# Imputation variance and explained variance (in vector autoregression)

I have a question concerning the coefficients of VAR models used on multiple imputed data (high missigness in some variables: up to 40%). In particular I would like to know how the coefficients are related to the explained variance.

I have used vector autoregression on multiple imputed data (m=10) and have then combined the estimated coefficient with rubin's rule. However, what confuses me is the fact that my imputation variance is quite small in relationship to the estimates and variance of coefficients, but the difference between the explained variance is huge (17% to 0.04%) between models.

My idea is that since the highest imputation variance across all systems is at the constant (around a third of the variance value but 3-4 times higher then in other coefficients) and that this critically affects the explained variance. But thats just a guess.

I would be very happy if somebody could help me here.

• After 5 month I finally update this question. I missed some basics since I can have the same coefficients with different explained variance – DUWUDA Oct 30 '13 at 1:38

The short answer is that a variable set of data can have the same coefficients but explains variance to different proportion. This explains the low variance within coefficients and the high variance within $R^2$.