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use crate::panel::{PanelResult, RandomEffectsResult};
use statrs::distribution::{ChiSquared, ContinuousCDF};
pub struct HausmanTest;
impl HausmanTest {
/// Compara Fixed Effects vs Random Effects.
/// H0: Random Effects is consistent (preferable).
/// H1: Random Effects is inconsistent (use Fixed Effects).
pub fn compare(fe: &PanelResult, re: &RandomEffectsResult) -> String {
let k = fe.params.len();
// 1. Diferença dos Betas (b_fe - b_re)
let diff_beta = &fe.params - &re.params;
// 2. Diferença das Variâncias (Var_fe - Var_re)
//Note: Simplification using only the diagonal (subsequent cross covariance null for simple test)
//The complete test would require the complete covariance matrices, but the diagonal is a good proxy.
let var_fe = fe.std_errors.mapv(|s| s.powi(2));
let var_re = re.std_errors.mapv(|s| s.powi(2));
let diff_var = &var_fe - &var_re;
//3. Chi2 Statistics (Quadratic Form)
// H = (b_diff)' * (Var_diff)^-1 * (b_diff)
//As we are using diagonal, simplifies for weighted sum
let mut chi2_stat = 0.0;
for i in 0..k {
if diff_var[i] > 0.0 {
chi2_stat += (diff_beta[i].powi(2)) / diff_var[i];
}
}
//4. P-Value
let Ok(dist) = ChiSquared::new(k as f64) else {
return "Invalid degrees of freedom".to_string();
};
let p_value = 1.0 - dist.cdf(chi2_stat);
//Format Output
let recommendation = if p_value < 0.05 {
"Reject H0. Use FIXED EFFECTS (RE is inconsistent)."
} else {
"Fail to reject H0. Use RANDOM EFFECTS (it is efficient)."
};
format!(
"\n=== Hausman Test ===\nChi2 Statistic: {:.4}\nP-Value: {:.4}\nResult: {}",
chi2_stat, p_value, recommendation
)
}
}