# Presentation: 167361

## Derivation of Factors 

**Derivation of Factors **
**to Estimate Daily Milk Yield **
**from Single Milkings for Holsteins Milked Two or Three Times Daily**

- M.M. Schutz, J.M. Bewley
- Department of Animal Sciences, Purdue University
- and H.D. Norman
- USDA-ARS, Animal Improvement Programs Laboratory

## Introduction

- Increasing number of herds utilizing AP testing plans
- Cost
- Convenience
- Necessity in herds milking around the clock
- AP programs easier for DHI service providers to test large herds
- Large herds have variable milk pick-up times

## Background

- Present factors to estimate daily milk from a single milking for milking interval (MI) in herds milked 2x (DeLorenzo and Wiggans, 1986).
- Factors derived from total milk yields
- Bulk tank component samples
- Used milking start and end times
- Accounted for differences in DIM
- Allow prediction by either look-up table or regression equations.

## Background

- Method extended to prediction of daily yield from one or two milkings in 3x herds (Wiggans, 1986).
- Based on 7 PA and 5 UT herds
- Factors allow prediction of daily yield by application of regression equations.

## Background

- Liu et al., 2000 explored several approaches to estimating daily yields from a single milking.
- 0.   DeLorenzo factors (no adjustment for DIM).
- 1.   MD = 2MP (MD = daily milk, MP = partial milk)
- 2.   MD = b0 + b1MP
- 3.   MD = b0 + b1MP + b2MI
- 4.   MD = b0 + b1MP  (by MIclass)
- 5.   MD = b0 + b1MP + b2(DIM – 158) (by MIclass)
- 6.   MD = b0 + b1MP (by parity x MIclass x DIMclass)

## Objective

- To derive preliminary factors to estimate daily yields from:
- One record for 2x milking
- One or two records from 3x milking
- Focus in this presentation on one record and Holsteins
- Compare factors derived by several methods for their accuracy in predicting true daily production

## Data

- Records were from 9 herds (5-2x and 4-3x) in IN, KS, IA, MI, and MN.
- Herds used Automatic Milk Recording, records processed through DRMS (except MN).

**Parity number**
**Test-d records**
**Cows**
**Herds**

**1**
**83,690**
**1842**
**5**

**2+**
**143,670**
**2957**
**5**

**1**
**41,657**
**779**
**4**

**2+**
**84,131**
**1999**
**4**

- 2X

- 3X

## Method 1

- DeLorenzo and Wiggans Method

**Factor = ****Σ****y / ****Σ****x **

- For each Milking Interval x Parity subclass.
- 24 MI classes (approx 9-15 h for 2x, 5-10.5 for 3x)
- 2 Parity classes (1, 2+)
- Factors smooth by weighted regression of their
- reciprocals on MI.
- Residuals regressed on DIM to develop stage of lactation adjustment.

## Method 2

- DeLorenzo and Wiggans Alternative Method

**Factor = ****Σ**** (y / ****x) / n **

- For each Milking Interval x Parity subclass.
- 24 MI classes (approx 9-15 h for 2x, 5-10.5 for 3x)
- 2 Parity classes (1, 2+)
- Factors smooth by weighted regression of their
- reciprocals on MI.
- Residuals regressed on DIM to develop stage of lactation adjustment.

## Method 3

- Liu et al. Model [6]

- MD = b0 + b1MP (by parity x MI class x DIM class)

- For each Parity x MI x DIMclass).
- 2 Parity classes (1, 2+)
- 7 MI classes (approx 9-14 h for 2x, 6 to 10 for 3x)
- 12 DIM classes (≤30, ≤ 60, ... ≤330, ≥330)
- Factors are not smooth.
- Adjustment uses regression coefficients.

## Distribution of numbers of cow-test-days with intervals prior to AM or PM milkings

**Distribution of numbers of cow-test-days with intervals prior to AM or PM milkings**

**Observations**

**Milking Interval**

**Holstein**

## Distribution of numbers of cow-test-days with intervals prior to 1st, 2nd, or 3rd milkings

**Distribution of numbers of cow-test-days with intervals prior to 1****st****, 2****nd****, or 3****rd**** milkings**

**Observations**

**Milking Interval**

**Holstein**

## Current and Method 2 factors by parity for AM milking

**Current and Method 2 factors by parity for AM milking**

**Factor**

**Milking Interval**

**Holstein**
**2x**

## Current and Method 2 factors by parity for PM milking

**Current and Method 2 factors by parity for PM milking**

**Factor**

**Milking Interval**

**Holstein**
**2x**

## Current and Method 2 factors by parity for Milking 1

**Current and Method 2 factors by parity for Milking 1**

**Factor**

**Milking Interval**

**Holstein**
**3x**

## Current and Method 2 factors by parity for Milking 2

**Current and Method 2 factors by parity for Milking 2**

**Factor**

**Milking Interval**

**Holstein**
**3x**

## Current and Method 2 factors by parity for Milking 3

**Current and Method 2 factors by parity for Milking 3**

**Factor**

**Milking Interval**

**Holstein**
**3x**

## Method 3 results for 12.5 to 13 h interval for AM milking by milk weight for DIM classes

**Method 3 results for 12.5 to 13 h interval for AM milking by milk weight for DIM classes**

**Predicted Daily Milk (kg)**

**Milking 1 Weight (kg)**

**Holstein**
**2x**

## Method 3 results for 11.0 to 11.5 h interval for PM milking by milk weight for DIM classes

**Method 3 results for 11.0 to 11.5 h interval for PM milking by milk weight for DIM classes**

**Milking 1 Weight (kg)**

**Predicted Daily Milk (kg)**

**Holstein**
**2x**

## Method 3 results for <10 h interval for PM milking by milk weight for DIM classes

**Method 3 results for <10 h interval for PM milking by milk weight for DIM classes**

**Milking 1 Weight (kg)**

**Predicted Daily Milk (kg)**

**Holstein**
**2x**

## Method 3 results for 180-210 DIM class for milking 1 by milk weight for interval classes

**Method 3 results for 180-210 DIM class for milking 1 by milk weight for interval classes**

**Milking 1 Weight (kg)**

**Predicted Daily Milk (kg)**

**Holstein**
**3x**

## Measures of variation and goodness of estimation of daily yield from AM yield for Holsteins

**Parity 1**
**Current**
**Method 1**
**Method 2**
**Method 3**
**Parity 2+**
**Current**
**Method 1**
**Method 2**
**Method 3**

**Correlation**
**With true**
**.955**
**.956**
**.956**
**.957**
**.964**
**.964**
**.964**
**.965**

**SD of**
**Estimates**
**18.76**
**18.59**
**18.82**
**17.03**
**26.48**
**26.39**
**26.74**
**24.30**

**Absolute **
**Error**
**3.78**
**3.62**
**3.80**
**3.58**
**4.94**
**4.87**
**5.16**
**4.71**

**Root **
**MSE**
**5.614**
**5.449**
**5.591**
**5.175**
**7.080**
**6.999**
**7.263**
**6.572**

**Abs. Diff. **
**Current**
**NA**
**0.90**
**0.67**
**1.71**
**NA**
**0.55**
**1.06**
**2.13**

## Measures of variation and goodness of estimation of daily yield from PM yield for Holsteins

**Parity 1**
**Current**
**Method 1**
**Method 2**
**Method 3**
**Parity 2+**
**Current**
**Method 1**
**Method 2**
**Method 3**

**Correlation**
**With true**
**.908**
**.945**
**.944**
**.947**
**.931**
**.954**
**.954**
**.955**

**SD of**
**Estimates**
**18.52**
**18.72**
**18.91**
**16.85**
**25.10**
**25.98**
**26.23**
**24.05**

**Absolute **
**Error**
**7.01**
**4.05**
**4.12**
**3.90**
**8.09**
**5.41**
**5.49**
**5.36**

**Root **
**MSE**
**9.070**
**6.149**
**6.272**
**5.724**
**10.583**
**7.827**
**7.973**
**7.443**

**Abs. Diff. **
**Current**
**NA**
**5.39**
**6.04**
**5.51**
**NA**
**5.83**
**5.49**
**5.92**

## Measures of variation and goodness of estimation of daily yield from single milking yield for Parity 1 Holsteins milked 3x

**Current**
**Method 2**
**Method 3**
**Current**
**Method 2**
**Method 3**
**Current**
**Method 2**
**Method 3**

**Correlation**
**With true**
**.937**
**.937**
**.938**
**.931**
**.931**
**.934**
**.926**
**.926**
**.930**

**SD of**
**Estimates**
**19.60**
**19.70**
**17.38**
**20.35**
**20.70**
**17.29**
**19.54**
**20.10**
**17.22**

**Absolute **
**Error**
**4.57**
**4.66**
**4.51**
**4.78**
**5.01**
**4.60**
**4.77**
**5.04**
**4.79**

**Root **
**MSE**
**6.865**
**6.961**
**6.408**
**7.415**
**7.7.4**
**6.633**
**7.439**
**7.708**
**6.827**

**Abs. Diff. **
**Current**
**NA**
**0.64**
**2.11**
**NA**
**1.27**
**2.71**
**NA**
**2.11**
**2.37**

- Milking 1

- Milking 2

- Milking 3

## Measures of variation and goodness of estimation of daily yield from single milking yield for Parity 2+ Holsteins milked 3x

**Current**
**Method 2**
**Method 3**
**Current**
**Method 2**
**Method 3**
**Current**
**Method 2**
**Method 3**

**Correlation**
**With true**
**.940**
**.939**
**.942**
**.936**
**.935**
**.939**
**.933**
**.933**
**.938**

**SD of**
**Estimates**
**29.41**
**29.69**
**26.31**
**30.84**
**31.03**
**26.21**
**29.01**
**30.50**
**26.21**

**Absolute **
**Error**
**6.95**
**7.24**
**6.85**
**7.59**
**7.79**
**6.88**
**7.16**
**7.76**
**6.90**

**Root **
**MSE**
**10.029**
**10.368**
**9.365**
**11.065**
**11.305**
**9.621**
**10.669**
**11.249**
**9.645**

**Abs. Diff. **
**Current**
**NA**
**1.66**
**3.06**
**NA**
**0.85**
**4.49**
**NA**
**4.58**
**3.68**

- Milking 1

- Milking 2

- Milking 3

## Conclusions

- Method 3 (regression within parity x MI x DIM subclasses) estimates of daily yield consistently had highest correlation with true daily yields, and smallest errors compared to actual daily yield.
- Measures of differences between estimated and actual yields were greater for parity 2.
- Error terms were greater for PM than AM milkings for 2x herds but similar across milkings for 3x herds.

## Implications and Future Work

- Data collection is ongoing to acquire
- more milk weight records for Jersey herds
- More test-day records for fat, protein, and SCC.
- While derived factors performed better than current factors for these herds, factors will need to be compared for robustness on more herds before new factors are implemented.

## Acknowledgments
Animal Improvement Programs Laboratory, provided financial support for data collection and analyses.

Dairy Records Management Services (John Clay and Tammie Guyer) assisted in data file management.

DHI Affiliate Managers, DHI Supervisors, and Herd Owners are also recognized for their contributions.

_**Acknowledgments**_
- Animal Improvement Programs Laboratory, provided financial support for data collection and analyses.
- Dairy Records Management Services (John Clay and Tammie Guyer) assisted in data file management.
- DHI Affiliate Managers, DHI Supervisors, and Herd Owners are also recognized for their contributions.