An application niche for finite mixture models in forest resource surveys

Abstract

We propose design-based inference with finite mixture models (FMM) in settings where heterogeneity cannot be addressed by more conventional modelling. In FMM, a model is estimated for each of K latent model subgroups in a population under study. We evaluated the FMM approach with a difference estimator with K = 2 in 600 replications of simulated equal probability sampling from 12 artificial populations. An example with a forest population in southern Norway demonstrated a practical implementation. The artificial populations were composed of one, two, three, or four actual model subgroups generated from models that were either of the same form as the estimation model or different. We compare bias and variance in estimates of a population mean with standard results for K = 1. All estimates with K = 2 were nearly unbiased. Bias was largest when actual subgroups were clustered on y. Variances in sample means with K = 1 were 60% larger than with K = 2. An important reduction in variance with K = 2 was confirmed in the case study. A reliable estimate of variance requires a medium to large sample size.