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I have to solve the following issue:

  1. I run my linear regression model many times (let's say 1000 times) with two variables: y - continuous dependent variable, x - continuous independent variable (mean of several consequent measurements).
  2. The independent variable in each model was randomly drawn using its mean and standard deviation
  3. I have the regression coefficient and standard error for this independent variable in each of the models.

Somehow I have to combine these results into one regression result. As far as I know the regression coefficients of 1000 models can be just averaged. However, this is not really clear to me how can I estimate the total variance of 1000 models.

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    $\begingroup$ I'm curious - how, mechanically, would you go about combining the 1000 sets of results using spss? $\endgroup$ – rolando2 Oct 10 '13 at 16:29
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The total variance for combined regression results can be estimated using the same approach as in multiple imputations. In the attached file, the formulas for combining the regression results and total variance are presented.

Combining (pooloing) results of several regression models into one

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    $\begingroup$ Could you provide a reference for the above screenshot? It is good practice to properly cite the work of others. By the way, this should be amended to your previous answer, not posted as a new one. $\endgroup$ – chl Oct 10 '13 at 13:34
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I have found it myself. If someone is interested, the solution is here: http://pic.dhe.ibm.com/infocenter/spssstat/v20r0m0/topic/com.ibm.spss.statistics.help/alg_mi-pooling_rubin.htm

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    $\begingroup$ Hi abc, it would be good to expand this answer, as links go bad. A simple note and/or reference about Rubin's rules for combining models should suffice. The SPSS docs give Li, K. H., T. E. Raghunathan, and D. B. Rubin. 1991. Large-Sample Significance Levels from Multiply Imputed Data Using Moment-Based Statistics and an F Reference Distribution. Journal of the American Statistical Association, 86, 1065-1073. and Schafer, J. L. 1997. Analysis of Incomplete Multivariate Data. London: Chapman and Hall. as references for the multiple imputation algorithm. $\endgroup$ – Andy W Oct 9 '13 at 12:50
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The above presented formulas are available in the SPSS help: Help > Algorithms > Multiple Imputation: Pooling Algorithms > Rubin's Rules (multiple imputation algorithms) > Combining Results after Multiple Imputation

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    $\begingroup$ Please, register your original account and merge it with this one; follow the instructions on our Help Center. Next, I would advise to merge your three different replies into one single answer. $\endgroup$ – chl Oct 10 '13 at 15:04

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