# Presentation: 665614

## INTRODUCTION

- In May 2006, AIPL began evaluation of U.S. bull fertility.  General research objectives: investigate options for modeling and trait definition that might improve accuracy
- Specific goal of this research: determine which available nuisance variables to include in the evaluation model and how to model them
- Factors considered were management (**mgt**) groups based on herd-yr-season-parity-registry status (**HYSPR**) , Yr-State (**St**)-Mo, cow age, DIM, lactation, service number, milk yield, cow effects, and short heat intervals
**MATERIALS & METHODS**
_**Comparing Predictors from Alternative Models**_
- Bulls’ predicted conception rates (**CR**) computed from estimation data (n=3,613,907) and compared to their average CR in set-aside data (n=2,025,884) using  accuracy, bias, and MSE; the 803 bulls with a min. of 50 matings for estimation and 100 matings in the set-aside data were included in comparisons.  Only AI cow breedings were included
_**Management Groups**_
- Minimum (target) group sizes tested were 3, 5, 10, 20
- Many small groups occurred; thus 3 basic strategies tested:
- Exclude records if HYSPR does not have the min. number (exact HYSPR groups)
- Combine groups until the target size is reached; exclude the group if target not reached
- Combine to target size but if HY has a specified minimum number of records, allow it into the evaluation; HY minimums were 2, 5, 10 when target sizes were 5, 10, and 20, respectively
- Model: y =  HYSPR + 1*Milk + 2*Milk2 + 3*AgeCow + 4*AgeCow2 + 5*DIM + 6*DIM + 7*FBull + 8*FMating + AgeBull + Stud-Yr + Service Sire (**SSR**) + ACow + PECow + e,                y = conception, yes or no
_**Other Factors**_
- Tested by dropping/adding factors of interest from/to the _**basic model**_ of:
- 	y = HYSPR + SSR variables + PE + A +** **AgeCow + DIM + Yr-St-Mo + Milk + Lact** **+ e
- SSR variables included: FSSR, FMating, AgeBull, Stud-Yr, SSR
- The HYSPR strategy used was to combine to a target group size of 20 and allow the HY into the evaluation if it had at least 10 breedings
- Preliminary results showed:
- Use of 305d-2x-ME milk yield provided as good or better predictions than use of test-day yields; ME records also did as well as FCM. Thus, ME milk yield used
- For quantitative nuisance variables (e.g., cow age), categorical variables found to be  preferable over linear and quadratic covariates; relationships with CR were not linear or quadratic. Thus, quantitative vars. fit as categorical
- Combining mgt groups implies some groups contain multiple seasons and lactations; inclusion of Yr-St-Month and Lactation (**Lact**) found to improve prediction and therefore included in all models

**RESULTS**

**CONCLUSIONS**
- Combining HYSPR groups to a target size of 20 and allowing HYs in with a min of 10 records maximized accuracy and thus will be implemented
- Other nuisance variables to include are: cow PE, cow breeding value, cow age, Yr-St-Mo, ME milk yield, lactation, service number, and a short breeding interval variable; quantitative nuisance variables will be fit as categorical variables.

| Management group |  | N. Records for estimation | Corr | Mean 
Diff (%) | Std. Dev. Diff |
| --- | --- | --- | --- | --- | --- |
| Min. N. | Strategy |  |  |  |  |
| 3 | No combine | 3,467,947 | 54.36 | -0.229 | 3.279 |
| 3 | Combine | 3,612,549 | 53.80 | -0.067 | 3.292 |
| 5 | No combine | 3,249,048 | 53.93 | -0.222 | 3.290 |
| 5 | Combine | 3,609,384 | 54.13 | 0.150 | 3.284 |
| 5 | Combine, allow 2 | 3,613,907 | 54.12 | 0.159 | 3.284 |
| 10 | No combine | 2,670,545 | 52.67 | -0.293 | 3.319 |
| 10 | Combine | 3,596,781 | 54.66 | -0.135 | 3.270 |
| 10 | Combine, allow 5 | 3,609,273 | 54.48 | -0.106 | 3.275 |
| 20 | No combine | 1,905,602 | 49.16 | -0.181 | 3.400 |
| 20 | Combine | 3,542,053 | 54.47 | 0.028 | 3.274 |
| 20 | Combine, allow 10 | 3,595,601 | 54.91 | 0.374 | 3.263 |

_**Management Groups**_

- Models are sorted from best to worst for each statistic (mean difference, correlation, and mean square error); the model listed first was the best for that statistic and the model listed last was the poorest
- The model without cow age (but with Lact; see basic model in methods) had the smallest mean difference but mean difference between bulls’ predicted CR and CR in the set-aside data was nearly 0 for all models, except when all nuisance variables dropped from the model (Omit All)
- The model with service number (**ServN**) and without DIM maximized accuracy and minimized MSE; correlations with both in the model were lower than with just service number because these 2 variables are highly correlated; the importance of including at least one is seen from the correlation when DIM was omitted without including ServN (Omit DIM)
- The range in correlations and MSEs, however, was generally small, except when all nuisance variables were omitted
- While simple average CR was 9% lower for breedings preceded by a short breeding interval (10-17 days, min. of 10 required), they accounted for only 2.5% of all breedings and the max percentage for any one bull was 9%; thus, this variable had minimal impact overall.  For bulls where these breedings accounted for at least 5% of their matings (52 out of 803), accuracy improved by 0.4% when this variable was included

- Generally, combining groups resulted in higher correlations of predicted CR with bulls’ average CR in set aside data, than did using exact HYSPRs (no combining); except in the case where min. group size was 3, restricting to exact HYSPRs resulted in the loss of too many records
- Allowing HYs into the evaluation that had fewer than the target number of records was beneficial only when target group size was 20; considerably more records were salvaged when target group size was 20 than when it was 5 or 10
- In general, though, differences among the options tested were small; provided that excessive data exclusion is avoided, formation of mgt groups will not have a large impact on accuracy
- Combining groups to a target group size of 20 and allowing HYs in if they have a min. of 10 records maximized accuracy. The small mean difference for this option was eliminated by categorization of quantitative nuisance variables, as can be seen below (Basic model)

_**Other Factors**_

| Model | Mean Diff (%) |   | Model | Corr |   | Model | MSE |
| --- | --- | --- | --- | --- | --- | --- | --- |
| Omit Cow Age | -0.011 |  | ServN, Omit DIM | 55.17 |  | ServN, Omit DIM | 3.254 |
| Basic Model | -0.019 |  | Lact*ServN, Omit DIM | 55.11 |  | Lact*ServN, Omit DIM | 3.256 |
| Omit DIM | -0.019 |  | Lact*ServN and DIM | 55.07 |  | Lact*ServN and DIM | 3.258 |
| Lact*ServN, Omit DIM | -0.020 |  | ServN and DIM | 55.06 |  | ServN and DIM | 3.259 |
| ServN, Omit DIM | -0.020 |  | DIM*ServN | 55.05 |  | Basic Model | 3.260 |
| Omit Cow | -0.021 |  | Basic Model | 54.97 |  | DIM*ServN | 3.260 |
| Lact*ServN and DIM | -0.022 |  | Omit Cow | 54.93 |  | Omit Cow Age | 3.263 |
| DIM*ServN | -0.028 |  | Omit Cow Age | 54.89 |  | Omit Cow | 3.265 |
| Omit Milk | -0.028 |  | Omit Milk | 54.72 |  | Omit Milk | 3.265 |
| ServN and DIM | -0.042 |  | Omit DIM | 53.35 |  | Omit DIM | 3.300 |
| Omit All | -0.257 |   | Omit All | 51.54 |   | Omit All | 3.501 |