Computing Optimal Strata Bounds Using Dynamic Programming

Stratification is a sampling design that can improve efficiency. It works by first partitioning the population into homogeneous subgroups and then performing simple random sampling within each group. For a continuous variable, stratification involves determining strata boundaries. Holding the number of strata fixed, a reduction in the width of a given stratum reduces its associated variance at the expense of the variances from the other strata. Dynamic programming provides a method for simultaneously minimizing all of the strata variances by determining optimal strata boundaries. This presentation describes a new user-written command, optbounds, that uses dynamic programming to find optimal boundary points for a continuous stratification variable. The command makes use of the variance minimization technique developed by Khan, Nand, and Ahmad (2008, Survey Methodology 34: 205-214). The user first chooses a known probability distribution that approximates the stratification variable. Parameter estimates are then generated from the data and goodness of fit statistics are used to assess the quality of the approximation. A brief overview of the theory, a description of the command and several illustrative examples will be provided.