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Verify Theoretical DER Predictions

Source: R/der_theorem_check.R
der_theorem_check.Rd

Compares empirical DER values against theoretical predictions from the decomposition theorems. This function checks how well the closed-form approximations match the numerically computed DER.

Usage

der_theorem_check(x)

Arguments

x

A svyder object.

Value

A data.frame with columns: param, param_type, der_empirical, der_theorem1 (for FE), der_theorem2 (for RE), relative_error, theorem_used. If the conservation law is applicable, the result has a "conservation_law" attribute.

Details

For fixed effects (Theorem 1):

  • fe_within: DER \(\approx\) DEFF.

  • fe_between: DER \(\approx\) DEFF \(\cdot\) (1 - B).

For random effects (Theorem 2):

  • DER \(\approx\) B \(\cdot\) DEFF \(\cdot\) kappa(J).

Also reports the conservation-law diagnostic (Corollary 1) when applicable: DER_mu + DER_theta_cond \(\approx\) DEFF (balanced intercept-only case). The conditional random-effect term is reported separately from the empirical marginal mean of the fitted random-effect DERs.

References

Lee, J., Williams, M. R., & Savitsky, T. D. (2026). Design Effect Ratios for Bayesian Survey Models: A Diagnostic Framework for Identifying Survey-Sensitive Parameters. Journal of Survey Statistics and Methodology. Submitted.

See also

der_decompose() for the full decomposition.

Other analysis: der_compare(), der_decompose(), der_sensitivity()

Examples

data(nsece_demo)
result <- der_diagnose(
  nsece_demo$draws,
  y = nsece_demo$y, X = nsece_demo$X,
  group = nsece_demo$group, weights = nsece_demo$weights,
  cluster = nsece_demo$psu, family = "binomial",
  sigma_theta = nsece_demo$sigma_theta,
  param_types = nsece_demo$param_types
)
thm <- der_theorem_check(result)
head(thm)
#>      param param_type der_empirical der_theorem1 der_theorem2 relative_error
#> 1  beta[1] fe_between     0.2626885    0.3781171           NA     0.43941210
#> 2  beta[2]  fe_within     2.6894416    2.5952698           NA     0.03501540
#> 3  beta[3] fe_between     0.3430527    0.3781171           NA     0.10221260
#> 4 theta[1]         re     3.3858856           NA     2.122360     0.37317436
#> 5 theta[2]         re     0.6759045           NA     1.396910     1.06672753
#> 6 theta[3]         re     1.1182861           NA     1.048017     0.06283619
#>          theorem_used
#> 1 Theorem 1 (between)
#> 2  Theorem 1 (within)
#> 3 Theorem 1 (between)
#> 4      Theorem 2 (RE)
#> 5      Theorem 2 (RE)
#> 6      Theorem 2 (RE)