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**Investigation of Macro Editing Techniques for Outlier Detection in Survey Data**

Katherine Jenny Thompson Office of Statistical Methods and Research for Economic Programs

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**Simplified Survey Processing Cycle**

Data Collection/ Analyst Review Micro-editing And Imputation Individual Returns Macro-editing Tabulated Initial Estimates Publication Estimates Analyst Investigation And Correction

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**Identifying Outlying Estimates**

Set of Estimates Unknown parametric distribution (robust) Contains outliers (resistant) Outlier-identification problems (Multiple Outliers) Masking: difficult to detect an individual outlier Swamping: too many false outliers flagged

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**Outlier Detection Approaches**

Sets of “bivariate” (Ratio) comparisons Same estimate from two consecutive collection periods (historic cell ratios) Different estimates in same collection period (current cell ratios) Multivariate comparisons Current period data

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**Method for Bivariate Comparisons**

Resistant Fences Methods Symmetrized Resistant fences Asymmetric Fences Robust Regression Hidiroglou-Berthelot Edit

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**Bivariate Comparisons (Current Cell Ratios)**

Linear relationship between payroll and employment No intercept

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**“Traditional” Ratio Edit (Current Cell Ratio)**

Outlier Region Acceptance Region Outlier Region “Cone-shaped” tolerances Goes through origin Strong statistical association

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**Resistant Fences Methods**

q25-1.5H q75+1.5H q25 q75 Different numbers of interquartile ranges (1.5 = Inner, 3 = Outer) Implicitly assumes symmetry May want to “symmetrize”, apply rule, use inverse transformation

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**Asymmetric Fences Methods**

q25+3 (m – q25) q75+3 (q75- m) Different numbers of interquartile ranges (3 = Inner, 6 = Outer) Incorporates skewness of distribution in outlier rule (“Fences”)

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**Robust Regression Resistant (minimizes median residual)**

Least Trimmed Squares Robust Regression Resistant (minimizes median residual) Outlier = |residual| 3 robust M.S.E.

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**Issue at Origin (Historic Cell Ratio)**

Alternative Approach (Ratio Editing) --Hidiroglou-Berthelot (HB) Edit Originally designed to detect outlying values in periodically collected micro-data Requires “complete” set of micro-data in an “industry” Characterized by dynamic tolerances

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**Hidiroglou-Berthelot (HB) Edit**

Accounts for magnitude of unit (variability at origin)

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**Hidiroglou-Berthelot (HB) Edit**

Two-step transformation (Ei) Centering transformation on ratios Magnitude transformation that accounts for the relative importance of large cases Asymmetric Fences “Type” Outlier Rule Key Parameter U = magnitude transformation parameter (0 U 1) C = controls width of outlier region

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**Multivariate Methods: Mahalanobis Distance**

Multivariate normal (,) T(X) estimates C(X) estimates p is the number of distinct variables (items) Prone to masking (difficult to detect individual outliers)

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**Robust Alternatives M-estimation (not considered) “Production Method”**

Minimum Volume Ellipse (MVE) Resistant (50% breakdown) and robust Minimum Covariance Determinant (MCD) Assumption of Normality Log-transformation

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**Evaluation: Classify Item Estimates**

Input Value Reported Final Value Tabulated Ratio Input/Final Not an Outlier Potential Outlier Outlier

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**Evaluation: Classify Ratios (Bivariate)**

Conservative Ratio is “outlier” if numerator or denominator is an outlier Anti-Conservative Ratio is “outlier” if numerator or denominator is an outlier or a potential outlier

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**Evaluation: Classify Records (Multivariate)**

Conservative Record is “outlier” at least one estimate is an outlier Anti-Conservative Record is “outlier” at least one estimate is an outlier or a potential outlier

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**Evaluation Statistics: Bivariate Comparisons**

Individual Test Level Type I Error Rate: proportion of false rejects Type II Error Rate: proportion of false accepts Hit Rate: proportion of flagged estimates that are outliers All-Test Level All-item Type II error rate

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**Evaluation Statistics: Multivariate Comparisons**

Type I error rate: the proportion of non-outlier records that are flagged as outliers Type II error rate: the proportion of outlier records that are not flagged as outliers (missed “bad” values)

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**Annual Capital Expenditures Survey (ACES)**

Sample Survey (Stratified SRS-WOR) ACE-1: Employer companies ACE-2: Non-employer companies (not discussed) New sample selection each year Total and year-to-year change estimates Total Capital Expenditures Structures (New and Used) Equipment (New and Used)

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**Capital Expenditures Data**

Characterized by Low year-to-year correlation (same company) Weak association with available auxiliary data Editing procedures focus on additivity Outlier correction at micro-level

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**Bivariate Comparisons**

Robust Regression Resistant Fences HB Edit Structures/Total New Structures/Structures New Structures/Used Structures Equipment/Total New Equipment/Equipment Resistant Fences: (Symmetric or Asymmetric) (Inner or Outer) HB Edit: (U = 0.3 or 0.5) (c = 10 or 20 )

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**Results – Individual Tests**

Robust Regression prone to swamping High Type I error rate (false rejects) Comparable performance with Asymmetric Inner Fences and HB Edit (U = 0.3, c = 10) Low Type I error rates High Hit Rates High Type II error rates Other variations of Resistant Fences and HB edit not as good

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**Results – All-Tests Very large Type II error rates (approx. 50%)**

Robust regression Symmetric resistant outer fences HB edit with c = 20 Improved Type II error rates (30% - 40%) Asymmetric inner fences HB edit (U = 0.3, C=10)

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**Multivariate Results Original Data: considered methods ineffective**

Log-transformed data: improved performance (MCD and MVE) Reduced Type I error rates Comparable Type II error rates (to original-data MCD and MVE)

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**Multivariate Versus Bivariate: Different Outcomes (Conservative)**

Combined HB edits flag more “outliers”: Higher Type I error rate Lower Type II error rates for the complete set of HB edits

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Comments Economic data with inconsistent statistical association between items in each collection period Critical values must be determined by the data set at hand (no “hard-coding”) Dynamically Standardize the comparisons (HB edit, log transformation) Compute outlier limits Could try hybrid approach: Multivariate a few current cell ratio tests with the HB edit Perform all bivariate tests, but unduplicate cells before analyst review

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**Final Thoughts/Next Steps**

Examine one set of economic data and considered only two separate collections from this program. Extrapolation would be foolish My results need to be validated on other economic data sets a more typical periodic business survey and/or a well-constructed simulation study

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**Any Questions? Katherine Jenny Thompson**

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