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A Study of Sources for the Error Structure in Estimates

of Census Coverage Error Components

Mary H. Mulry

U.S. Census Bureau

2009 International Total Survey Error Workshop

June 16, 2008

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Census Coverage Error Definitions

• Net census coverage error = omissions – erroneous enumerations

• Components of coverage error• Erroneous enumerations• Omissions

• Estimated net error in Census 2000 was small, but evidence indicated component errors were larger

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Net census coverage error• DSE used to estimate net coverage error• Case-by-case matching of enumeration(E) &

independent population(P) samples • Processing employs balancing of errors that

improves net error estimates

• Net error estimate is unbiased if no model error: net error = DSE – census

• However, balancing of errors causes upward bias in weighted nonmatches and weighted erroneous enumerations

• Not suitable for component errors

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Components of coverage errors omissions & erroneous enumerations

• Component error estimation needs processing without balancing of errors needed for net error• Collect more data from respondents• More processing of DSE data • Different estimators

• Estimators: EEs = weighted erroneous enumerations Omissions = net error + EEs

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Error structure in component errors

• Recent studies (Mulry 2008, Spencer 2008)

• Error structure in estimate of erroneous enumerations yields understanding of error structure in estimate of omissions

• Some offsetting of errors in estimates of omissions• Errors present in estimate of EEs for net error

offset in estimate of EEs for components

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Definition of Components of Census Coverage Error

• Erroneous enumerations• Duplicate enumerations• People born after Census Day• People who died before Census Day• Enumerations for people not residents of a HU in the U.S.

• Omissions• People who should have been enumerated in the Census

but were not

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Definition of Correct Location for Enumeration

• For net error• Persons must be enumerated in a

HU within the search area of their ‘usual residence’

• For component errors• Persons must be enumerated in a

HU once anywhere in the U.S.

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SufficientInformation for

Net Error Processing

InsufficientInformation for

Net Error Processing

Data-DefinedEnumerations

Various Levels ofM issing Data

(census imputes)

Non-Data-DefinedEnumerations

Census

Varying amounts of data reported for Census enumerations

E1 E0

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Data-defined EnumerationsE1 has sufficient info for net error

CE1 = correct enumerations

EE1 = erroneous enumerations

WL1 = enumerations in wrong location, but only enumeration for person

E0 has insufficient info for net error

CE0 = correct enumerations

EE0 = erroneous enumerations

WL0 = enumerations in wrong location, but only enumeration for person

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Estimates of Erroneous Enumerations

EE EE WL Enet 1 1 0

EE EE EEcom ponen t 1 0

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Notation for errors in status in enumeration sample

True statuscoded status

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True status vs coded status for enumeration sample

coded status correct erroneous wrong location

correct CE CE EE CE WL CE

erroneous CE EE EE EE WL EE

wrong location CE WL EE WL WL WL

True status

Subscript is coded status

True values are sums of columnsEstimates are sums of rows

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Net error terms are important for component error estimates

e CE W LWL CE W L CE

e EE W LWL EE W L EE

e CE EECE EE EE CE

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Types of errors in data

• Identification of duplicate enumerations

• Membership in housing unit population

• Usual residence

• Geocoding housing unit containing the enumeration

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How Errors Occur

Failure to detect

False detection

Types of errors•Duplication•Population member•Usual residence•Geocoding

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Correct Enum coded Erroneous

•False duplicate

•Undetected HU pop member

•Undetected usual residence•Has duplicate that is misclassified as usual residence

Erroneous Enum coded Correct

•Undetected duplicate

•Falsely HU pop member

•False usual residence•Has duplicate that is usual residence

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Correct Enum coded Wrong Location

•Undetected usual residence•Another HU misclassified as usual residence & not enumerated there

•False geocoding error & only enumeration

Wrong Location coded Correct Enum

•False usual residence•Another HU is usual residence & not enumerated there

•Undetected geocoding error & only enumeration

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Erroneous Enum coded Wrong Location

•Undetected duplicate •Misclassified as only residence, but also enumerated at usual residence

•Falsely HU pop member •Misclassified as in HU pop at wrong location

Wrong Location coded Erroneous Enum•False duplicate

•Usual residence outside search area & not enumerated there

•Undetected HU pop member at wrong location

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Sources of errors

• Processing errors• 2 studies evaluate 2010 CCM

• Data collection errors• 4 studies evaluate for 2010 CCM

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Info on processing error

• Matching Error Study• All types of errors

• Administrative Records Study• Types of error: Duplication, HU pop

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Info on data collection error

• Respondent debriefings• Types of error: usual residence, HU pop

• Study of Missed Housing Units• Type of error: geocoding

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Info on data collection error

• Recall bias study• Type of error: usual residence

• Comparison of census operations with CCM results• Type of error: geocoding

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Summary of error sources

• Synthesis of info from CCM evaluations • Designing simulation study to aid

analysis of error structure

• Develop better understanding of error structure

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mary.h.mulry@census.gov

U.S. Census Bureau