bias should usually be determined according to need. This is of particular importance when determining priorities across areas based on small area estimates. If an area’s true poverty rate is 50% and the method yields an estimator of 10% due to a biased model, there is a real risk that this area may not be given assistance when needed. Molina (2019) suggests 5 or 10 percent of absolute relative bias as an acceptable threshold. An additional problem for unit-context models in many applications is it is not possible to match census and survey PSUs; in some cases it is due to confidentiality reasons and in others it is due to different sampling frames used for the survey. The latter is something that is likely to affect applications where census and surveys correspond to different years. Under these scenarios, unit-context models are unlikely to be superior to FH and alternative area models.

# **5 Conclusions**

In this paper we have illustrated that one of the most important aspects of SAE applications with Census EB methods under unit models is selecting a proper model; especially the issue of data transformation. Such a finding is not new, and has been quite often echoed by others in the area (see Marhuenda et al. 2017; Molina and Marhuenda 2015; Tzavidis et al. 2018). Here we show how data transformations can lead to improved results. For example, under onefold nested error models, the aggregate gains from moving to a log-shift transformation as opposed to just taking the natural logarithm are close to 30 percent in terms of MSE. Nevertheless, as Marhuenda et al. (2017) note, finding an appropriate transformation is not always straightforward and the resulting data could stray from normality which would lead to biased estimates as we also find here. Consequently, model checks and residual analysis are something that every SAE application should include in order to test if the model’s assumptions are not completely invalidated. In case of data deviating from model assumptions, the model should be changed accordingly. For instance, in case of area outliers, fixed effects could be included for those outlying areas in the model to reduce the design bias. If their sample sizes are not too small, the efficiency of the resulting model-based estimates might be acceptable in this case, even if specific model parameters are specific to these areas.

Second, we have validated SAE applications under model-based simulation and design-based simulation methods. Under model-based validation, where the data generating process follows a twofold nested error model, we note the ELL method still performs poorly in terms of MSE even with contextual level variables. The result is most evident in scenarios where area random effects are larger than cluster random effects, since contextual variables do not explain a sufficient amount of the area’s variability. Issues regarding the underestimation of this noise under ELL are not evaluated here, but should be considered by future practitioners, particularly when the noise is estimated under the MI inspired bootstrap method (see Corral et al. 2020; Das and Chambers 2017; Marhuenda et al. 2017 ). On the other hand, model-based simulations conducted here provide further evidence to the finding from Marhuenda et al. (2017) that misspecification of the model under the onefold CensusEB, i.e. modeling random effects at the area level only, when the true model has cluster and 37