## Rubin's Rule

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kellyham
Posts: 1
Joined: Fri Mar 19, 2010 5:00 pm

### Rubin's Rule

Hi,

I'm trying to combine results across 5 imputed data sets using Rubin's Rule. MLwiN only provides the standard error, and not the estimated variance for each main effect and interaction. The variance is necessary in the calculation.

I'm just wondering if anyone has used results from MLwiN and calculated Rubin's Rule using Excel and if they would care to walk me through it? I believe that most of my calculations are correct; the only issue is that I am unsure of how to convert the standard error into variance. One would think it would be as simple as multiplying the standard error by the square root of the sample, and then squaring that result... But I have main effects which are significant across all imputations and which are not even close to significance after using Rubin's Rule.

Any information on how MLwiN calculates standard error (I am using weights at the individual level - maybe that is effecting it?), how to convert an MLwiN standard error to variance, or the best approach to calculate Rubin's Rule 'by hand' using data from MLwiN would be very appreciated.

Thanks!
suep71
Posts: 2
Joined: Sun May 09, 2010 9:31 pm

### Re: Rubin's Rule

It's my understanding that Rubin's formulas calculate the within-imputation and between-imputation variance using the beta estimates and their corresponding standard errors from each of the imputed datasets; i.e., you need only the betas & std errors. There is a nice clear description of how to average the estimates at the following website: http://www.stat.psu.edu/~jls/mifaq.html.