Possible Change

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

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, and should be constructed for each trait EPD.

When calculating the possible change table values, inbreeding is assumed to be zero. The relationship between possible change and BIF Accuracy is,

$a_{BIF}=1-{\sqrt {\frac {\sigma _{p}^{2}}{\sigma _{u}^{2}}}}$

${\sqrt {\frac {\sigma _{p}^{2}}{\sigma _{u}^{2}}}}=1-a_{BIF}$

${\frac {\sigma _{p}^{2}}{\sigma _{u}^{2}}}=(1-a_{BIF})^{2}$

$\sigma _{p}^{2}=(1-a_{BIF})^{2}\sigma _{u}^{2}$

$\sigma _{p}=(1-a_{BIF})\sigma _{u}$

where $a_{BIF}$ is the BIF Accuracy; $\sigma _{u}^{2}$ is the additive genetic variance of the trait for which the possible change values are being calculated; and $\sigma _{p}^{2}$ 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 $\sigma _{p}$ 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 EPD is then calculated as,

$\sigma _{PC}={\frac {\sigma _{p}}{2}}={\frac {(1-a_{BIF})\sigma _{u}}{2}}$

which is then used to calculate possible change values for corresponding BIF Accuracy values. 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.

Recommendations

BIF recommends that possible change be published as one standard error of prediction of EPDs.