How do I combine the results across the multiply imputed sets of data?
Rubin (1987) presented this method for combining results from a data analysis performed m times, once for each of m imputed data sets, to obtain a single set of results. From each analysis, one must first calculate and save the estimates and standard errors. Suppose that is an estimate of a scalar quantity of interest (e.g. a regression coefficient) obtained from data set j (j=1,2,…,m) and is the standard error associated with . The overall estimate is the average of the individual estimates, For the overall standard error, one must first calculate the within-imputation variance, and the between-imputation variance, The total variance is The overall standard error is the square root of T. Confidence intervals are obtained by taking the overall estimate plus or minus a number of standard errors, where that number is a quantile of Student’s t-distribution with degrees of freedom A significance test of the null hypothesis Q=0 is performed by comparing the ratio to the same t-distributio
