Complete Workflow with hbsaems 1.1.0

library(hbsaems)

A typical Bayesian SAE workflow with hbsaems v1.1.0 follows seven steps, each backed by a single primary function. This vignette walks through the canonical pipeline.

See also

For deeper coverage of topics beyond this introductory workflow, see the articles on the package website:

https://madsyair.github.io/hbsaems/articles/

The articles cover:

0. Inspect the data

data("data_fhnorm")
str(data_fhnorm, max.level = 1)
#> 'data.frame':    100 obs. of  9 variables:
#>  $ y         : num  6.98 9.01 6.22 10.47 10.62 ...
#>  $ D         : num  0.921 2.643 1.704 0.659 1.017 ...
#>  $ x1        : num  -0.9026 -0.7527 -0.2606 0.0759 0.2118 ...
#>  $ x2        : num  0.712 -0.878 -0.607 -1.077 -0.502 ...
#>  $ x3        : num  1.431 -0.318 -1.029 -1.071 -0.496 ...
#>  $ theta_true: num  8.5 9.73 8.54 9.68 11.86 ...
#>  $ u         : num  -0.8531 -0.0145 -1.2505 -0.5989 1.5845 ...
#>  $ regency   : chr  "regency_001" "regency_002" "regency_003" "regency_004" ...
#>  $ province  : chr  "province_01" "province_01" "province_01" "province_01" ...
#>  - attr(*, "datalabel")= chr "data_fhnorm"
#>  - attr(*, "var.labels")= chr [1:9] "" "" "" "" ...
head(data_fhnorm[, c("regency", "province", "y", "D", "x1", "x2", "x3")], 4)
#>       regency    province         y         D         x1         x2         x3
#> 1 regency_001 province_01  6.982249 0.9213655 -0.9026345  0.7116302  1.4305563
#> 2 regency_002 province_01  9.005801 2.6432183 -0.7526745 -0.8779797 -0.3182451
#> 3 regency_003 province_01  6.216509 1.7035092 -0.2605613 -0.6066989 -1.0293040
#> 4 regency_004 province_01 10.469687 0.6586857  0.0759456 -1.0766939 -1.0711613

data_fhnorm is a simulated Fay-Herriot dataset: 100 regencies nested within 5 provinces, with a known sampling variance D per area and three covariates.

1. Prior predictive check

# This is the production call.  Replace `chains`, `iter` with your
# usual values; the lighter settings below are a quick demonstration.
model_prior <- hbm(
  formula           = brms::bf(y ~ x1 + x2 + x3),
  data              = data_fhnorm,
  re                = ~ (1 | regency),     # area-level random effect (Fay-Herriot)
  sampling_variance = "D",                 # KNOWN sampling variance D_i
  sample_prior      = "only",
  prior             = c(
    brms::prior(normal(0, 1),  class = "b"),
    brms::prior(normal(10, 5), class = "Intercept"),
    brms::prior(normal(0, 2),  class = "sd")
  ),
  chains = 2, iter = 1000
)
pc <- prior_check(model_prior,
                  data         = data_fhnorm,
                  response_var = "y")
plot(pc)

The sampling_variance = "D" argument is the defining feature of a Fay-Herriot model: the sampling variance is treated as known from the design (it is not estimated), so brms pins the observation-level to . Omitting this argument makes the model unidentified because the residual and the area random-effect would compete to explain the same variance, typically producing divergent transitions and very wide credible intervals.

2. Fit the model

model <- hbm(
  formula           = brms::bf(y ~ x1 + x2 + x3),
  data              = data_fhnorm,
  re                = ~ (1 | regency),
  sampling_variance = "D",
  control           = list(adapt_delta = 0.99),
  chains            = 4, iter = 4000, warmup = 2000, cores = 4
)
summary(model)

Two settings deserve attention:

A small fitted model to demonstrate the rest of the workflow

For the remainder of the vignette we use a tiny model (very few iterations) so that the diagnostic and prediction chunks below have a real object to operate on. In your own analysis, use the full production settings shown above, not the toy settings here.

# Mini fit -- iter = 200, chains = 1 -- for vignette demonstration only.
# Do NOT use these settings for inference: the chains have not
# converged at this length and the posterior will be biased.
fit_demo <- suppressWarnings(
  hbm(
    formula           = brms::bf(y ~ x1 + x2 + x3),
    data              = data_fhnorm,
    re                = ~ (1 | regency),
    sampling_variance = "D",
    chains  = 1,
    iter    = 200,
    warmup  = 100,
    refresh = 0,
    seed    = 1
  )
)

3. Convergence diagnostics

# Operate on the mini fit_demo above (NOT a substitute for production
# diagnostics on full chains).
diag <- convergence_check(fit_demo)
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> No divergences to plot.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
is_converged(fit_demo)
#> [1] FALSE
summary(diag)
#> 
#> ===== Convergence Diagnostics Summary =====
#> 
#> Divergent transitions: 0 (0.00%)
#> E-BFMI (min over chains): 0.930
#> Max-treedepth hit rate: 0.00%
#> 
#> R-hat:
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#>  0.9904  0.9961  1.0030  1.0126  1.0175  1.1435 
#> 
#> Bulk ESS:
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#>   43.85  131.49  171.06  160.25  200.00  200.00 
#> 
#> Tail ESS:
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#>   21.15   64.12   76.15   75.61   90.20  116.78 
#> 
#> Geweke test (Z-scores):
#> [[1]]
#> 
#> Fraction in 1st window = 0.1
#> Fraction in 2nd window = 0.5 
#> 
#>                      b_Intercept                             b_x1 
#>                         0.439675                         0.675512 
#>                             b_x2                             b_x3 
#>                        -0.110359                        -1.329367 
#>            sd_regency__Intercept                        Intercept 
#>                        -0.351228                         0.518596 
#> r_regency[regency_001,Intercept] r_regency[regency_002,Intercept] 
#>                         1.482982                         0.578184 
#> r_regency[regency_003,Intercept] r_regency[regency_004,Intercept] 
#>                         0.064829                        -1.694880 
#> r_regency[regency_005,Intercept] r_regency[regency_006,Intercept] 
#>                        -0.086819                        -1.550906 
#> r_regency[regency_007,Intercept] r_regency[regency_008,Intercept] 
#>                        -0.225457                        -1.634221 
#> r_regency[regency_009,Intercept] r_regency[regency_010,Intercept] 
#>                        -0.573915                         0.352415 
#> r_regency[regency_011,Intercept] r_regency[regency_012,Intercept] 
#>                         0.329977                        -1.152600 
#> r_regency[regency_013,Intercept] r_regency[regency_014,Intercept] 
#>                        -0.184377                         0.994029 
#> r_regency[regency_015,Intercept] r_regency[regency_016,Intercept] 
#>                        -0.734035                        -0.459930 
#> r_regency[regency_017,Intercept] r_regency[regency_018,Intercept] 
#>                         1.866025                        -0.857966 
#> r_regency[regency_019,Intercept] r_regency[regency_020,Intercept] 
#>                        -0.910251                        -0.124925 
#> r_regency[regency_021,Intercept] r_regency[regency_022,Intercept] 
#>                        -0.638350                        -1.228459 
#> r_regency[regency_023,Intercept] r_regency[regency_024,Intercept] 
#>                        -2.227878                         0.009446 
#> r_regency[regency_025,Intercept] r_regency[regency_026,Intercept] 
#>                        -0.570614                         0.706367 
#> r_regency[regency_027,Intercept] r_regency[regency_028,Intercept] 
#>                        -0.153144                         0.666069 
#> r_regency[regency_029,Intercept] r_regency[regency_030,Intercept] 
#>                        -0.675936                         0.019550 
#> r_regency[regency_031,Intercept] r_regency[regency_032,Intercept] 
#>                         0.157159                         0.068315 
#> r_regency[regency_033,Intercept] r_regency[regency_034,Intercept] 
#>                        -1.454501                        -1.038916 
#> r_regency[regency_035,Intercept] r_regency[regency_036,Intercept] 
#>                        -1.488091                        -1.626934 
#> r_regency[regency_037,Intercept] r_regency[regency_038,Intercept] 
#>                         0.353194                         0.786427 
#> r_regency[regency_039,Intercept] r_regency[regency_040,Intercept] 
#>                        -1.751016                         0.171068 
#> r_regency[regency_041,Intercept] r_regency[regency_042,Intercept] 
#>                         0.223230                        -1.462420 
#> r_regency[regency_043,Intercept] r_regency[regency_044,Intercept] 
#>                        -1.376935                        -0.370675 
#> r_regency[regency_045,Intercept] r_regency[regency_046,Intercept] 
#>                        -1.063761                        -0.341718 
#> r_regency[regency_047,Intercept] r_regency[regency_048,Intercept] 
#>                         0.665556                        -1.282668 
#> r_regency[regency_049,Intercept] r_regency[regency_050,Intercept] 
#>                        -1.338728                        -0.110090 
#> r_regency[regency_051,Intercept] r_regency[regency_052,Intercept] 
#>                        -0.292501                        -0.653364 
#> r_regency[regency_053,Intercept] r_regency[regency_054,Intercept] 
#>                         0.761260                        -0.265161 
#> r_regency[regency_055,Intercept] r_regency[regency_056,Intercept] 
#>                        -0.781514                        -1.031518 
#> r_regency[regency_057,Intercept] r_regency[regency_058,Intercept] 
#>                        -1.326952                        -0.026405 
#> r_regency[regency_059,Intercept] r_regency[regency_060,Intercept] 
#>                         0.556657                         1.998405 
#> r_regency[regency_061,Intercept] r_regency[regency_062,Intercept] 
#>                        -0.076548                        -0.893495 
#> r_regency[regency_063,Intercept] r_regency[regency_064,Intercept] 
#>                         1.830265                         1.063698 
#> r_regency[regency_065,Intercept] r_regency[regency_066,Intercept] 
#>                        -1.320349                        -2.125862 
#> r_regency[regency_067,Intercept] r_regency[regency_068,Intercept] 
#>                         0.086755                         0.826772 
#> r_regency[regency_069,Intercept] r_regency[regency_070,Intercept] 
#>                        -2.425150                        -1.021848 
#> r_regency[regency_071,Intercept] r_regency[regency_072,Intercept] 
#>                        -0.921946                        -0.061025 
#> r_regency[regency_073,Intercept] r_regency[regency_074,Intercept] 
#>                         1.882800                        -2.702286 
#> r_regency[regency_075,Intercept] r_regency[regency_076,Intercept] 
#>                        -1.796570                         0.426268 
#> r_regency[regency_077,Intercept] r_regency[regency_078,Intercept] 
#>                         1.079833                         0.048222 
#> r_regency[regency_079,Intercept] r_regency[regency_080,Intercept] 
#>                        -0.276625                        -0.434901 
#> r_regency[regency_081,Intercept] r_regency[regency_082,Intercept] 
#>                         0.373386                        -1.262929 
#> r_regency[regency_083,Intercept] r_regency[regency_084,Intercept] 
#>                        -1.747763                         0.778250 
#> r_regency[regency_085,Intercept] r_regency[regency_086,Intercept] 
#>                         0.027099                         0.458924 
#> r_regency[regency_087,Intercept] r_regency[regency_088,Intercept] 
#>                         1.064617                        -1.144627 
#> r_regency[regency_089,Intercept] r_regency[regency_090,Intercept] 
#>                        -0.268693                         0.005188 
#> r_regency[regency_091,Intercept] r_regency[regency_092,Intercept] 
#>                         0.625051                         0.007719 
#> r_regency[regency_093,Intercept] r_regency[regency_094,Intercept] 
#>                        -1.305631                        -0.166948 
#> r_regency[regency_095,Intercept] r_regency[regency_096,Intercept] 
#>                        -0.715510                         0.749165 
#> r_regency[regency_097,Intercept] r_regency[regency_098,Intercept] 
#>                        -1.672694                        -2.087388 
#> r_regency[regency_099,Intercept] r_regency[regency_100,Intercept] 
#>                        -0.694299                        -1.305847 
#>                           lprior                             lp__ 
#>                        -0.052890                        -1.287801 
#>                         z_1[1,1]                         z_1[1,2] 
#>                         1.025456                         0.657983 
#>                         z_1[1,3]                         z_1[1,4] 
#>                        -0.007537                        -1.689116 
#>                         z_1[1,5]                         z_1[1,6] 
#>                        -0.185234                        -1.505061 
#>                         z_1[1,7]                         z_1[1,8] 
#>                        -0.189963                        -1.297634 
#>                         z_1[1,9]                        z_1[1,10] 
#>                        -0.611099                         0.524402 
#>                        z_1[1,11]                        z_1[1,12] 
#>                         0.250522                        -1.047651 
#>                        z_1[1,13]                        z_1[1,14] 
#>                        -0.179149                         1.020036 
#>                        z_1[1,15]                        z_1[1,16] 
#>                        -0.693134                        -0.585218 
#>                        z_1[1,17]                        z_1[1,18] 
#>                         2.100592                        -0.860425 
#>                        z_1[1,19]                        z_1[1,20] 
#>                        -1.204257                        -0.143581 
#>                        z_1[1,21]                        z_1[1,22] 
#>                        -0.639256                        -1.453809 
#>                        z_1[1,23]                        z_1[1,24] 
#>                        -2.248067                        -0.017670 
#>                        z_1[1,25]                        z_1[1,26] 
#>                        -0.369461                         0.547181 
#>                        z_1[1,27]                        z_1[1,28] 
#>                        -0.231902                         0.524318 
#>                        z_1[1,29]                        z_1[1,30] 
#>                        -0.648019                        -0.013206 
#>                        z_1[1,31]                        z_1[1,32] 
#>                         0.128067                         0.077570 
#>                        z_1[1,33]                        z_1[1,34] 
#>                        -1.271948                        -0.932256 
#>                        z_1[1,35]                        z_1[1,36] 
#>                        -1.468568                        -1.599269 
#>                        z_1[1,37]                        z_1[1,38] 
#>                         0.301756                         0.989599 
#>                        z_1[1,39]                        z_1[1,40] 
#>                        -1.740444                         0.216227 
#>                        z_1[1,41]                        z_1[1,42] 
#>                         0.416618                        -1.274363 
#>                        z_1[1,43]                        z_1[1,44] 
#>                        -1.133581                        -0.041793 
#>                        z_1[1,45]                        z_1[1,46] 
#>                        -1.152071                        -0.337986 
#>                        z_1[1,47]                        z_1[1,48] 
#>                         0.762589                        -1.349635 
#>                        z_1[1,49]                        z_1[1,50] 
#>                        -1.280454                        -0.225432 
#>                        z_1[1,51]                        z_1[1,52] 
#>                        -0.303364                        -0.562894 
#>                        z_1[1,53]                        z_1[1,54] 
#>                         0.639453                        -0.043853 
#>                        z_1[1,55]                        z_1[1,56] 
#>                        -0.564568                        -1.157184 
#>                        z_1[1,57]                        z_1[1,58] 
#>                        -1.152060                        -0.099215 
#>                        z_1[1,59]                        z_1[1,60] 
#>                         0.935305                         1.811214 
#>                        z_1[1,61]                        z_1[1,62] 
#>                        -0.092633                        -0.761527 
#>                        z_1[1,63]                        z_1[1,64] 
#>                         1.720061                         1.020080 
#>                        z_1[1,65]                        z_1[1,66] 
#>                        -1.753982                        -2.212438 
#>                        z_1[1,67]                        z_1[1,68] 
#>                         0.202992                         0.872749 
#>                        z_1[1,69]                        z_1[1,70] 
#>                        -2.673858                        -1.243029 
#>                        z_1[1,71]                        z_1[1,72] 
#>                        -0.910726                        -0.115829 
#>                        z_1[1,73]                        z_1[1,74] 
#>                         1.713765                        -2.525547 
#>                        z_1[1,75]                        z_1[1,76] 
#>                        -1.877583                         0.737048 
#>                        z_1[1,77]                        z_1[1,78] 
#>                         1.104834                        -0.037961 
#>                        z_1[1,79]                        z_1[1,80] 
#>                        -0.308535                        -0.377443 
#>                        z_1[1,81]                        z_1[1,82] 
#>                         0.281008                        -1.239269 
#>                        z_1[1,83]                        z_1[1,84] 
#>                        -1.444329                         0.529094 
#>                        z_1[1,85]                        z_1[1,86] 
#>                         0.062075                         0.368325 
#>                        z_1[1,87]                        z_1[1,88] 
#>                         1.414949                        -1.230895 
#>                        z_1[1,89]                        z_1[1,90] 
#>                        -0.334978                        -0.094349 
#>                        z_1[1,91]                        z_1[1,92] 
#>                         0.474061                        -0.059493 
#>                        z_1[1,93]                        z_1[1,94] 
#>                        -1.482723                         0.052240 
#>                        z_1[1,95]                        z_1[1,96] 
#>                        -0.933766                         0.583424 
#>                        z_1[1,97]                        z_1[1,98] 
#>                        -1.645358                        -2.388447 
#>                        z_1[1,99]                       z_1[1,100] 
#>                        -0.720579                        -1.331146
hbm_warnings(fit_demo)
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> Warning: The ESS has been capped to avoid unstable estimates.
#> [1] "R-hat > 1.1: model may not have converged."

The full set of diagnostics on your production fit would also include trace plots, R-hat / ESS tables, and pp-checks. These all follow the same calling convention:

plot(diag, type = "trace")
plot(diag, type = "rhat")
plot(diag, type = "ess")

4. Goodness-of-fit

gof <- model_compare(model)    # single-model: LOO, WAIC, pp_check
summary(gof)
plot(gof, type = "pp_check")

5. Compare alternatives

model2 <- hbm(brms::bf(y ~ x1 + x2), data = data_fhnorm,
              re = ~ (1 | regency),
              sampling_variance = "D",
              control = list(adapt_delta = 0.99),
              chains = 4, iter = 4000)
model3 <- hbm(brms::bf(y ~ x1),      data = data_fhnorm,
              re = ~ (1 | regency),
              sampling_variance = "D",
              control = list(adapt_delta = 0.99),
              chains = 4, iter = 4000)

model_compare(model, model2)
model_compare_all(full = model, medium = model2, simple = model3)

6. Small-area estimates

The simplest call uses the data the model was fit on – no newdata argument needed:

# In-sample prediction (default): operates on the data stored
# inside the fitted object.
est <- sae_predict(fit_demo)
summary(est)
#> 
#> ===== Small Area Estimation Summary =====
#> 
#> Areas       : 100 
#> Overall RSE : 7.2 %
#> 
#> Predictions:
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#>   6.336   8.938   9.769   9.855  10.637  13.537 
#> 
#> RSE by area:
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#>   4.416   5.981   7.062   7.196   8.171  11.258
head(est$result_table, 5)
#>   Prediction        SD RSE_percent
#> 1   8.131821 0.6843505    8.415711
#> 2   9.340465 0.7375581    7.896375
#> 3   8.286397 0.7710245    9.304701
#> 4  10.378301 0.7482991    7.210228
#> 5  10.442262 0.7160301    6.857041

To predict at fresh data points, pass newdata. When you do, any internal offset columns the original fit needed (e.g. .hbsaems_sigma_fixed = sqrt(D) for the Fay-Herriot sugar) are repopulated automatically when the new data frame has the same number of rows as the training data – the standard “predict at the same areas with updated covariates” use case.

# Out-of-sample prediction at new areas:
est_new <- sae_predict(fit_demo, newdata = data_new)

Bayesian model averaging

For model averaging, fit several candidate models, then either let model_average() weight them by stacking weights (LOO-based) or supply your own weights:

# Stacking weights (default, derived from LOO)
avg_stacked <- model_average(model, model2, model3)

# User-specified weights -- must sum to 1
avg_manual  <- model_average(model, model2, weights = c(0.7, 0.3))

# The returned object is an `hbsae_results`, identical in shape to
# what sae_predict() returns, so all post-processing helpers
# (sae_transform, sae_scale, sae_filter, sae_aggregate) work on it.
plot(avg_stacked, type = "predictions")

Visualisations

# Visualisations (require a graphics device):
plot(est, type = "predictions")
plot(est, type = "uncertainty")

7. Post-processing predictions

All sae_* post-processing helpers operate on the hbsae_results object returned by either sae_predict() or model_average():

log_est  <- sae_transform(est, log)
sc_est   <- sae_scale(est)
hi_est   <- sae_filter(est, est$pred > stats::median(est$pred))
agg_est  <- sae_aggregate(sae_predict(model),
                          sae_predict(model2),
                          method = "mean")

Session info

sessionInfo()
#> R version 4.6.0 (2026-04-24)
#> Platform: x86_64-pc-linux-gnu
#> Running under: Ubuntu 24.04.3 LTS
#> 
#> Matrix products: default
#> BLAS:   /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3 
#> LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.26.so;  LAPACK version 3.12.0
#> 
#> locale:
#>  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
#>  [3] LC_TIME=en_US.UTF-8        LC_COLLATE=C              
#>  [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
#>  [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
#>  [9] LC_ADDRESS=C               LC_TELEPHONE=C            
#> [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       
#> 
#> time zone: Asia/Jakarta
#> tzcode source: system (glibc)
#> 
#> attached base packages:
#> [1] stats     graphics  grDevices utils     datasets  methods   base     
#> 
#> other attached packages:
#> [1] hbsaems_1.1.0
#> 
#> loaded via a namespace (and not attached):
#>   [1] tidyselect_1.2.1      dplyr_1.2.1           farver_2.1.2         
#>   [4] loo_2.9.0             S7_0.2.2              fastmap_1.2.0        
#>   [7] TH.data_1.1-3         tensorA_0.36.2.1      rpart_4.1.27         
#>  [10] digest_0.6.39         estimability_1.5.1    lifecycle_1.0.5      
#>  [13] StanHeaders_2.32.10   survival_3.8-6        processx_3.9.0       
#>  [16] magrittr_2.0.5        posterior_1.7.0       compiler_4.6.0       
#>  [19] rlang_1.2.0           sass_0.4.10           tools_4.6.0          
#>  [22] yaml_2.3.12           knitr_1.51            bridgesampling_1.2-1 
#>  [25] pkgbuild_1.4.8        curl_7.1.0            plyr_1.8.9           
#>  [28] RColorBrewer_1.1-3    multcomp_1.4-28       abind_1.4-8          
#>  [31] withr_3.0.2           purrr_1.2.2           nnet_7.3-20          
#>  [34] grid_4.6.0            stats4_4.6.0          jomo_2.7-6           
#>  [37] xtable_1.8-8          mice_3.19.0           inline_0.3.21        
#>  [40] ggplot2_4.0.3         emmeans_1.11.2        scales_1.4.0         
#>  [43] iterators_1.0.14      MASS_7.3-65           dichromat_2.0-0.1    
#>  [46] cli_3.6.6             mvtnorm_1.3-7         rmarkdown_2.31       
#>  [49] reformulas_0.4.4      generics_0.1.4        otel_0.2.0           
#>  [52] RcppParallel_5.1.11-2 rstudioapi_0.17.1     reshape2_1.4.5       
#>  [55] minqa_1.2.8           cachem_1.1.0          rstan_2.32.7         
#>  [58] stringr_1.6.0         splines_4.6.0         bayesplot_1.15.0     
#>  [61] parallel_4.6.0        matrixStats_1.5.0     brms_2.23.0          
#>  [64] vctrs_0.7.3           boot_1.3-32           V8_8.2.0             
#>  [67] glmnet_5.0            Matrix_1.7-5          sandwich_3.1-1       
#>  [70] jsonlite_2.0.0        callr_3.7.6           mitml_0.4-5          
#>  [73] foreach_1.5.2         jquerylib_0.1.4       tidyr_1.3.2          
#>  [76] glue_1.8.1            pan_1.9               nloptr_2.2.1         
#>  [79] codetools_0.2-20      ps_1.9.3              distributional_0.7.0 
#>  [82] stringi_1.8.7         gtable_0.3.6          shape_1.4.6.1        
#>  [85] QuickJSR_1.9.2        lme4_2.0-1            tibble_3.3.1         
#>  [88] pillar_1.11.1         htmltools_0.5.9       Brobdingnag_1.2-9    
#>  [91] R6_2.6.1              Rdpack_2.6.6          evaluate_1.0.5       
#>  [94] lattice_0.22-9        rbibutils_2.4.1       backports_1.5.1      
#>  [97] broom_1.0.13          bslib_0.10.0          rstantools_2.6.0     
#> [100] Rcpp_1.1.1-1.1        coda_0.19-4.1         gridExtra_2.3        
#> [103] nlme_3.1-169          checkmate_2.3.4       xfun_0.57            
#> [106] zoo_1.8-14            pkgconfig_2.0.3