Principal component regression analysis in lifetime milk yield prediction of crossbred cattle strain Vrindavani of North India

Abstract

The study aims to devise most appropriate prediction model for lifetime milk production of Vrindavani, a crossbred cattle strain developed and maintained at Institute, based on principal components formulated on initially expressed part lactation records as predictors. Principal components (PCs) were derived on a data set pertaining to 10-year period (1999–2009). Part lactation records of 100, 170 and 240 days of first and second lactations and their respective total milk yields were used. Using principal component regression analysis (PCRA), the principal components were used as predictors for predicting lifetime milk yield as total milk yield up to 4 lactations (LTMY4), and up to 5 lactations
(LTMY5). Eight types of model were fitted to identify the best fitted model for both the traits (LTMY4 and LTMY5) with the first principal component (PC_1) as a predictor. The equation LTMY4=4410.305+0.596PC_1-1.171PC_3 and LTMY5 = 7987.560– 2.301PC_3 explained 54.46% and 39.74% variation in the estimated values. The curve estimation analysis showing the appropriateness of power function was the most appropriate model for both the lifetime traits. The
model LTMY4=32.609 (PC_1)0.671 was found best fit and explained 53.50% variation in estimation. In the other lifetime trait, model LTMY5==103.769 (PC_1)0.566, explained 38.40% variation in estimated values. These prediction equations may be helpful in selection at an early stage of Vrindavani cattle based on early part lactation records.
Key words: Vrindavani cattle, Lifetime milk production, Part lactation, Principal component regression analysis

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Present address: 1Senior Scientist (takhan@ivri.res.in),
2, 4Principal Scientist 2(drakstomar@gmail.com, 4bhushan.drbharat
@gmail.com), 3Jt. Director (jdee@ivri.up.nic.in).
India with 210.2 million head of cattle contributes to
14.7% of the total cattle population of the world. The
country’s per capita milk availability in 2010–11 was at 281
g/day (compared to the World average of 279.4 g/day) (BAHS
2012). To increase milk availability, efficient planning and
management tools are to be developed. Principal component
analysis (PCA) is a mathematical procedure that transforms
a number of (possibly) correlated variables into a (smaller)
number of uncorrelated variables called principal components
(Pearson 1901, Lukibisi et al. 2008a, Hotelling, 1933, Rao
1964). Chapman et al. (2001) used principal component
analysis for sensory characterization of ultra pasteurized milk
quality and found as much as 81.0% variation in estimation.
Rugoor et al. (2000) investigated advantages and
disadvantages of principal components regression (PCR) and
partial least squares (PLS) for livestock management
research. Bhatacharya and Gandhi (2005) compared multiple
regression analysis and principal components to predict
lifetime production of Karan Fries cattle and found advantage
of principal components analysis.
Indian Journal of Animal Sciences 83 (12): 1288–1291, December 2013/Article
Principal component regression analysis in lifetime milk yield prediction of
crossbred cattle strain Vrindavani of North India
T A KHAN1, A K S TOMAR2, TRIVENI DUTT3 and BHARAT BHUSHAN4
Indian Veterinary Research Institute, Izatnagar, Uttar Pradesh 243 122 India
Received: 20 April 2013; Accepted: 28 August 2013
ABSTRACT
The study aims to devise most appropriate prediction model for lifetime milk production of Vrindavani, a crossbred
cattle strain developed and maintained at Institute, based on principal components formulated on initially expressed
part lactation records as predictors. Principal components (PCs) were derived on a data set pertaining to 10-year period
(1999–2009). Part lactation records of 100, 170 and 240 days of first and second lactations and their respective total
milk yields were used. Using principal component regression analysis (PCRA), the principal components were used as
predictors for predicting lifetime milk yield as total milk yield up to 4 lactations (LTMY4), and up to 5 lactations
(LTMY5). Eight types of model were fitted to identify the best fitted model for both the traits (LTMY4 and LTMY5)
with the first principal component (PC_1) as a predictor. The equation LTMY4=4410.305+0.596PC_1-1.171PC_3 and
LTMY5 = 7987.560– 2.301PC_3 explained 54.46% and 39.74% variation in the estimated values. The curve estimation
analysis showing the appropriateness of power function was the most appropriate model for both the lifetime traits. The
model LTMY4=32.609 (PC_1)0.671 was found best fit and explained 53.50% variation in estimation. In the other lifetime
trait, model LTMY5==103.769 (PC_1)0.566, explained 38.40% variation in estimated values. These prediction equations
may be helpful in selection at an early stage of Vrindavani cattle based on early part lactation records.
Key words: Vrindavani cattle, Lifetime milk production, Part lactation, Principal component regression analysis
Lifetime production is an important economic parameter
when defining the breeding objective. Khan et al. (2012),
formulated the lifetime prediction model based on birth
weight, 5 initially expressed reproductive traits age at first
calving (AFC), first service period (FSP), first dry period
(FDP), first calving interval (FCI) and first lactation length
(FLL)) and part lactation records of 100, 170 and 240 days
of first lactation, second lactation and their respective total
milk yields and explained 40.32% variation in estimated
lifetime yields (total of first 4 lactations) in Vrindavani cattle.
Malhotra and Singh (1980) predicted lifetime production
(total milk yield in the first 3 lactations) for Red Sindhi cows
on the basis of traits available in early life. Puri and Sharma
(1965) studied first lactation yield and age at first calving on
lifetime production and determines the relative importance
of them for selection purposes in Red Sindhi and crossbred
cows. Shinde et al. (2010) predicted lifetime milk production
up to third lactation in Phule Triveni cows. Vrindavani cattle
is a synthetic crossbred cattle strain with exotic inheritance
(50 to 75%) of Holstein-Friesian, Brown Swiss, Jersey and
indigenous inheritance (25 to 50%) of Hariana cattle,
developed at Indian Veterinary Research Institute, Izatnagar
(Singh et al. 2011). The climate of Izatnagar is semi tropical

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49
and conditions are hot humid for many months of the year,
especially during summer and monsoon seasons.
Since data on traits expressed by animals are correlated
and huge in size, present study was initiated to formulate
prediction models for lifetime production based on principal
components formulated on initially expressed part lactation
records as predictors. These models may be used in early
selection of animals.
MATRIALS AND METHODS
Ten year data records (1/4/1999 to 31/3/2009) of
Vrindavani were used to formulate lifetime prediction
models. The data set consisted of parity-wise part milk yields
of 100, 170 and 240 days in first lactation (MY100_1,
MY170_1, MY240_1), in second lactation (MY100_2,
MY170_2, MY240_2) and their respective total milk yields
(TLMY1, TLMY2) along with total milk yield of first 2
lactations (LTLMY2) and principal components (PCs) were
derived using the princomp procedure of SAS 9.2. Principal
component regression analysis (PCRA) was performed to
predict lifetime milk yield up to 4 (LTMY4) and 5 parities
(LTMY5) using principal components as predictors (Draper
and Smith 1986, Proc Reg procedure, SAS 9.2).
Eigen values (> 1) and scree plot methods were used to
identify the principal components to be retained as predictors.
Residual and diagnostics plots were examined to find out
appropriate fitted model (SAS Inc 2009).
Curve estimation analysis was undertaken to know the
appropriateness of the models (lifetime yields with first
principal as predictor). Eight types of models, viz. linear,
quadratic, cubic, logarithmic, inverse, power, S-curve, and
exponential were fitted for prediction of LTMY4 and
LTMY5. The adequacy of the best fitted model was adjudged
based on adjusted R2-value and significance of coefficients
(Draper and Smith 1986, SPSS Inc. 2003).
RESULTS AND DISCUSSION
Principal component analysis could retain following first
3 components explained 93.08% variation of the original
variables. The first principal component showed 61.86%
variation followed by second principal component (26.14%)
and third principal component (5.09%) (Table 1; Fig. 1). Here
first 2 PCs had eigen values more than one, but scree plot
showed the appropriateness of first 3 components (clearly
as curve bend at PC_3). So, first 3 PCs were retained to be
used as predictors.
Table 1. Eigen values and proportion of the variance of principal
components (PC) of the correlation matrix of original variables
PC Eigen value Difference Proportion Cumulative
1 5.5674 3.2149 0.6186 0.6186
2 2.3525 1.8949 0.2614 0.8800
3 0.4577 0.1502 0.0509 0.9308
4 0.3074 0.1673 0.0342 0.9650
5 0.1401 0.0439 0.0156 0.9806
6 0.0962 0.0544 0.0107 0.9913
7 0.0419 0.0051 0.0047 0.9959
8 0.0368 0.0368 0.0041 1.0000
Fig. 1. Scree plots of Principal components formulated in
Vrindavani cattle part milk yield data
The following 3 principal components (PCs) were
retained:
PC_1 = 0.316 MY100_1 + 0.331 MY_170_1 + 0.331
MY240_1 +0.313TLMY1+ 0.309 MY100_2 + 0.336
MY170_2+ 0.346 MY240_2+ 0.312 TLMY2+ 0.398
LTMY2
PC_2 = 0.329 MY100_1 + 0.368 MY_170_1 + 0.381
MY240_1 + 0.350 TLMY1 -.339 MY100_2 -.357
MY170_2 -.341 MY240_2 -.360 TLMY2 -.016
LTMY2
PC_3 = 0.430 MY100_1 + 0.245 MY_170_1 + 0.046
MY240_1 -.442 TLMY1+ 0.398 MY100_2 + 0.199
MY170_2+ 0.051 MY240_2 -.336 TLMY2 -.494
LTMY2
The PCRA for lifetime milk yield (LTMY4) evolved
equation, LTMY4=4410.305**+0.596*PC_1-1.171*PC_3 and
could explained 54.46% variation in the estimated values
with adjusted R2= 53.20% (*-Significant p<0.05, **-
significant P<0.01).

1290 KHAN ET AL. [Indian Journal of Animal Sciences 83 (12)
50
In case of lifetime milk yield prediction up to 5 parities
(LTMY5) the following evolved equation, LTMY5 =
7987.560**- 2.301**PC_3 could explained 39.74% variation
in the estimated values of lifetime milk yield with adjusted
R2= 38.92%.
Fit diagnostics for LTMY4 and LTMY5 showed goodness
of fit of the models. The quantile plot and histogram of
residuals indicated observance of normality assumption.
Residual plots indicated absence of heteroscedasticity
(among the PCs). The observed values verses the predicted
values plot indicated a good fit for the model. The fit-mean
residual plot indicated that the fitted model accounted for a
good deal of variability in both LTMY4 and LTMY5.
Curve estimation: The regression coefficients along with
standard errors of the fitted models (lifetime yields-Y with
first principal component-PC_1, as predictor) are presented
in Table 2. The value of adjusted R2, by the models for
LTMY4 showed maximum variation (53.50%) by power
function with minimum in inverse function (47.00%). Since
in power function, regression coefficient was highly
significant (P<0.01) and had maximum adjusted R2, the
function was decided to be more appropriate for estimating
the LTMY4, though intercept was not significant (Fig. 2).
Same trend was observed for LTMY5 and values of adjusted
R2, by the fitted models showed major variation (39.30%)
explained by power function and minimum by inverse
function (34.93%). So in both the lifetime traits (LTMY4
and LTMY5) the power function was more appropriate. The
power function explained 38.40% variation in estimated
values of LTMY5, which was found more appropriate
(Fig. 3).
The study was to show the use of principal components
Table 2. Significance of coefficients of fitted models and respective adjusted R2- values
Model LTMY4 LTMY5
b0b1b2b3Adj. R2b0b1b2b3Adj. R2
Linear 4250.0** 1.178** - - 50.00 6609.843** 1.295** - - 38.30
(973.143) (0.136) (1352.684) (0.189)
Quadratic –127.389NS 2.476* –9.2E–05NS - 50.50 4106.786NS 2.037NS –5E–05NS - 37.30
(3472.125) (0.997) (7E–05) (4874.072) (1.400) (1E–04
Logarithmic –56941.458** 7862.887** - - 50.70 –60017.832** 8570.997** - - 38.20
(7912.128) (895.449) (11084.718) (1254.505)
Cubic 5425.791NS –0.217NS 3E–04NS –2E–08NS 50.10 3143.927NS 2.505NS –1E–04NS 4E–09NS 36.80
(9216.147) (4.257) (0.001) (3E–08) (12975.327) (5.993) (0.001) (4E–08)
Inverse 19333.760** –4562588.172** - - 47.00 23080.531** –4942712.185** - - 34.90
(859.087) (558658.324) (1191.144) (7745930.581)
Power 32.609NS 0.671** - - 53.50 103.769NS 0.566** - - 39.30
(20.860) (0.072) (74.238) (0.081)
S-curve 10.007** –3959.246** - - 51.30 10.138** –3313.178** - - 37.10
(0.069) (445.942) (0.076) (496.106)
Exponent 6122.418** 9.9E–05** - - 51.30 8519.867** 8E–05** - - 38.40
(489.643) (1.1E–05) (750.036) (1E–05)
Figures in parenthesis are standard error of coefficient. *,>significant (P<0.05); **, > significant (P<0.01). NS, > nonsignificant.
Fig. 3. Appropriateness of power function in estimation of
LMMYS (kg).
Fig. 2. Appropriateness of power function in estimation of
LTMY4 (kg).

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regression analysis as PCs are orthogonal contrasts, free from
problem of multicolliniarity. Since expression of animals
traits on growth, production and reproduction is very much
complex and correlated, the information generated out of all
the traits studied, can be included as null hypothesis as their
contribution towards the lifetime production. We may
formulate the principal components to reduce the data (into
components) with the variability explained in the original
set of observed traits (variables), as discussed by many
workers (Hotelling 1933, Chapman et al. 2001, Rugoor et
al. 2000).
PCRA with step-wise procedure, showed fitted models for
LTMY4 and LTMY5 with the 3 predictors (PC_1, PC_2 and
PC_3): LTMY4=4410.305**+0.596*PC_1-1.171*PC_3 and
LTMY5 = 7987.560**- 2.301**PC_3 and could explain
54.46% and 39.74% variation in the estimated values of
LTMY4 and LTMY5, respectively. Curve estimation analysis
showed that power function was the most appropriate model
for both the lifetime traits. The model LTMY4=32.609
(PC_1)0.671 was found best fit and explained 53.50% variation
in estimation. The relationships LTMY5==103.769
(PC_1)0.566, explained 38.40% variation in estimated values
of LTMY5. Since every biological phenomenon is curvilinear
in nature and the variation explained in estimation of LTMY4
and LTMY5 by step-wise procedure and curve estimation are
at par, these models are recommended as best fitted models.
In both the traits, the regressions were highly significant
(P<0.01) whereas intercepts were not significant (as the curve
is crossing y-axis nearby the origin as observed in Figs 2, 3).
Khan et al. (2012), found 40.32% variation in estimated life
time yields (total of first 4 lactations- LTMY4) with initial
growth, reproduction, part lactation records with step-wise
procedure of regression analysis in Vrindavani cattle. Whereas
principal components based on only part lactation records
could estimate 54.46% variation in estimation in the same
crossbred strain. Bhatacharya and Gandhi, (2005) have
compared multiple regression analysis and principal
components analysis to predict lifetime milk production and
found that total variance was lower from the model having
PCs as compared to original variables in the regression model.
This showed the importance of principal component
regression analysis (PCRA) in estimation of lifetime
production traits. So, it is concluded that fitted prediction
model LTMY4=32.609 (PC_1)0.671 and LTMY5==103.769
(PC_1)0.566, may be helpful in early selection of Vrindavani
cattle based on initial part lactation records.
ACKNOWLEDGEMENT
Authors are thankful to Director and Incharge Livestock
Production and Management Section, IVRI, for constant
encouragement and providing facilities
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