Purdue Pork Page Archive
Potential Means to Reduce Biases in Estimating Carcass Value
E.P. Berg, A.P. Schinckel, J.C. Forrest, J.R. Wagner, and W. Chen
Department of Animal Sciences
Introduction
Each genetic line of swine possesses different carcass characteristics. Different lines will produce pork carcasses which differ in conformation, lean and fat distribution, and overall percentage of lean. The sex of the pig also influences pork carcass characteristics. Value based carcass procurement systems are most often incapable of accurately predicting carcass diversity as influenced by such traits as genotype and sex. Thus, it can be stated that the means for establishing carcass value may be biased in their predictive capacity, especially when single site measurements (such as last rib backfat thickness) are used for predicting carcass composition. If the biases associated with the prediction equations are systematic, equations overestimate the value of fat carcasses and underestimate the value of lean carcasses. It is therefore conceivable that the prediction biases could be reduced by including an independent variable associated with the source of the bias. Inclusion of the average backfat of the line may reduce the prediction errors associated with the value of that particular line of pigs, identifying its value more precisely from the entire population slaughtered that day.
Objective
The objective of this study was to improve estimation of carcass value by identifying independent variables which reduce genotype and sex biases.
Materials and Methods
One hundred fifty-four market hogs were used from data of the 1991 Purdue Cooperative Lean Growth Trial. Equal numbers of barrows and gilts, from seven genetic lines, were raised in the same facilities to target weights of 100, 113, and 127 kg. Carcass value was calculated as a component model where the value of the loin ($4.60/kg), ham ($2.74/kg), all other lean ($1.26/kg), fat ($.53/kg), and a constant byproduct value ($11.89) were added together for a carcass value/100kg. Component prices were based upon 1992 Yellow sheet quotations. Carcasses were probed for fat and loin depth between the 3rd and the 4th from last rib interface with a Hennessey Optical grading probe (HGP). Midline backfat thickness was measured adjacent to the last rib on the split surface of the carcass. Ham total electrical conductivity (phase index) was measured in a primal cut electromagnetic scanner (Meat Quality Inc). Mean fat thickness and mean ham lean phase index for each genotype/sex class were calculated and adjusted for hot carcass weight (HCWT) and used in regression equations for predicting carcass value. Independent variables for predicting $/100kg are as follows:
Statistical analyses were conducted on each of the six regression equations for their ability to reduce inherent bias associated with genetic line and sex. Definitions of the various statistics listed in Tables 1 and 2 are given in Appendix A.
Results and Discussion
Table 1 shows the base equation 1 to possess a low R2 and relatively high root mean square error (RMSE). This suggests that buying systems using simply hot carcass weight and a last rib backfat measurement are accounting for a mere 42% of the variability of carcass value on an individual pig basis and can be off as much as $8.31/100kg. Also, the variability due to genetic line, sex, and the interaction of line and sex are all relatively high. The low p-values associated with line, sex and line*sex imply that the sum of squares (SS) can be further reduced, which would further reduce the bias associated with predicting carcass value.
Table 2 shows that equation 1 is able to correctly rank the value of carcasses based on differences in genetic line and sex with a correlation of r = .815 (nearer 1.0 is best). The low standard deviation (Std Dev) implies that equation 1 is not accounting for the variation (or spread) between the genotype and sex groups. The low variance ratio (VR%) implies this equation is only accounting for 33.1% of the variability in carcass value based on backfat. The regression coefficient greater than 1 (bA*P = 1.416) implies that the actual carcass values are much more spread apart than the values predicted by equation 1.
The addition of XLRFAT in equation 2 and XHAM in equation 3 show an increase in R^{2} and a reduction in RMSE, while at the same time reducing the sum of squares associated with line, sex and line*sex. Further proof that equations 2 and 3 reduce the bias associated with genotype and sex is shown in Table 2. The correlation between actual and predicted mean carcass value (r) shows improvement at the same time the Std Dev is increased and the VR% increased to 93%.
Equations 4, 5, and 6 incorporate independent variables obtained from electronic devices commonly used for the prediction of carcass value. Again, incorporation of mean adjusted variables show a reduction of the prediction bias.
Conclusion
It is conceivable that a progressive packer could incorporate mean adjusted variables into the carcass procurement scheme. The common use of the optical grading probe necessitates identification of carcasses to establish payment. Hogs from particular production systems are quite often marketed from common genotype, gender, and management systems. The methodology for assessing carcass value could quite easily incorporate averages of these specific production groups under today's computerized systems. This theory would require additional testing, encompassing several genetic lines. However, it appears possible for the purveyors of pork carcasses to more accurately and efficiently assess true carcass value.
Table 1. Regression^{b} analysis of equations predicting carcass value($)/100kg from direct carcass measurements and electronic grading instruments.
Equation^{a} |
R2 |
RMSE |
C.V. |
SS |
P |
SS |
P |
SS |
P |
Residual SS |
---|---|---|---|---|---|---|---|---|---|---|
Direct Carcass Measurement and Mean Adjusted Ham Phase Index |
||||||||||
1. |
.412 |
8.31 |
4.89 |
1481 |
<.001 |
729 |
<.001 |
302 |
<.50 |
2618 |
2. |
.480 |
7.84 |
4.61 |
1131 |
.003 |
204 |
.05 |
328 |
.41 |
1750 |
3. |
.517 |
7.56 |
4.45 |
803 |
.03 |
88 |
.20 |
180 |
.76 |
1096 |
Electronic Grading Instruments |
||||||||||
4. |
.727 |
5.65 |
3.32 |
276 |
.19 |
28 |
.34 |
146 |
.58 |
450 |
5. |
.733 |
5.61 |
3.29 |
220 |
.31 |
2.32 |
.78 |
171 |
.47 |
398 |
6. |
.733 |
5.61 |
3.29 |
234 |
.27 |
6.6 |
.62 |
156 |
.53 |
401 |
^{a}Independent variables for predicting $/100kg:
^{b}Regression statistics are defined in Appendix A
Table 2. Statistical analysis^{b} displaying a reduction in prediction equation bias created by genotype and sex variability within the sample population.
Equation^{a} |
r |
Std Dev^{c} |
V.R.% |
bA*P |
---|---|---|---|---|
Direct Carcass Measurement and Mean Adjusted Ham Phase Index | ||||
1. |
.815 |
3.91 |
33.1 |
1.416 |
2. |
.850 |
6.20 |
83.5 |
.924 |
3. |
.900 |
6.54 |
93.0 |
.934 |
Electronic Grading Instruments |
||||
4. |
.968 |
5.96 |
77.3 |
1.101 |
5. |
.968 |
6.54 |
93.1 |
1.003 |
6. |
.968 |
6.49 |
95.7 |
1.011 |
^{a}Independent variables for predicting $/100kg are reported in Table 1.
^{b}Regression statistics are defined in Appendix A.
^{c}Actual sample standard deviation = 6.78.
Appendix A
Definitions of statistical terms:
R^{2} |
Coefficient of determination. The percentage of variability attributed to carcass value/100kg that is explained by the predictor variables. |
---|---|
RMSE |
Root mean square error (residual standard deviation). The standard deviation of residuals (actual value/100kg - predicted value/100kg) from the regression line. |
C.V. |
Coefficient of variation. Standard deviation / sample mean. |
p |
Probability. Level of significance of adding the effect of genetic line or sex to the equation. The remaining sum of squares after additional predictor variables are added to the equation can be further reduced if the level "p" remains significant. |
Residual SS (Line*Sex) |
Total remaining sum of squares caused by all line and sex effects. |
r |
Coefficient of correlation. A measure of the strength of the linear relationship between actual mean carcass value/100kg and the predicted mean carcass value/100kg. An r equal to 1.0 would show a one to one linear relationship for each subpopulation. |
Std Dev |
Sample variance. The square root of the summation of the individual carcass values/100kg minus the mean carcass value/100kg. |
V.R.% |
Variance ratio (Std Devpredicted/Std Devactual)2. The proportion of variance among genetic line and sex accounted for by the prediction equation. A variance ratio closer to 100% accounts for more of the variability within the sample population that is attributed to prediction bias associated with line and sex. |
bA*P |
Regression of actual carcass values/100kg on predicted values. Nearer to 1 is better. |
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