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[[Category: Genetic Evaluation]]
'''The information contained in this page is a DRAFT under consideration for inclusion in the official BIF Guidelines.  It should not be considered to be part of the Guidelines until this message has been removed'''
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Organizations involved in producing [[Expected Progeny Difference | EPDs]] will often provide a table of "possible change" values. Possible change is a measure of the potential difference
Organizations involved in producing [[Expected Progeny Difference | EPDs]] will often provide a table of "possible change" values. Possible change is a measure of the potential difference
between an EPD and the true progeny difference, and should be constructed for each [[Traits | trait]] EPD.  
between an EPD and the true progeny difference.  Possible change values are different for each [[ Traits | trait]] because they are constructed using traits' genetic variances.  Also, possible change values are different at each level of [[Accuracy | accuracy]].


When calculating the possible change table values, inbreeding is assumed to be zero.  The relationship between possible change and [[Accuracy | BIF Accuracy]] is,
When calculating the possible change table values, inbreeding is assumed to be zero.  The possible change values should be calculated from the following expression:
<center>
<math>
a_{BIF}=1-\sqrt{\frac{\sigma_{p}^{2}}{\sigma_{u}^{2}}}
</math><br><br><math>
\sqrt{\frac{\sigma_{p}^{2}}{\sigma_{u}^{2}}}=1-a_{BIF}
</math><br><br><math>
\frac{\sigma_{p}^{2}}{\sigma_{u}^{2}}=(1-a_{BIF})^{2}
</math><br><br><math>
\sigma_{p}^{2}=(1-a_{BIF})^{2}\sigma_{u}^{2}
</math><br><br><math>
\sigma_{p}=(1-a_{BIF})\sigma_{u}
</math>
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where <math>a_{BIF}</math> is the [[Accuracy | BIF Accuracy]]; <math>\sigma_{u}^{2}</math> is the additive genetic variance of the trait for which the possible change values are being calculated; and <math>\sigma_{p}^{2}</math> is the prediction error variance corresponding to a given level of BIF Accuracy (i.e., It is the expected value of the mean squared difference between the true value and the estimated breeding value at the corresponding level of accuracy).


The <math>\sigma_{p}</math> is the standard error of prediction for an estimated breeding value.  Because an EPD is one-half of the estimated breeding value, the standard error of prediction for an [[Expected Progeny Difference | EPD]] is then calculated as,
<center>
<center>
<math>
<math>
\sigma_{PC}=\frac{\sigma_{p}}{2}=\frac{(1-a_{BIF})\sigma_{u}}{2}
PC={t}\frac{(1-a_{BIF})\sigma_{u}}{2}
</math>
</math>
</center>
</center>
The defacto standard for possible change is to publish it as being one EPD standard prediction error (square root of the prediction error variance divided by 2) at each tenth of a BIF accuracy value. Thus, the true value should fall within the range of plus or minus one possible change from the EPD 68% of the time for a given level of BIF Accuracy.  It will fall within plus or minus two possible changes from the EPD 95% of the time, etc.
where PC is a possible change value for a corresponding [[Accuracy | BIF Accuracy value]] (<math>a_{BIF}</math>); <math>\sigma_{u}</math> is the additive genetic standard deviation for that trait; and, t is either 1 or 2 depending on the desired width of the confidence interval. Some organizations publish possible change values as one EPD standard prediction error (t=1). One standard prediction error means the true value should fall within the range of plus or minus one possible change from the EPD 68% of the time for a given level of BIF Accuracy.  Other organizations choose to publish possible change values as two standard prediction errors (t=2) and the true value will fall within plus or minus the possible change value 95% of the time.
==Recommendations==
==Recommendations==
''BIF recommends that possible change be published as one standard error of prediction of EPDs.''
''BIF recommends that possible change tables should be clearly labelled as representing 68% or 95% confidence ranges''

Latest revision as of 10:06, 12 April 2021

Organizations involved in producing EPDs will often provide a table of "possible change" values. Possible change is a measure of the potential difference between an EPD and the true progeny difference. Possible change values are different for each trait because they are constructed using traits' genetic variances. Also, possible change values are different at each level of accuracy.

When calculating the possible change table values, inbreeding is assumed to be zero. The possible change values should be calculated from the following expression:

where PC is a possible change value for a corresponding BIF Accuracy value (); is the additive genetic standard deviation for that trait; and, t is either 1 or 2 depending on the desired width of the confidence interval. Some organizations publish possible change values as one EPD standard prediction error (t=1). One standard prediction error means the true value should fall within the range of plus or minus one possible change from the EPD 68% of the time for a given level of BIF Accuracy. Other organizations choose to publish possible change values as two standard prediction errors (t=2) and the true value will fall within plus or minus the possible change value 95% of the time.

Recommendations

BIF recommends that possible change tables should be clearly labelled as representing 68% or 95% confidence ranges

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