Exploring Balanced Sampling via the INCA Algorithm and the Cube Method

Thomas M. Menino Convention & Exhibition Center 

Balanced sampling uses auxiliary information to enhance sample representativeness in multipurpose survey settings. The USDA's National Agricultural Statistics Service (NASS) has traditionally implemented this through the Multivariate Probability Proportional to Size (MPPS) design, an extension of Brewer sampling. In collaboration with the National Opinion Research Center (NORC) at the University of Chicago, we assessed whether the cube method can further improve MPPS by incorporating balanced sampling principles. This presentation also evaluates integer‑calibration (INCA) algorithms, which apply discrete optimization over a constrained integer lattice, as a potential alternative to the cube method. We compare the statistical performance and computational requirements of INCA, originally developed for the U.S. Census of Agriculture, with those of the cube method. Using data from the 2017 Census of Agriculture, we quantify and contrast the relative errors produced by each approach, highlighting their practical implications for large‑scale survey design.

Auxiliary information

Balanced sampling

Discrete optimization

Multipurpose survey

MPPS sampling

Relative errors 

Survey Research Methods Section