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- BIAS in Regression Parameter Estimates

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11-17-2013 12:52 AM

Is there a proc or formula to calculate the magnitude of bias in regression parameter estimates?

Thanks,

Krishna.

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11-18-2013 09:30 AM

Well, we know that the MSE is equal to the bias squared plus the variance for an estimator. So now it all depends on what you know about the distribution of the estimator. If the distribution has a known variance, you can calculate the MSE from the estimator's standard error, subtract the population variance, and get the squared bias.

This all requires knowing the population mean and variance for the estimator in question.

Steve Denham

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11-18-2013 10:53 PM

Thank you, Steve and Paige.

Currently, I am working on a project that involves missing data analysis of sample data. I wanted to know if there is a way to measure bias for regression models for different "Missing Data" Deletion or Imputation methods -- I mean, in Listwise or Pairwise or Mean Substitution methods, I know the estimates are highly biased compared to those in Multiple Imputation or Expectation Maximization, but is it possible to calculate bias in the regression parameter estimates.

It seems since there is no "correct estimate" for non-missing sample data, the "amount of bias" cannot be calculated.

Please let me know if you have any other thoughts.

Thanks,

K

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11-18-2013 10:42 AM

If you are talking about Ordinary Least Squares Regression, and you are estimating the correct model, then it is my understanding that the bias is zero.

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04-08-2014 08:48 AM

Are you asking about Linear or Logistic regression? If Logistic Regression, then there is a very good paper by King and Zeng, "Logistic Regression in Rare Events Data" that gives a formula for bias to account for missing data.