R: Summary Method for 'fitsae' Objects

summary.fitsae {tipsae}

R Documentation

Summary Method for `fitsae` Objects

Description

Summarizing the small area model fitting through the distributions of estimated parameters and derived diagnostics using posterior draws.

Usage

## S3 method for class 'fitsae'
summary(
  object,
  probs = c(0.025, 0.25, 0.5, 0.75, 0.975),
  compute_loo = TRUE,
  ...
)

Arguments

`object`	An instance of class `fitsae`.
`probs`	A numeric vector of `quantile`s of interest. The default is `c(0.025,0.25,0.5,0.75,0.975)`.
`compute_loo`	Logical, indicating whether to compute `loo` diagnostics or not.
`...`	Currently unused.

Details

If printed, the produced summary displays:

Posterior summaries about the fixed effect coefficients and the scale parameters related to unstructured and possible structured random effects.
Model diagnostics summaries of (a) model residuals; (b) standard deviation reductions; (c) Bayesian P-values obtained with the MCMC samples.
Shrinking Bound Rate.
loo information criteria and related diagnostics from the loo package.

Value

A list of class summary_fitsae containing diagnostics objects:

raneff: A list of data.frame objects storing the random effects posterior summaries divided for each type: ⁠$unstructured⁠, ⁠$temporal⁠, and ⁠$spatial⁠.
fixed_coeff: Posterior summaries of fixed coefficients.
var_comp: Posterior summaries of model variance parameters.
model_estimates: Posterior summaries of the parameter of interest \theta_d for each in-sample domain d.
model_estimates_oos: Posterior summaries of the parameter of interest \theta_d for each out-of-sample domain d.
is_oos: Logical vector defining whether each domain is out-of-sample or not.
direct_est: Vector of input direct estimates.
post_means: Model-based estimates, i.e. posterior means of the parameter of interest \theta_d for each domain d.
sd_reduction: Standard deviation reduction, see details section.
sd_dir: Standard deviation of direct estimates, given as input if type_disp="var".
loo: The object of class loo, for details see loo package documentation.
shrink_rate: Shrinking Bound Rate, see details section.
residuals: Residuals related to model-based estimates.
bayes_pvalues: Bayesian p-values obtained via MCMC samples, see details section.
y_rep: An array with values generated from the posterior predictive distribution, enabling the implementation of posterior predictive checks.
diag_summ: Summaries of residuals, standard deviation reduction and Bayesian p-values across the whole domain set.
data_obj: A list containing input objects including in-sample and out-of-sample relevant quantities.
model_settings: A list summarizing all the assumptions of the input model: sampling likelihood, presence of intercept, dispersion parametrization, random effects priors and possible structures.
call: Image of the function call that produced the input fitsae object.

References

Janicki R (2020). “Properties of the beta regression model for small area estimation of proportions and application to estimation of poverty rates.” Communications in Statistics-Theory and Methods, 49(9), 2264–2284.

Vehtari A, Gelman A, Gabry J (2017). “Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC.” Statistics and Computing, 27(5), 1413–1432.

De Nicolò S, Gardini A (2024). “The R Package tipsae: Tools for Mapping Proportions and Indicators on the Unit Interval.” Journal of Statistical Software, 108(1), 1–36. doi:10.18637/jss.v108.i01.

Examples

library(tipsae)

# loading toy dataset
data("emilia_cs")

# fitting a model
fit_beta <- fit_sae(formula_fixed = hcr ~ x, data = emilia_cs, domains = "id",
                    type_disp = "var", disp_direct = "vars", domain_size = "n",
                    # MCMC setting to obtain a fast example. Remove next line for reliable results.
                    chains = 1, iter = 150, seed = 0)

# check model diagnostics via summary() method
summ_beta <- summary(fit_beta)
summ_beta

[Package tipsae version 1.0.1 Index]

Summary Method for fitsae Objects