rubin_orig_df: Original Rubin degrees of freedom approximation

In rbmi: Reference Based Multiple Imputation

Original Rubin degrees of freedom approximation

Description

Compute the degrees of freedom according to the original Rubin (1987) approximation.

Usage

rubin_orig_df(v_com, var_b, var_t, M)

Arguments

v_com	Ignored in this function.
var_b	Between-imputation sample variance of the point estimates across multiply imputed datasets.
var_t	Estimate (according to Rubin's rules) of the variance of the point estimates.
M	Number of imputations (integer larger than 1).

Details

Let V_W = V_T - (1 + 1 / M) V_B be the within-imputation variance and r = (1 + 1 / M) V_B / V_W be the relative increase in variance due to nonresponse. The returned degrees of freedom are (M - 1) (1 + 1 / r)^2. Note that the internal computation is algebraically simplified to (M - 1) ((M V_T) / ((M + 1) V_B))^2.

Value

Degrees of freedom according to the original Rubin approximation. If the between-imputation variance is zero, returns Inf.

References

Rubin, D.B. (1987). Multiple Imputation for Nonresponse in Surveys. John Wiley & Sons, New York. [Section 3.3]

rbmi documentation built on Oct. 15, 2026, 9:06 a.m.