Principal component analysis in modelling lactation milk yield in Hariana cows
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Date
2009
Authors
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Publisher
CCSHAU
Abstract
A total of 244 first lactation records of Hariana cows
maintained in the Department of Animal Breeding, C.C.S.H.A.U.,
Hisar over a period of 14 years (1989 to 2003) were analyzed.
The first lactation traits used for multiple linear regression and
principal component regression model were: first lactation milk
yield (FLMY), age at first calving (AFC), first peak yield (FPY), first
lactation length (FLL), first dry period (FDP), first service period
(FSP) and first calving interval (FCI). The phenotypic correlations
among explanatory variables were significant at 5 % level of
significance. It gave an indication of multicollinearity. Using
stepwise regression technique the maximum value of coefficient
of determination was obtained as 0.648. The multicollinearity
among different explanatory variables made it very difficult to
identify the contribution of each explanatory variable. There
were non-significant regression coefficients giving an indication
of loosing information on some of important explanatory
variables. Therefore principal component regression model was
fitted. The phenotypic correlations among the traits were used to
derive principal component scores and correlation coefficients of
these variables with the original variables (component loadings)
were analyzed. The first, second, third and fourth principal
components (PC’s) explained 45.24, 25.70, 15.33 and 11.68 of
total variation in the data. The first four PC’s explained 97.94 %
of variance cumulatively. The correlations of first PC with AFC,
FPY and FLL were positive ranging from 0.13 to 0.34, while it’s
correlations with FDP, FSP and FCI were very high and negative
ranging from -0.91 to -0.93. The correlations of second PC were
positive with all the variables (ranging from 0.30 to 0.88) except
FDP (-0.27). The third PC was positively correlated with all the
variables except FPY (-0.47) while the fourth PC was positively
correlated with AFC (0.33), FPY (0.58) and FDP (0.24) and
negatively with FLL (-0.44), FSP (-0.03) and FCI (-0.01). The first
PC can be interpreted as reproduction and production
component, the second and fourth PC as production component
and the third PC as maturity component.
The number of meaningful PC’s were retained on the basis
of Kaiser’s, Scree plot, Proportion of variance accounted for (only
those PC’s are retained which account for at least 10 % of
variation of data), Cumulative percent of variance accounted for
(only those PC’s are retained which account for 85% to 90% of
variation of data cumulatively) and Jollife (1972) criterions.
When we regressed the retained PC’s on FLMY, PC’s retained on
basis of “cumulative percent of variance accounted for” criterion
gave best results. When we compare the stepwise regression
results with the principal component regression model (when
FLMY regressed on first three PC’s) we found that there is no
significant change in R2 but in the principal component
regression model there is contribution of each and every
variable. So principal component regression model increases the
accuracy and validity of the model.
Description
Keywords
Storage, Storage structures, Fruits, Vegetables, irrigation, Carbon, Planting, Costs, Relative humidity, Refrigeration equipment