Ridge regression estimator for milk production in cattle
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Date
2006
Authors
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Publisher
CCSHAU
Abstract
The prediction of life time production of an animal on farm may
be helpful to decide, whether particular animal should cull or not on the
basis of performance of first lactation only. The present investigation
has been conducted to find out an appropriate estimation procedure to
estimate the regression coefficients of life time production multiple
linear regression model of Hariana breed of cattle.
To find out an appropriate estimation procedure, life time
production multiple linear regression model of Hariana breed of cattle
has been studied in detail. Normal probability plot and histogram used
to check the normality assumption of model. Plots of standardized
residuals against each regressor were utilized to detect the outlier cases
in this study. Presence of influential observations was detected with the
help of three different measures. Each influential observation and their
different combinations excluded from the model one by one to check the
considerable change in mean square error value, coefficient of
determination value, in sign and significance of regression coefficients.
Presence of multicollinearity in independent variables was
diagnosed with the help of examination of correlation matrix, variance
inflation factors, eigenvalues inspection and condition indices. The
result revealed that problem of multicollinearity was serious in the
study.
In this investigation two estimation procedures, i.e., ordinary least
squares and ridge regression technique were compared. Criterion of
mean square error, sign and significance of regression coefficients were
used to compare the performance of each estimator. The value of ridge
constant (K)was estimated by three different methods and accordingly
the optimum value of ridge constant (K) was found. The ridge
regression estimator by using optimum value of ridge constant was
found better as compared to ordinary least squares estimator in terms of
mean square error criterion.
Description
Keywords
Ridge regression, Ordinary least squares, Outliers, Influential Observations, Normal probability plot, Histogram, Multicollinearity.