BayesianSAE using hierarchical bayes.pdf

Spatial random effects where there is modest under

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spatial random effects, where there is modest under-coverage, for the reasons already discussed. In contrast, there are severe problems with the coverage of the synthetic estimator, probably due to the fact that it has high bias and high variability. 6.2. Classification of areas We have selected the area level model and unit level Model 3 among unit level models (on the grounds of giving good results and having a better convergence) to rank the areas, using some of the different classification criteria discussed in Section 5. For the ranking method based on the posterior mean ranks, we have com- puted the mean root MSE (which seems a more reasonable criterion for ranks than the relative measures, MARB and MRRMSE) to assess which model is the best in terms of ranking the areas. In general, each type of model produces a very similar ranking, but models with unstructured random effects perform better in this regard. Furthermore, unit level models produce a slightly better ranking than area level models. In particular, mean root MSE for unit level model 3 with independent random effects is 101.76 whilst for the area level model with the same random effects it is 103.63. Thus the models that achieve the best small area estimates do not necessarily produce the most accurate rankings. As discussed earlier, Shen and Louis (1998) propose the use of triple- goal estimates to produce good small area estimates that also produce a good ranking of the areas. Figure 1 shows an example of the posterior ranking obtained with area level model with unstructured and spatial random effects. Although only the results for one survey sample are shown here, the results for the other samples are similar. Figure 1(a) displays posterior mean ranks and 95% credible intervals, with an ordering based on the true area ranks. It is clear that it is difficult to separate the low ranked areas from the medium ranked ones as many intervals overlap. Similarly, Figure 1(b) shows the posterior small area estimates of the average income per household.
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Bayesian Statistics for Small Area Estimation 21 Table 1. Summary of the performance of the small area estimates and their variance estimates for different models fitted to the 1% survey samples. The values are averaged over the n replicates. Model MARB MRRMSE DIC * MARBvar MRRMSEvar Cov. n × 100 × 100 × 100 × 100 rate ] Direct 0.5 6.5 68.7 68.8 0.94 100 Area level Synthetic 3.5 3.6 89.3 89.3 0.17 100 Bayesian u i 2.0 3.1 3246 58.8 69.1 0.93 100 v i 2.1 2.8 3279 80.2 89.7 0.91 100 u i + v i 1.8 2.9 3232 60.9 72.0 0.93 96 Unit level Synthetic 6.0 6.0 94.6 99.4 0.06 100 Bayesian Model 1 u i 3.0 4.3 495714 122.8 185.4 0.94 98 v i 3.7 4.3 495825 109.4 144.6 0.85 98 u i + v i 2.8 3.6 490784 109.6 130.0 0.93 72 Bayesian Model 2 u i 2.0 3.5 474461 42.4 61.5 0.93 100 v i 2.8 3.3 474682 102.5 124.6 0.88 100 u i + v i 1.9 3.2 474122 49.4 69.6 0.91 75 Bayesian Model 3 u i 2.0 3.5 474118 43.9 64.0 0.93 94 v i 2.0 3.0 474077 62.3 72.6 0.90 94 u i + v i 1.9 3.2 474363 56.2 76.5 0.94 76 * Area and unit DICs are not comparable because they are computed using different data.
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  • Spring '16
  • Yessi
  • Regression Analysis, Mean squared error, Bayesian inference, Bayesian statistics

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