1. SAS® Macros for Constraining Arrays of Numbers Charles D. Coleman Economic Statistical Methods Division US Census Bureau

2. Why Constrain Data Make estimates consistent with external totals. Disclosure avoidance Make data sum to data of higher precision Presentation Reduce data anomalies

3. Raking: “Multiplicative” Controlling One dimension (i.e., individual variables), a.k.a. “scaling” – Nonzero data, control of same sign Ordinary rake – Multiply by ratio of control to sum. – Monotonic: All data move in same direction as control. – Preserves order: Order of data in output vector same as input vector. – Preserves ratios: Ratios of pairs of elements of output vector same as input vector. – %RAKE With BY-groups – %RAKEBY – Data of Mixed sign Generalized rake – Weighted sum of ordinary rake and difference between control, original sum. – Monotonic – Preserves order – Does not preserve ratio – Nonunique solution – %GENRAKE

4. Raking: “Multiplicative” Controlling Two dimensions (matrices) – Nonnegative data, fixed positive marginals (controls) Two-way rake, a.k.a. RAS algorithm, matrix scaling… – Alternately multiply columns, rows to controls ÷ corresponding sums – Iterate until convergence – Always converges when feasible solution exists – %RAKE2WAYS – Nonnegative data, marginals in intervals Range-RAS algorithm – %RRAS

5. Controlled Rounding Round data to preserve original sum. – Requires unconventional “wrong-way” rounding. Two Dimensions – Cox-Ernst Algorithm minimizes total cost of rounding. Sands (2003) NESUG paper covers the method. Macro based on transportation problem example in SAS documentation. – Requires SAS 9.2+. – %CONTROLROUND One Dimension – Greatest Mantissa Algorithm Simplification of Cox-Ernst Algorithm Assign output data the integral parts of input data Round up mantissas in decreasing order until sum of output data equals sum of input data %GMROUND – With BY-group processing %GMROUNDBY

6. Raking and Rounding in 1 Macro One dimension – %RAKEANDGMROUND One dimension with BY-groups – %RAKEANDGMROUNDBY Two dimensions – %RAKEANDROUND2WAYS Two dimensions with BY-groups – %RAKEANDROUND2WAYSBY

7. Files Location http://sourceforge.net/p/constrainingarrays/cod e/ci/master/tree/ – Also in paper.