Variance Estimation for Local Pivotal Method via Monte Carlo Modeling of Joint Inclusion Probabilities

Thomas M. Menino Convention & Exhibition Center 

Spatially balanced designs, like the local pivotal method (LPM), reduce variance by inducing negative dependence among nearby units in covariate space. While the Horvitz-Thompson estimators remain design-unbiased, variance estimation is challenging because second-order inclusion probabilities are often intractable or near zero. Existing solutions follow two paths: Monte Carlo simulation to empirically estimate these probabilities, which is computationally prohibitive for large populations, or neighborhood-based estimators that bypass joint probabilities by sacrificing the use of standard design-unbiased estimators.
We link these approaches via a Monte Carlo modeling framework for variance estimation under LPM. A key limitation with Monte Carlo simulation is, without a computationally prohibitive number of samples, the empirical inclusion probabilities for spatially distant, independent pairs will falsely deviate from independence due to Monte Carlo noise. This noise inflates variance estimates which use purely empirical inclusion probabilities. To address this, we empirically estimate joint-inclusion probabilities for a subset of unit pairs, including all sampled pairs, using a feasible number of samples and train a logistic regression model to estimate the probability that a pair is independent given its covariate distance. Then, we calculate final predicted inclusion probabilities by blending the empirical estimates with the probability of independence. Using these predicted inclusion probabilities produces variance estimates that outperform existing methods without the computational burden of pure Monte Carlo estimation.

Local Pivotal Method

Spatially Balanced Designs

Variance Estimation

Second-Order Inclusion Probabilities

Monte Carlo 

Survey Research Methods Section