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Enhancing the prediction accuracy of bovine lameness models through transformations of limb movement variables

J. Liu^*, N. K. Neerchal, U. Tasch^*,1, R. M. Dyer and P. G. Rajkondawar

^* Department of Mechanical Engineering, and
Department of Mathematics and Statistics, University of Maryland, Baltimore County, Baltimore 21250
Department of Animal and Food Sciences, University of Delaware, Newark 19717
Bou-Matic LLC, Madison, WI 53708

¹ Corresponding author: tasch{at}umbc.edu

The issue of modeling bovine lameness was explored by testing the hypothesis that B-spline transformation of limb movement variables (LMV) employed in predictive models improved model accuracy. The objectives were to determine the effect of number of B-spline knots and the degree of the underlying polynomial approximation (degree of freedom) on model accuracy. Knot number used in B-spline transformation improved model accuracy by improving model specificity and to a lesser extent model sensitivity. Degree of polynomial approximation had no effect on model predictive accuracy from the data set of 261 cows. Model stability, defined as changes in predictive accuracy associated with the superimposition of perturbations (0.5 and 1.0%) in LMV on the measured data, was explored. Model specificity and to a lesser degree, sensitivity, increased with increased knot number across data set perturbations. Specificity and sensitivity increased by 43 and 11%, respectively, when knot number increased from 0 to 7 for a perturbation level of 0.5%. When the perturbation level was 1%, the corresponding increases in specificity and sensitivity were 32 and 4%, respectively. Nevertheless, different levels of LMV perturbation varied the optimal knot number associated with highest model accuracy. The optimal knot number for 0.5% perturbation was 8, whereas for 1% perturbation the optimal knot number was 7. The B-spline transformation improved specificity and sensitivity of predictive models for lameness, provided the appropriate number of knots was selected.

Key Words: dairy cattle • lameness • limb movement variable • spline transformation