a structure questionnaire to ask some housing items of a knowledgeable respondent, such as the building manager instead of each household. (See further description in Chapters 5 and 6.)
• Tabulation and publication systems. This area includes tests of procedures to improve processing of the short-form tabulations that are produced for local review and for redistricting use by the states.
• Work force issues. This area includes tests of ways to improve the selection, retention, and productivity of enumerators, for example, using teams of enumerators in hard-to-count areas.

The concepts and procedures proposed for testing listed under each of the above headings represent those that remained after a prior selection process. Moreover, although the staff originally assigned the objectives to three priority categories, top Census Bureau planners have indicated that their intent is to request funding for all the 1986 pretest objectives. The rationale is that there are few opportunities to test new or improved census procedures and hence that the Census Bureau must move forward to test as many promising ideas as possible. The planned tests generally include efforts, often substantial, to improve upon 1980 census methodology, but do not include radical changes in methodology, such as replacing the census with a large sample survey or obtaining census information completely from administrative records. A potentially very significant improvement over 1980 census methodology could result from the effort to develop automated procedures that can expedite data processing and lead to more timely availability of the data. Adjustment of the census counts, if it were to be implemented based on the research and testing of coverage evaluation and adjustment methods currently going forward, would also represent an important change for the 1990 census.

Finally, in fall 1984, the Census Bureau prepared a position paper updating its research plan on adjustment and proposing a specific research program for coverage evaluation in 1990 and possible adjustment of the census counts (Wolter, 1984). In brief, this paper described the Census Bureau’s plans to develop and test a design for a post-enumeration or possibly pre-enumeration sample survey to use as the major coverage evaluation program providing information that could be used for adjustment. The paper indicates that the currently preferred design is for an independent survey, instead of an existing data collection vehicle such as the Current Population Survey, and for a compact area cluster sample as opposed to a list sample, that is, a sample including all residences within selected small geographic areas, such as city blocks. The Census Bureau explicitly ruled out using the reverse record check methodology or administrative list matching, except possibly as an adjunct to the independent survey.

The paper also described plans to design and test operational procedures that could be used to adjust the census results. The paper stated that the Census Bureau’s goals are to develop procedures that, if successful, would permit adjustment of all census figures, including the population count and characteristics, in time for delivery of adjusted state population counts to the President by December 31, 1990, and in a manner such that the individual micro records could be aggregated in any possible way for tabulations and analysis. The paper acknowledged that development of satisfactory coverage evaluation and adjustment procedures would require many important improvements in methodology, including successful

implementation of a fast and accurate computer matching program. (See further discussion in Chapters 7 and 8.)

ASSESSMENT AND GENERAL RECOMMENDATIONS

The panel believes it can contribute to the choice of methodology for the 1990 census by providing a careful critique of the Census Bureau’s research and testing plans. How well the Census Bureau designs its research and testing program will crucially affect its success in improving accuracy and timeliness of the 1990 census while containing costs.

Review of 1985 Pretest Plans

The panel’s interim report, which was prepared to provide early guidance to the Census Bureau regarding proposed research and pretest plans, commented extensively on several aspects of the 1985 pretest plans, particularly the two-stage census pretest in Jersey City. The panel, on balance, did not support this methodology and recommended that research be carried out based on prior censuses before reaching a decision to commit resources to a field test (see National Research Council, 1984:Ch. 3). The Census Bureau field staff suggested that a two-stage procedure would make it possible to speed collection of the count in the first stage and thereby significantly improve the timeliness of the basic information. The Census Bureau believed it was important to obtain an early determination of the likely gains in timeliness from a two-stage procedure and, hence, proceeded with the test as planned.

The panel did not scrutinize plans for the Tampa pretest of automation procedures because the panel is not specifically addressing operational aspects of the decennial census relating to field control of the address list, data entry, and so on. However, the panel supports efforts by the Census Bureau to develop improved automated procedures that have the potential to speed up data collection, improve accuracy, and reduce costs. The panel also supports efforts to automate matching operations that may be used in coverage evaluation and coverage improvement programs.

The panel commented in the interim report on the coverage evaluation tests being conducted in Tampa and on other research in progress related to coverage evaluation and adjustment. Chapters 7 and 8 of this report comment further.

Finally, the panel recommended in the interim report that a question asking parents for names and addresses of children not residing in the household receive early testing as a coverage improvement measure (National Research Council, 1984:24). At present such a question is being considered for testing in 1987 (see further discussion in Chapter 5).

Review of 1986 Pretest Plans

For this report the panel reviewed the Census Bureau’s descriptions of proposed 1986 pretests and the proposed coverage evaluation and adjustment research program, along with the research plans listed earlier and other documents. We provide below an overall assessment of the Census Bureau’s 1990 research and testing planning process and recommend strategies for choosing priority projects. Subsequent chapters present recommendations on pretest and research plans in specific areas.

The panel has several major concerns with the research and testing program outlined for 1986. These concerns relate to the time schedule for planning the 1990 census, budget and staff resources, and the emphasis given to field testing over other kinds of research.

The panel has noted elsewhere that there is not much time to get ready for 1990. On the face of it, this reality may appear to argue for the need to test as many ideas as possible as early as possible. On the contrary, however, the panel suggests that it is likely to be self-defeating to try to handle a very large and many-faceted testing program. To be useful for making timely decisions on census methodology, test data must be obtained, analyzed, assessed, and discussed and the findings used to design subsequent tests. This process is itself time-consuming and requires ample staff and other resources (such as computer resources). If too many studies are planned for a testing cycle, there is a danger that there will not be sufficient time to obtain and assimilate results from more than a fraction of the tests for use in planning further studies or in making choices of methodology to use for the census.

Moreover, field tests are very resource-intensive, and budget resources and staff time devoted to designing and implementing a wide range of pretests are likely to take away from budget resources and staff tine available to obtain and digest the pretest results. Even though ample funds may have been allowed for the analysis phase, these funds are typically more at risk of diminution than the funds for the actual tests themselves. If the costs of testing exceed estimates, as frequently happens, the most likely outcome is a reduction in budget available for analysis.

The panel believes that the Census Bureau should give greater recognition to the problems involved in a large-scale testing program posed by the constraints of calendar and staff time needed to evaluate and assimilate the results. We believe that the Census Bureau will need to pare back its 1986 testing program if key data are to be analyzed in time to support major decisions. The program outlined appears too ambitious for the time remaining before the census and for the staff resources likely to be available.

The Census Bureau should exercise greater selectivity in several ways. First, the planning staff should carefully review all the proposed pretests to determine if some ideas should be dropped from the research and testing

program entirely. We recommend a strategy of identifying the more promising projects and pursuing only those projects from the top of the list that fit the overall time and resource constraints, even though this entails the risk that useful ideas will be ignored. Some ideas that cannot be accommodated in the 1990 research program should be considered for testing on an experimental basis in the 1990 census itself with a view toward further improvements in methodology for the year 2000.

Second, Census Bureau staff should determine if there are useful ideas that can be pursued without requiring the time and expense of full-scale pretests. There are a number of projects listed in the Census Bureau’s pretest package that we believe can be researched with much less expense and effort via other methods, such as thorough review of the Census Bureau’s own previous tests and research. The panel suggests elsewhere in the report projects for which the Census Bureau could usefully carry out research in 1986 that does not involve field tests of the kind planned for 1985 and 1986. One example is investigation of the feasibility of using administrative records to obtain improved housing structure data (see the discussion in Chapter 6).

Moreover, research other than field tests carried out in 1986 could be very helpful for designing pretests for 1987. For example, research on new questions or alternative question wording could be carried out initially by means of focus groups and laboratory experiments, in addition to the National Content Test (a large mail survey) planned for 1986. The 1986 field tests should include tests of questions related to coverage improvement (see the discussion in Chapter 5) but could well omit other question tests in order to simplify the logistical problems and costs of fielding the tests. Results from the National Content Test and small group research carried out in 1986 could suggest further question tests for the 1987 field program.

Finally, there may be proposed tests of procedures that do not need to be conducted until the 1988 dress rehearsals. For example, one proposed project is to test automated searching and updating for persons found in the Casual Count operation. This operation was low in cost in both 1970 and 1980 but also low in yield in terms of number of persons added to the count. Assuming it is worthwhile to continue the program, it does not appear that the program merits extensive testing. It could be omitted from 1986 and 1987 tests and incorporated into the dress rehearsals, which will include every procedure planned for 1990; an advantage of this approach is that by 1988 the Census Bureau should have made a decision on the type of automation system that it will use in the field.

1. Can be pursued with other research methods and omitted from the 1986 field test program;
2. Can be safety deferred for research or testing until 1987 or until the dress rehearsals;
3. Are unlikely to be viable for 1990 but should be incorporated on an experimental basis into the 1990 census as a test for future censuses; and
4. Should be omitted entirely from consideration for the 1990 census, based on previous census experience or other survey research results.

In Chapters 5 through 8 we comment on the Census Bureau’s proposed research and testing program in specific key areas of census methodology related to the panel’s charge, including: coverage improvement methods (Chapter 5), uses of sampling and administrative records (Chapter 6), adjustment methods (Chapter 7), and coverage evaluation methods (Chapter 8). The reader should note that, given the particular nature of its charge and its expertise, the panel did not undertake to review many other important aspects of census methodology, such as enumeration procedures, geographic support systems, and data entry procedures.

Chapters 5 through 8 provide specific recommendations of ideas and procedures that the panel regards as high priority for research and testing as soon as possible, as well as ideas that the panel believes can safely be given a lower priority or show little promise and should be dropped. The panel’s recommendations generally indicate a preference for the use of less resource-intensive research methods whenever possible and appropriate. The panel’s recommendations in many instances call for the Census Bureau to complete studies or reanalyze data that are already available from the 1980 census and the experiments and pretests conducted for 1980.

In general, the panel believes that research with existing data is likely to result in important additions to knowledge with low expenditure of costs compared with other methods. Obviously, more expensive methods, including full-scale field tests, are required to develop the methodology for 1990, but the research and testing program should provide resources to exploit existing data as well.

APPENDIX 3.1
AN OVERVIEW OF SEQUENTIAL HOT-DECK IMPUTATION

The Census Bureau makes use of an extremely sophisticated sequential hot-deck imputation to correct for item nonresponse in the decennial census. We briefly describe some of the features of this system. Due to its complexities, we do not attempt a complete description; see Bureau of the Census (1983e) for further information.

The individual records are processed sequentially.¹ At the start of this process, an imputation table exists that has initial values stored in it for use with various combinations of nonresponse. For example, when, at the early stages of this process, a record is encountered with age and sex missing but race, etc., responded to, this table will have an entry that will give reasonable values for the age and sex of an individual with similar characteristics. However, as more complete (or at least more complete than the nonresponse represented by entries in the imputation table) questionnaires are processed, substitute values are continually used to replace the values in the imputation table. The benefit of this substitution arises from the geographic continuity implied by the processing of the census questionnaires. The closer the donor respondent is to the nonrespondent in the census processing, the closer the two are likely to be geographically. This procedure amounts to the use of detailed geographic stratification for imputation purposes.

Although the above description gives the fundamentals of the sequential hot-deck procedure used by the Census Bureau in imputing for the decennial census dataset, there are several further complications, two of which we touch on here. Both of these complications relate to the difficult problem of using an imputation mechanism that produces a “consistent” data set when the process is finished. These two examples may give some idea of the magnitude of the problems encountered in devising an imputation procedure for the decennial census dataset.

First, it is important to understand that the order of imputation of variables is key, since there is a strong dependence between the answers given on the census questionnaire. For example, consider the situation of yes-no questions followed by further responses if the answer to the previous question was yes.

Second, consider the case of imputing age of spouse. A simple-minded suggestion would be to substitute the age of spouse for a similar respondent. Unfortunately, it is quite easy to impute the “existence” of situations that one would consider to be rather unlikely, such as spouses substantially

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¹ The short-form records and long-form records of the decennial census are treated separately. However, the differences between the imputations for the two forms are only of degree and not of kind.

older or younger than their mates. This is something that one might characterize as weak inconsistency. To avoid the above possibilities, the Census Bureau imputes so that the difference between the spouse’s and his or her mate’s ages is substituted. (One might also consider substituting based on the ratio of their ages.) This lessens the problem of having spouses and mates of vastly different ages. However, it does not necessarily address the difficulty of spouses with siblings older than their mother or father. Single cases such as age of spouse, if identified, can be treated. However, these possibilities must be noticed so that the need for these additional features in the imputation process is appreciated. Fellegi and Holt (1976) provide a solution to the problem of consistency of imputations whether carried out one variable at a time or in a multiple mode.

One of the major motivations to the use of hot-deck imputation is that imputation of averages and zeros, as well as other types of cold-deck methods, which are relatively effective as far as estimates of means and central tendencies of the dataset are concerned, severely distort the remainder of the distribution, especially the variance, of the affected variables. This is because the values imputed are far less variable than the observed responses would have been. This is especially true of imputation of averages, whose use clearly results in a reduction of the estimate of the variance of any estimate based on the dataset with imputations. Hot-deck imputation avoids this by imputing typical values from the raw dataset, thereby attempting to mimic the variance of the hypothetical complete dataset.

A relatively recent advance, termed multiple imputation (Rubin, 1978), which represents an expansion of the simple imputation strategy, may often lead to more accurate inference than single imputation. In his paper, Rubin demonstrates that at least in some simple situations—for example, estimating a mean from a simple random sample with some random nonresponse—this generalization of imputation gives rise to an unbiased estimate of the variance of the sample mean.

Ideally, it is highly desirable to control the level of imputation (by achieving high levels of good response) so that imputation will be more for user convenience than to affect the estimated mean and variances of the variables concerned.

APPENDIX 3.2
A DESCRIPTION OF ITERATIVE PROPORTIONAL FITTING

One component of the census process briefly described in Chapter 3 is the data processing component, which includes a step to relate the long-form to the short-form information. The long-form information published by the Census Bureau is acquired on a sample basis. However, for the subset of variables that also appear on the short form, information is available for all respondents. In order to promote consistency between the short-form and the long-form tabulations as well as to reduce variance and any sample biases, the Census Bureau adjusts some of the sample information so that the sample estimates agree with the 100 percent information. Iterative proportional fitting has been used by the Census Bureau since 1970 to accomplish this. Iterative proportional fitting uses the 100 percent information at an aggregate level—that is, cross-tabulations for geographic “weighting” areas of broad categories of some of the short-form variables (see Bureau of the Census, 1983f)—to weight the individual long-form records.

In a more general context, the objective of iterative proportional fitting is to allocate population totals for aggregated groups down to individual records by weighting the individual records so that totals for individuals over the subgroups agree with population totals for the aggregates. Therefore iterative proportional fitting has the potential for carrying down information from coverage evaluation programs, which is necessarily collected at an aggregate level, to the individual record level of the decennial census data set. This would ensure that the adjusted dataset would be consistent, in a manner described in Chapter 7. Consider the two-way table given in Table 3.1. The n_i+ and n_+j in Table 3.1 are the sample totals (e.g., from the long form). The m_i+ and m_+j are the row and column totals from the superior source (e.g., the short form). The problem is to use the m_i+ and m_+j , the row and column marginal totals, to adjust the elements of the table.

TABLE 3.1 Notation for Iterative Proportional Fitting for a Small Two-Way Table

Iterative proportional fitting was first proposed in Deming and Stephan (1940). The first step of this algorithm reweights the entries in column 1 by the factor . Then, assuming the values throughout all columns in the table have been altered in this manner, a new table of n_ij is created and the same operation is performed by rows, etc. After each iteration, each individual cell has been assigned a weight that applies to each member of the cell. The iteration proceeds until convergence (see Fienberg, 1970). The procedure can also be applied to multiway tables of more than two dimensions. Iterative proportional fitting will, in many situations, reduce the error of the resulting single-cell estimated totals.

In the case of controlling the long form to the short form, because the adjustment factor uses row and column totals from the sample data in the denominator, a zero row or column total will clearly require a modification to allow the resulting estimates to be finite. It is common practice to combine adjacent rows or columns if one row or column total is zero or small. If there are many zero cells in the interior of the table, the rate of convergence may be adversely affected.

Iterative proportional fitting provides the user with weights, which can be used to construct estimates of other characteristics. When iterative proportional fitting is used for the purpose of assigning weights, and not merely for adjusting tables of cross-classified counts, it is often called raking ratio estimation. Iterative proportional fitting is a generalization of synthetic estimation (described in Chapter 7), which is used on one-way contingency tables.

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