Enhanced comment feature has been enabled for all readers including those not logged in. Click on the Discussion tab (top left) to add or reply to discussions.
Heterogeneous variance: Difference between revisions
(Created page with "Heterogenous variance<ref>Garrick, D. J., E. J. Pollak, R. L. Quaas and L. D. Van Vleck. 1989 Variance Heterogeneity in Direct and Maternal Weight Traits by Sex and Percent Pu...") |
No edit summary |
||
| Line 1: | Line 1: | ||
Heterogenous variance<ref>Garrick, D. J., E. J. Pollak, R. L. Quaas and L. D. Van Vleck. 1989 Variance Heterogeneity in Direct and Maternal Weight Traits by Sex and Percent Purebred for Simmental-Sired Calves. v67:10 2515-2528.</ref> between | Heterogenous variance<ref>Garrick, D. J., E. J. Pollak, R. L. Quaas and L. D. Van Vleck. 1989 Variance Heterogeneity in Direct and Maternal Weight Traits by Sex and Percent Purebred for Simmental-Sired Calves. v67:10 2515-2528.</ref> between groups of animals within a trait in a single genetic evaluation can exist. Often the heterogeneous variance between groups may result from differences in trait expression by, for example, breed and/or sex. Often the difference in variance between groups of animals within a genetic evaluation is the result of scaling effects on the traits' expression. For example, bulls may express more variation in yearling weight than heifers simply because they are, on average, larger. | ||
Another situation where variance may be heterogenous is when different procedures are used to measure or score a trait between groups of cattle. For example, it is apparent that using a hoof tape measure is very highly correlated to birth weight (very near 1) and is frequently used, especially by larger cattle breeding enterprises. However, it has been observed that the variance in the birth weight values forecasted by the hoof tape measures is about 75% of that of real birth weights. Additionally, | Another situation where variance may be heterogenous is when different procedures are used to measure or score a trait between groups of cattle. For example, it is apparent that using a [[Hoof Tape| hoof tape measure]] is very highly correlated to birth weight (very near 1) and is frequently used, especially by larger cattle breeding enterprises. However, it has been observed that the variance in the birth weight values forecasted by the hoof tape measures is typically about 75% of that of real birth weights. Additionally, reporting weights to the nearest 5 or 10 pounds can result in heterogeneous variance. | ||
In a model where no heterogeneous variance is considered the observation, <math>y_{i}</math>, for some trait may be modelled as, | In a model where no heterogeneous variance is considered the observation, <math>y_{i}</math>, for some trait may be modelled as, | ||
| Line 9: | Line 9: | ||
</math> | </math> | ||
</center> | </center> | ||
where <math>b_{j}</math> is some jth fixed effect on the observation, <math>u_{i}</math> | where <math>b_{j}</math> is some jth fixed effect on the observation, <math>u_{i}</math> is the [[Glossary#B | breeding value]] of the ith animal for the trait, and <math>e_{i}</math> is the random residual (error) on the observation with a distribution of <math>I\sigma_{e}^{2}</math>. Notice that for all observations the residual variance is assumed to be the same. | ||
When considering heterogeneous variance<ref>Quaas, R. L., D. J. Garrick, and W. H. McElhenny. 1989. Multiple Trait Prediction for a Type of Model with Heterogeneous Genetic and Residual Covariance Structures. J. Anim. Sci. v67:10 2529-2535.</ref> the model becomes, | |||
<center> | <center> | ||
<math> | <math> | ||
| Line 17: | Line 16: | ||
</math> | </math> | ||
</center> | </center> | ||
where <math>\epsilon_{k}</math> is a coefficient that scales the breeding value's expression | where <math>\epsilon_{k}</math> is a coefficient that scales the true breeding value's expression and <math>e_{ik}</math> is the residual effect with a residual variance from the kth residual variance group. This group may be a sex class, a breed class or other category (e.g., hoof tape birth weight observation). | ||
The <math>\epsilon_{k}</math> and <math>\sigma_{e_{k}}^{2}</math> do not necessarily have to scale together to keep the heritability of the trait the same between heterogeneous variance groups. In some situations, this may be desirable and in others, there may be a difference in the observed (effective) heritability of the | The <math>\epsilon_{k}</math> and <math>\sigma_{e_{k}}^{2}</math> do not necessarily have to scale together to keep the heritability of the trait the same between heterogeneous variance groups. In some situations, this may be desirable and in others, there may be a difference in the observed (effective) heritability of the trait between groups. | ||
Revision as of 22:59, 20 February 2019
Heterogenous variance[1] between groups of animals within a trait in a single genetic evaluation can exist. Often the heterogeneous variance between groups may result from differences in trait expression by, for example, breed and/or sex. Often the difference in variance between groups of animals within a genetic evaluation is the result of scaling effects on the traits' expression. For example, bulls may express more variation in yearling weight than heifers simply because they are, on average, larger.
Another situation where variance may be heterogenous is when different procedures are used to measure or score a trait between groups of cattle. For example, it is apparent that using a hoof tape measure is very highly correlated to birth weight (very near 1) and is frequently used, especially by larger cattle breeding enterprises. However, it has been observed that the variance in the birth weight values forecasted by the hoof tape measures is typically about 75% of that of real birth weights. Additionally, reporting weights to the nearest 5 or 10 pounds can result in heterogeneous variance.
In a model where no heterogeneous variance is considered the observation, , for some trait may be modelled as,
where is some jth fixed effect on the observation, is the breeding value of the ith animal for the trait, and is the random residual (error) on the observation with a distribution of . Notice that for all observations the residual variance is assumed to be the same. When considering heterogeneous variance[2] the model becomes,
where is a coefficient that scales the true breeding value's expression and is the residual effect with a residual variance from the kth residual variance group. This group may be a sex class, a breed class or other category (e.g., hoof tape birth weight observation).
The and do not necessarily have to scale together to keep the heritability of the trait the same between heterogeneous variance groups. In some situations, this may be desirable and in others, there may be a difference in the observed (effective) heritability of the trait between groups.
- ↑ Garrick, D. J., E. J. Pollak, R. L. Quaas and L. D. Van Vleck. 1989 Variance Heterogeneity in Direct and Maternal Weight Traits by Sex and Percent Purebred for Simmental-Sired Calves. v67:10 2515-2528.
- ↑ Quaas, R. L., D. J. Garrick, and W. H. McElhenny. 1989. Multiple Trait Prediction for a Type of Model with Heterogeneous Genetic and Residual Covariance Structures. J. Anim. Sci. v67:10 2529-2535.
