Acta agriculturae Slovenica, suplement 2 (september 2008), 195–200. 
 
 
  
Agris category codes: L01, Q04 COBISS Code 1.08 
COMPARISON OF CALCULATION METHODS OF DAILY MILK YIELD, FAT AND 
PROTEIN CONTENTS FROM AM/PM MILKINGS 
Janez JENKO a), Tomaž PERPAR a), Betka LOGAR a), Jože VERBIČ a) and Milena KOVAČ b) 
a) Agricultural Institute of Slovenia, Hacquetova 17, SI-1000 Ljubljana, Slovenia, e-mail: janez.jenko@kis.si 
b) Univ. of Ljubljana, Biotechnical Fac., Dept. of Animal Science, Groblje 3, SI-1230 Domžale, Slovenia 
ABSTRACT 
For prediction of daily milk yield (DMY), daily fat percentage (DFP), and daily protein 
percentage (DPP) from alternate AM/PM recording scheme, three different methods were tested. 
The data comprised information on 483 813 test-day records. Methods were compared on the 
whole data set or just on the upper or the lower quartile of the records according to DMY, DFP, 
DPP, and milking interval (MI). Method 1 included DMY, DFP or DPP as a dependent variable 
in regression analysis. In Method 2 ratio of partial AM/PM to daily yield was included as a 
dependent variable, whereas Method 3 is based on doubling milk yield from AM/PM milking 
while DFP and DPP are expected to be the same as the AM or PM milking. The bias on the 
whole data set was low. With respect to high DMY, DFP, and DPP on the upper quartile of data 
set bias in underestimation of records was noticed for Method 1 whereas with this method, data 
from the lower quartile of data set were overestimated. With respect to the short MI on the 
average DMY was underestimated whereas DFP and DPP were overestimated with Method 3. 
DMY with long MI were overestimated on the average with Method 3 while DFP and DPP were 
underestimated. That kind of bias was not detected with Method 2. 
Key words: cattle / dairy cows / milking / alternating recording scheme / bias / milk / composition / fat / proteins / 
models 
PRIMERJAVA RAZLIČNIH METOD ZA IZRAČUN DNEVNIH MLEČNOSTI TER 
VSEBNOSTI MAŠČOB IN BELJAKOVIN IZ JUTRANJE ALI VEČERNE MOLŽE 
IZVLEČEK 
Za napoved dnevne količine mleka (DMY), dnevne vsebnosti maščobe (DFP) in dnevne 
vsebnosti beljakovin (DPP) na podlagi alternirajoče kontrole (molža zjutraj ali zvečer) smo 
uporabili tri metode. Primerjavo smo opravili na 483 813 dnevnih kontrolah mlečnosti. 
Primerjava je bila izvedena na celotnem podatkovnem setu ali le na zgornjem oziroma spodnjem 
kvartilu glede na DMY, DFP, DPP in interval med molžama (MI). DMY, DFP ali DPP so kot 
odvisne spremenljivke nastopale v Metodi 1. V Metodi 2 je kot odvisna spremenljivka nastopalo 
razmerje med delno (jutranja/večerna) in dnevno količino mleka, maščob in beljakovin. Metoda 
3 ocenjuje DMY na podlagi podvojitve količine mleka zjutraj oziroma zvečer, medtem, ko delne 
vsebnosti maščob in beljakovin ostajajo enake dnevnim. V celotni množici podatkov je bila 
pristranost ocen nizka. V primeru visokih DMY, DFP in DPP so bili podatki v povprečju 
podcenjeni z metodo 1, medtem ko ta metoda nizke vrednosti preceni. Metoda 3 je v kratkih MI 
v povprečju podcenila DMY ter precenila DFP in DPP, medtem ko je v dolgih MI precenila 
DMY in podcenila DFP in DPP. Takšnih pristranosti ocen z metodo 2 ni zaznati. 
Ključne besede: govedo / krave / molznice / molža / alternirajoča kontrola / pristranost / mleko / sestava / maščobe / 
beljakovine / modeli 
http://aas.bf.uni-lj.si 
Acta agriculturae Slovenica, suplement 2 (september 2008). 
 
196 
INTRODUCTION 
Recording system is important for herd management and genetic improvement in dairy cattle 
(Liu et al., 2000). Under the constant pressure of reducing costs, several studies (Cassandro et 
al., 1995; DeLorenzo and Wiggans, 1986; Klopčič et al., 2003; Klopčič, 2004; Lee and Wardrop, 
1984; Liu et al., 2000; Wiggans, 1981) considered the implementation of alternate recording 
scheme (AT) based on morning (AM) or evening (PM) milking. Potential benefits from the 
adoption of AT recording scheme are the following: more herds can be served by one supervisor, 
recording costs per cow are lower (Everett and Wadell, 1970a, b; Hargrove and Gilbert, 1984), 
allowing more young bulls to be tested per year without reducing genetic gain (Schaeffer and 
Rennie, 1976), flexibility in scheduling the work of a supervisor is greater and the method 
disrupts the milking routine less (Cassandro et al., 1995). The AT recording scheme with method 
proposed by Klopčič et al. (2003) and Klopčič (2004) was introduced in Slovenia in March 2004 
replacing of the A4 (monthly records of daily milkings) ICAR standard reference recording 
scheme (Sadar et al., 2005).  
There were two objectives of this study. The first was to compare adequacy of different 
methods for the estimation of daily milk yield, fat and protein content on a whole data set. The 
second was to compare these three models in case of high or low daily milk yield (DMY), daily 
fat percentage (DFP) or daily protein percentage (DPP), and in case of short or long milking 
interval (MI). 
MATERIAL AND METHODS 
Data 
Milk production data were collected from central cattle database GOVEDO, which is hosted 
at and maintained by Agricultural institute of Slovenia (Logar et al., 2005). Data were combined 
from regular and supervised dairy recordings carried out from March 2004 through February 
2008. Daily yields were calculated from AM and PM records. Database included altogether 
497,842 records.  
 
Table 1. Descriptive statistics of milk yield and milk composition 
 
Daily (D) Evening (PM) Morning (AM) 
Trait Number of records Mean Std Mean Std Mean Std 
Milk yield (MY), kg 483 813 18.1 7.1 8.8 3.6 9.2 3.8 
Ratio PM : DMY 241 914   0.49 0.05   
Ratio AM : DMY 241 899     0.51 0.05 
Fat yield, kg 483 813 0.74 0.29 0.37 0.15 0.38 0.16 
Fat percentage, % 483 813 4.18 0.71 4.22 0.82 4.15 0.82 
Ratio PM : DFY 241 914   0.49 0.07   
Ratio AM : DFY 241 899     0.51 0.07 
Protein yield (PY), kg 483 813 0.61 0.22 0.30 0.11 0.31 0.12 
Protein percentage, % 483 813 3.41 0.38 3.43 0.39 3.40 0.39 
Ratio PM : DPY 241 914   0.49 0.05   
Ratio AM : DPY 241 899     0.51 0.05 
Milking interval, min 483 813   705 44 732 47 
 
Jenko, J. et al. Comparison of calculation methods … from AM/PM milkings. 
 
197
Records were excluded from the analysis if days in milk (DIM) was less than 5 days, MI less 
than 540 minutes or more than 870 minutes, if there were more than two milkings per day or 
some problems detected at testing. For the analysis, 483 813 test-day records were prepared. 
They were collected from 120 971 lactations of 89 376 cows from 26 046 test-days in 5 051 
herds. The data included records from successive AM/PM or PM/AM milkings with no traits 
missing. Variables included in the study were daily (D) as well as partial (P) milk yield, fat and 
protein percentage, MI, and DIM.  
During the night, MI was on the average 26 minutes longer than daily interval (Table 1). 
PMY in AM milking was higher for 0.4 kg, compared to PM milking. Slightly higher values 
were observed for PFP and PPP from PM milking. On the other hand, partial fat yield (PFY) and 
partial protein yield (PPY) were higher from AM milking. The reason can be found in higher 
milk from AM than PM milk milking. 
Prediction equations for daily milk yield, fat and protein content 
Three methods were compared for estimation of daily milk yield, fat and protein content in 
AT recording scheme. Method 1 was proposed by Klopčič et al. (2003) and Klopčič (2004). 
Method 2 is a combination of DeLorenzo and Wiggans model (1986) and model by Klopčič et 
al. (2003) and Klopčič (2004) and was developed in Slovenia by Jenko et al. (2008). In 
Method 3, DMY is expected to be twice the amount of milk from AM or PM milkings, while 
DFP and DPP are expected to be the same as partial measurements. Adjustment factors for 
Method 1 and Method 2 were calculated on these dataset in a preliminary study (unpublished 
results) 
Method 1: 
ijkijijkijijijk tbxby *ˆ*ˆˆˆ 21 ++= µ  (1) 
Daily value ( ijkŷ ) for record k and trait i (DMY, DFP or DPP) from milking j (AM, PM) is 
estimated by regression equation (1) which contains partial measurements ( ijkx ) of the same trait 
and milking interval ( ijkt ) as independent variables. Estimated ijb1̂  and ijb2ˆ  stand for regression 
coefficient and ijµ̂  for intercept. 
Method 2: 
ijkijkijk Fxy ˆ/ˆ =  (2) 
Method 2 (equation 2) estimates daily yield ( ijkŷ ) from the corresponding partial value ( ijkx ) 
applying a factor from equation (4). Partial yield for PFY and PPY (equation 3) is calculated 
from partial milk yield ( milkx ) and corresponding percentage ( ijkx ). 
100/)%( ijkmilkijk xxx ∗=  (3) 
In method 2, factors ( ijkF̂ ) to account for unequal MI are the ratios between partial and daily 
yield. Factors are derived by regression analysis containing milking interval ( ijkt ) as the only 
independent variable. Estimated ijf̂  is the intercept of ratio and ijb̂  denotes corresponding 
regression coefficient.  
ijkijijijk tbfF ∗+= ˆˆˆ  (4) 
Acta agriculturae Slovenica, suplement 2 (september 2008). 
 
198 
Method 3: 
milkmilk xy *2ˆ =  (5) 
Methods were evaluated on the basis of accuracy, bias, and correlation between estimated and 
true values. Additionally, the three methods were compared at extreme daily values for observed 
traits and extreme MI, where more problems were expected. Calculations were done by R 
statistics package (R Development Core Team, 2008). 
RESULTS AND DISCUSSION 
On the whole data set, correlation coefficients between the predicted and true value did not 
differ among the three methods (Table 2). The overall bias was zero as well. DFP is most 
accurately predicted by Method 1, whereas accuracy of DMY and DPP does not differ between 
the methods.  
 
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Figure 1. Bias of estimates for daily milk yield from AM (a) and PM milking (b) obtained by 
different methods. 
 
The three methods did not perform equally when observed over a range of daily milk yields 
(Fig. 1). Close to the average the differences are not important and thus, the methods worked 
well for a large proportion of records. However, extreme records where the differences become 
larger are especially important for selection or culling decision. The Method 1 overestimates low 
DMY and underestimates high DMY from either AM or PM milking. Because of longer MI 
during the night (Table 1), Method 3 overestimates DMY from AM milking and underestimates 
DMY from PM milking (Fig. 1). Bias in DMY was the smallest with Method 2 on the observed 
interval. 
Further analysis was focused on lower or upper quartile where the most problems were 
expected. The boundaries were set to 12.9 kg for DMY, 3.71% for DFP, and 3.14% for DPP for 
the lower quartile and to 22.4 kg for DMY, 4.62% for DFP, and 3.66% for DPP for the upper 
quartile. Differences in correlation coefficient between methods were negligible either for lower 
and upper quartile (Table 2). On the average, Method 1 overestimates DMY, DFP, and DPP for 
0.3 kg, 0.20% and 0.02% in the lower quartile, respectively. The values were low for DMY and 
Jenko, J. et al. Comparison of calculation methods … from AM/PM milkings. 
 
199
DPP. In both cases, they were smaller than 10% of standard deviation. The bias in DFP was 
larger and accounted for 1/3 of standard deviation. The Method 1 was biased in upper quartile as 
well. The size of bias was similar to lower quartile, but the values were underestimated. 
However, the Method 1 performed well when judged on accuracy, especially in DFP. On the 
other hand, Method 2 and Method 3 were unbiased for all traits in lower as well as upper 
quartile. Method 3 revealed as the least accurate method for estimating daily milk records. 
 
Table 2. Correlation, bias, and accuracy in the complete dataset, lower, and upper quartile 
 
Whole data set Lower quartile 3 Upper quartile 4 
Trait Method 
r 1 Bias Acc 2 r 1 Bias Acc 2 r 1 Bias Acc 2 
Method 1 0.980 0.0 0.961 0.897 0.3 0.816 0.925 – 0.4 0.864 
Method 2 0.980 0.0 0.961 0.908 0.0 0.823 0.928 – 0.0 0.862 
Daily milk 
yield (DMY), 
kg Method 3 0.971 0.0 0.943 0.881 – 0.0 0.776 0.894 – 0.0 0.800 
Method 1 0.879 0.00 0.815 0.657 0.20 0.533 0.710 – 0.21 0.612 
Method 2 0.879 – 0.01 0.775 0.657 – 0.00 0.423 0.709 – 0.01 0.508 
Daily fat 
percentage 
(DFP), % Method 3 0.871 0.00 0.761 0.639 0.00 0.400 0.701 0.00 0.496 
Method 1 0.975 0.00 0.952 0.902 0.02 0.827 0.921 – 0.03 0.859 
Method 2 0.975 0.00 0.950 0.902 0.00 0.814 0.921 0.00 0.848 
Daily protein 
percentage 
(DPP), % Method 3 0.974 0.00 0.949 0.900 0.00 0.809 0.920 0.00 0.846 
1 Correlation coefficient between the estimated and measured DMY, DFP and DPP; 2 Accuracy; 3 DMY < 12.9 kg 
for DMY, DFP < 3.71% for DFP, and DPP < 3.14% for DPP; 4 DMY > 22.4kg for DMY, DFP > 4.62% for DFP, 
and DPP > 3.66% for DPP 
 
The dataset was also split to the upper and lower quartile on the basis of milking interval. 
Lower quartile contained records with MI shorter than 690 minutes and upper quartile with MI 
longer than 750 minutes. Differences in the correlation coefficient between methods were again 
negligible (Table 3).  
 
Table 3. Correlation, bias, and accuracy in the lower and the upper quartile with respect to short 
or long MI 
 
Lower quartile 3 Upper quartile 4 
Trait Method 
r 1 Bias Acc 2 r 1 Bias Acc 2 
Method 1 0.975 0.0 0.951 0.982 0.1 0.962 
Method 2 0.975 0.0 0.950 0.982 0.0 0.964 
Daily milk 
yield (DMY), 
kg Method 3 0.973 – 1.3 0.950 0.980 1.4 0.951 
Method 1 0.856 0.00 0.789 0.895 0.00 0.834 
Method 2 0.856 – 0.01 0.757 0.895 0.00 0.780 
Daily fat 
percentage 
(DFP), % Method 3 0.854 0.16 0.740 0.893 – 0.14 0.791 
Method 1 0.968 0.00 0.940 0.977 0.00 0.956 
Method 2 0.967 0.00 0.937 0.977 0.00 0.953 
Daily protein 
percentage 
(DPP), % Method 3 0.967 0.01 0.936 0.976 – 0.01 0.953 
1, 2 For description see Table 2; 3 Milking interval < 690 min; 4 Milking interval > 750 min 
 
In the lower quartile, Method 3 underestimates DMY for 1.3 kg, whereas DFP and DPP are 
overestimated for 0.16%, and 0.01%, respectively. Method 3 overestimates DMY in the upper 
quartile for 1.4 kg, whereas DFP and DPP are underestimated on the average for 0.14% and 
Acta agriculturae Slovenica, suplement 2 (september 2008). 
 
200 
0.01%, respectively. For estimation of DMY and DPY, the accuracy between the methods does 
not differ much. DFP is estimated with the highest accuracy with method 1. 
Our study revealed that the decision as to which method should be chosen for the estimation 
of DMY, DFP, and DPP is important. It is necessary to analyse the effect of methods not only on 
the whole data set but also on the lower or upper portion of DMY, DFP, DPP, and MI. 
CONCLUSIONS 
Three methods were analysed in the Slovenian dairy recording system. Correlation coefficient 
among estimated and measured value were high and almost the same. Bias imposed by the level 
of production or milking interval could be removed with the application of appropriate method. 
Method 1 produced biased but more accurate estimates at extremes, especially in DFP, whereas 
Method 3 proved to be biased with respect to short or long MI. That kind of bias was not 
detected with Method 2, while the accuracy was close to Method 1. Hereby Method 2 was 
introduced in the Slovenian dairy recording scheme. 
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