Effects of temporally external auxiliary data on model-based inference

One of the benefits of model-based inference relative to design-based inference is that probability samples are not required which means that models can be constructed using data external to the area of interest. Although “external” usually means spatially or geographically external, it could also be used in the temporal sense that the model is constructed using data whose dates are temporally external to the dates of the data to which the model is applied. This study focuses on assessing the effects of such temporally external application data on model-based inference using remotely sensed auxiliary information. The study area was in Burkina Faso, and the variable of interest was firewood volume (m³/ha). A sample of 160 field plots was selected from the population and measured, and auxiliary datasets from Landsat 8 were acquired. Models were fit using weighted least squares; the population mean, μ, was estimated; and the variance of the population mean, Varμ̂, was estimated using both an analytical variance estimator, V̂−μ̂_an, and an empirical bootstrap estimator, Vμ̂_boot. The estimates, μ̂ and Var̂μ̂, were compared for models constructed using calibration and application data of the same date and models constructed using calibration and application data whose dates differed. The primary results were twofold. First, for cases for which the dates of the model calibration and application data were the same, μ̂, V̂−μ̂_an, Vμ̂_boot and Biaŝμ̂ were similar across datasets. These results suggest that the particular date of the dataset from which the calibration and application data are obtained may be mostly arbitrary assuming the relation between the dependent and independent variables does not change over time. Second, for a model for which the calibration and application data were obtained from temporally different datasets, V̂−μ̂_an, Vμ̂_boot, and Biaŝμ̂ were all greater than when the calibration and application data were not temporally different. Further, the criterion for screening candidate models must be based on estimation of μ̂ and Var̂μ̂ rather than the model prediction accuracy or goodness of fit. The adverse effects of differing dates for the calibration and application data were exacerbated as the difference in dates increased. Finally, because the temporal differences also affected the analytical variance calculation, the bootstrapping procedure is recommended.