Convert Variance Inflation Factor to Variance — vif_to_variance • DPprior

Converts a Variance Inflation Factor (VIF) specification to the actual variance of \(K_J\).

Usage

vif_to_variance(mu_K, vif)

Arguments

mu_K: Numeric; target prior mean of \(K_J\).
vif: Numeric; Variance Inflation Factor (must be >= 1 for A1 feasibility).

Value

Numeric; variance of \(K_J\) computed as \((\mu_K - 1) \times \text{VIF}\).

Details

The VIF is defined as: $$\text{VIF} = \frac{\sigma^2_K}{\mu_K - 1}$$

Interpretation:

VIF = 1: Poisson variance (exact boundary for A1)
VIF > 1: Overdispersion (required for A1 feasibility)
VIF < 1: Underdispersion (infeasible for A1, not allowed)

See also

confidence_to_vif for mapping confidence levels to VIF, cv_alpha_to_variance for CV-based specification

Examples

# VIF = 2 means variance is twice the Poisson variance
vif_to_variance(mu_K = 5, vif = 2)  # Returns 8
#> [1] 8

# Use with DPprior_a1
fit <- DPprior_a1(J = 50, mu_K = 5, var_K = vif_to_variance(5, 2))