Investigation of Macro Editing Techniques for Outlier Detection in Survey Data Katherine Jenny Thompson Office of Statistical Methods and Research for Economic Programs

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

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

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

Method for Bivariate Comparisons Resistant Fences Methods Symmetrized Resistant fences Asymmetric Fences Robust Regression Hidiroglou-Berthelot Edit

Bivariate Comparisons (Current Cell Ratios) Linear relationship between payroll and employment No intercept

“Traditional” Ratio Edit (Current Cell Ratio) Outlier Region Acceptance Region Outlier Region “Cone-shaped” tolerances Goes through origin Strong statistical association

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

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”)

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

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

Hidiroglou-Berthelot (HB) Edit Accounts for magnitude of unit (variability at origin)

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

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)

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

Evaluation: Classify Item Estimates Input Value Reported Final Value Tabulated Ratio Input/Final Not an Outlier Potential Outlier Outlier

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

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

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

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)

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)

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

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 )

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

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)

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)

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

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

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

Any Questions? Katherine Jenny Thompson Katherine.J.Thompson@census.gov