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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 Analyst Investigation And Correction Publication Estimates

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

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Resistant Fences Methods q 25 q 75 q 25 -1.5 H q 75 +1.5 H 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 q 75 +3 (q 75 - m) q 25 +3 (m – q 25 ) Different numbers of interquartile ranges (3 = Inner, 6 = Outer) Incorporates skewness of distribution in outlier rule (Fences)

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Robust Regression 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)

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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 (E i ) –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) –Resistant (50% breakdown) and robust Assumption of Normality –Log-transformation

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Evaluation: Classify Item Estimates Input Value Reported Final Value Tabulated Ratio Input/Final Outlier Potential Outlier Not an 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 Katherine.J.Thompson@census.gov

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