The efficiency of poststratification compared with model-assisted estimation

Abstract

Survey sampling with model-assisted estimation has recently gained popularity in forest inventory. Another option for utilizing the auxiliary information is to use poststratification, which is a special case of model-assisted estimation with class variables as explanatory variables. In this study, we compared the efficiency of poststratification with an increasing number of strata with model-assisted estimation. We carried out a study based on a simulated population. We considered four different types of poststratifications, namely (i) stratification based on predictions of a linear model, (ii) stratification based on a regression tree model, (iii) stratification based on the first principal component of the explanatory variables, and (iv) stratification based on the regression tree model with the first principal component as the only explanatory variable. Furthermore, we examined both the traditional poststratification mean and variance estimators and the difference estimator and its variance estimator for poststratification. Within the recommended range of number of strata, the model-assisted approach was more efficient than poststratification. With a large number of strata, poststratification produced smaller standard error of estimates, but problems such as empty strata were encountered with small sample sizes. Using the first principal component directly for stratification or as an explanatory variable was the most efficient approach.