Extracts and summarizes the variance decomposition from a fitted BHF model. Provides estimates for multiple estimands: Policy (A), Descriptive (B), and De-attenuated (A*).
Arguments
- fit
An object of class
bhf_fitfrombhf_fit().- prob
Numeric. Probability for credible intervals. Default is 0.95.
Logical. If TRUE, prints a formatted summary. Default is TRUE.
Value
A list with components:
- logit
Variance components on logit scale (Estimand A)
- prob
Variance components on probability scale (Estimand B)
- deatten
De-attenuated variance components (Estimand A*)
- summary_table
Formatted summary table
Details
The function extracts three sets of variance components:
- Estimand A (Policy, logit scale)
Variance decomposition on the latent logit scale.
icc_state= sigma_state^2 / (sigma_state^2 + sigma_psu^2 + pi^2/3)- Estimand B (Descriptive, probability scale)
Variance decomposition on the observed probability scale.
icc_prob = Var(p_s) / (Var(p_s) + E(p_s(1-p_s)))- Estimand A* (Policy adjusted, de-attenuated)
Estimand B with finite-sample variance inflation removed.
icc_deatten = (Var(p_s) - V_hat) / (Var(p_s) - V_hat + E(p_s(1-p_s)))
Interpretation
The ICC (Intraclass Correlation Coefficient) represents the proportion of total variance attributable to between-domain differences. Higher values indicate more geographic heterogeneity.
The difference between ICC_B and ICC_A* represents the amount of apparent heterogeneity that is actually due to sampling noise rather than true substantive differences.
Examples
if (FALSE) { # \dontrun{
# After fitting
fit <- bhf_fit(prepared_data, model = model)
# Get variance decomposition
vd <- variance_decomposition(fit)
# Access specific components
vd$logit$icc_mean # ICC on logit scale
vd$prob$icc_mean # ICC on probability scale
vd$deatten$icc_mean # De-attenuated ICC
} # }