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J. Anim Sci. 1983. 57:885-891.
© 1983 American Society of Animal Science
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A Monte-Carlo Comparison of Estimators of Average Daily Gain in Body Weight1

Suwat Rattanaronchart2, M. Grossman, R. L. Fernando3 and R. D. Shanks

University of Illinois at Urbana-Champaign, Urbana 61801

Abstract

Weighted or generalized curvilinear least-squares regression was considered as an estimate of average daily gain in body weight (ADG). Estimated ADG
Figure 1
was calculated as
Figure 2
+
Figure 3
, where
Figure 4
and
Figure 5
are estimates of the linear and quadratic regression coefficients of age on body weight, and a1 and aT are initial and final ages. Six methods of estimating ADG were compared: five based on least-squares and the "usual" estimator obtained by dividing the difference between final and initial weights by the number of days between them. Estimates of mean square error
Figure 6
, obtained by Monte-Carlo simulation, was the basis for comparison. Estimated generalized least-squares (EGLS), which takes into account the variance-covariance of successive body weights using the matrix V estimated from the data, gave lowest
Figure 7
and (
Figure 8
) + (
Figure 9
) among estimators of ADG, except for generalized least-squares with known V, where
Figure 10
and
Figure 11
are variance components of
Figure 12
due to sire and error, estimated by Henderson's Method 1. The usual estimator was better than ordinary least-squares, which assumes homogeneous variance and covariance among body weights. The EGLS was preferred to the usual estimator of ADG because EGLS gave more precise estimates of ADG and also provided estimates of ADG that yielded more precise estimate of variance components.

Footnotes

1 Dept. of Dairy Sci. Contribution of Project No. 35-306 of the illinois Agr. Exp. Sta. as a part of the research of NC-2 entitled "Improving Dairy Cattle Through Breeding, with Special Emphasis on Selection." Supported in part by a grant from the Univ. of Illinois Research Board. The authors thank Drs. H. W. Norton and D. Gianola for suggestions, and Dr. H. W. Norton and D. Gianola for suggestions, and Dr. M. E. Bock for help in proving the matrix equality in equation (11), WHICH IS Available upon request from authors. Address reprint requests to M. Grossman.

2 Present address: Faculty of Agriculture, Chiangmai Univ., Chiangmai, Thailand.

3 Dept. of Anim. Sci






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