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Feb 4, 2015 11:57 AM
(1541 views)

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Solution

Michelle,

Very good question! When there is no missing data the design parameter estimates are easily calculated by hand and agree with the software output. That is because all of the wonderful properties that orthogonal designs display. As soon as you have missing data however the design becomes unbalanced and correlations arise in the model terms which can bias the parameter estimates. As you mention the calculations are indeed close but do not agree with the software output. That is because the software output is calculating the parameter estimate which includes the bias that occurs as a result of the missing row(s) of data. If you use the evaluate design capability in JMP and look at the color map on the correlations with the data table with the rows of data with missing values excluded you will see the bias that is included in the parameter estimate.

I hope this helps.

4 REPLIES

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Michelle,

Very good question! When there is no missing data the design parameter estimates are easily calculated by hand and agree with the software output. That is because all of the wonderful properties that orthogonal designs display. As soon as you have missing data however the design becomes unbalanced and correlations arise in the model terms which can bias the parameter estimates. As you mention the calculations are indeed close but do not agree with the software output. That is because the software output is calculating the parameter estimate which includes the bias that occurs as a result of the missing row(s) of data. If you use the evaluate design capability in JMP and look at the color map on the correlations with the data table with the rows of data with missing values excluded you will see the bias that is included in the parameter estimate.

I hope this helps.

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Feb 4, 2015 3:33 PM
(1076 views)

Thanks Lou - super helpful! Would it be fair to say, then, that:

(a) it is nontrivial to hand-calculate the effects in the same way as the software (i.e., there is no (relatively) simple formula for this)

(b) the effects calculated by the software are better (more accurate) than those that I hand calculate by simply omitting the missing data - so I should use those

(c) that the results from the software are still OKAY even with the missing data (especially if the majority of the data is there...)

It really bugs me that I cannot calculate the effects by hand; I would like to have a little more control over the analysis, and use the software more as a tool for throughput rather than outsourcing understanding how the calculations work.

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Feb 4, 2015 4:15 PM
(1076 views)

Michelle,

I'm sure you could calculate it however it would involve some matrix calculations. Practically speaking however the fact that you completed a full factorial design there are certainly enough degrees of freedom to fit a model that delineates your responses despite having missing values. The parameter estimates may be somewhat biased but your conclusions whether or not an effect is significant should do just fine.

Lou

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Feb 4, 2015 2:44 PM
(1076 views)