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Comparison of the 3-phase segmented linear regression and artificial neural network models to predict broiler hatchability
©2011 Poultry Science Association, Inc.
Comparison of the 3-phase segmented linear regression and artificial neural network models to predict broiler hatchability M. Chamsaz,* A. H. Perai,† S. Asadpour,*1 and R. Hosseini Shahidi‡2
Primary Audience: Breeder Farms, Hatchery Managers, Researchers SUMMARY The objective of this study was to compare the performance of an artificial neural network (ANN) model and a 3-phase segmented linear regression model to describe the relationship between flock age and hatchability in broiler breeder flocks. The predictive quality of these models was tested for an external validation set of 14 wk, randomly chosen from 39 wk. The accuracy of the models was determined by the r2 value, mean square error, bias, and Theil’s Ustatistic parameters. The r2 values of the 3-phase segmented linear regression and ANN models were 0.4003 and 0.9984, respectively. Therefore, the ANN produced more accurate predictions of hatchability than the 3-phase segmented linear regression model. We conclude, based on the results of this study in commercial broiler breeder flocks, that hatchability is a function of flock age and that the relationship can be described by an ANN model. Key words: age, artificial neural network, broiler breeder, hatchability, 3-phase segmented linear regression model 2011 J. Appl. Poult. Res. 20:447–453 doi:10.3382/japr.2010-00249
DESCRIPTION OF PROBLEM The production of first-quality chicks depends on the breeding and hatching performance of the parent flocks. An increase of 1 unit in the hatchability of total eggs, which is considered a primary criterion of productivity on broiler breeder farms, would significantly increase cost effectiveness. Numerous factors affect egg
1 2
hatchability, including 1) breeding; 2) management decisions in the preincubation and incubation periods, such as the nutritional feeding program, cockerel-to-hen ratio, length of fertile egg storage, and provision of appropriate conditions during the incubation period; and 3) the physiological condition of the male and female broiler breeders in relation to their age (egg production, egg weight). Mauldin [1] analyzed the records
Corresponding author: [email protected] Present address: Faculty of Veterinary Medicine, Ferdowsi University of Mashhad, PO Box 9177948974, Mashhad, Iran.
Downloaded from http://japr.oxfordjournals.org/ at University of New Orleans on June 6, 2015
*Department of Chemistry, Faculty of Sciences, Ferdowsi University of Mashhad, PO Box 91735-654, Mashhad, Iran; †Excellence Center for Animal Science Research and Department of Animal Science, Faculty of Agriculture, Ferdowsi University of Mashhad, PO Box 91775-1163, Mashhad, Iran; and ‡Department of Veterinary Medicine, Islamic Azad University–Garmsar Branch, PO Box 144/35815, Garmsar, Iran
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MATERIALS AND METHODS Data Set The data set used to describe the relationship between hatchability and age was composed of weekly hatchability records for 3 Ross broiler breeder flocks from 1 commercial hatchery [7]. Hatchability was defined as the ratio of the total number of hatched eggs to the total number of incubated fertile eggs, expressed as a percentage. The sex ratio for all flocks was the same. All the flock records were from the same integrated operation, which applied standard procedures in housing, photoschedules, prophylactic measures, spiking, hatching egg collection and storage, and dietetic and incubation practices.
The original data were partitioned randomly into 2 subsets for modeling purposes. The first subset was the training set (n = 25), which was used for developing the 3-phase segmented linear regression and ANN models. The second subset was the validation set (n = 14), which was not used during the training and was used to validate the performance of the models. Development of the ANN Model The ANN used in this study was a multilayer feed-forward network that consisted of 3 layers: an input layer, a hidden layer, and an output layer. The network was trained using an error back-propagation training algorithm. When a multilayer ANN with a back-propagation training algorithm was used, the signals were transferred from the input neurons through the hidden layer to the output neurons. The difference between the predicted output and the observed data was calculated. The error was propagated backward through the hidden layer to the input layer to iteratively adjust weights and was biased to minimize the error in prediction. To avoid overtraining and consequent deterioration of the generalization ability of the ANN, the predictive performance of the ANN after each weight adjustment was checked on the validation data. The number of neurons in the hidden layer was determined by a trial-and-error process, always seeking networks with few hidden neurons and a good generalization capacity. The input, hidden, and output layers consisted of 1, 9, and 1 neurons, respectively. The neural network toolbox of MATLAB [8] was used to construct the ANN model. Development of the 3-Phase Segmented Linear Regression Model The 3-phase segmented linear regression model contained 2 change points. More specifically, the program estimated 3 regression equations that held for different ranges of the independent variable and estimated the change points for each subject separately. The relationship between the dependent variable (hatchability) and its independent variable (age) is described by 3 regression equations, which hold for different ranges of the independent variable. The 3-phase segmented linear regression model can be described as follows:
Downloaded from http://japr.oxfordjournals.org/ at University of New Orleans on June 6, 2015
of different integrated broiler breeder farms and observed that even on different commercial farms with variations in management decisions and dietetic practices, hatchability was essentially a function of age. Mauldin suggested a curvilinear model to describe the relationship between broiler breeder age and hatchability. The model developed assumed a steep increase to the peak of hatchability, followed by a constant decrease during the latter part of the production cycle. Analyzing the hatchability records of 51 broiler breeder flocks from 4 strains, Creel et al. [2] suggested that under commercial conditions and hatchery practices, hatchability was essentially a function of age [2]. They approached the relationship between age and hatchability by using a 3-phase segmented linear regression model with 7 parameters and concluded that this model had better predictive ability than the model by Mauldin [1] for hatchability and the management of broiler breeder flocks. Artificial neural networks (ANN) are inspired by the neurological structures and processing functions of the human brain. As described in the poultry science literature, ANN models are applicable in diagnosing ascites [3], modeling broiler growth [4], predicting amino acid levels [5], and determining the TMEn value [6] of feedstuffs. In this study, we evaluated the application of the 3-phase segmented linear regression and ANN models to describe the relationship between age and hatchability in broiler breeder flocks and then compared the predictive ability of these models.
Chamsaz et al.: MODELING OF HATCHABILITY
y = a1 + b1x + e, for x ≤ s1,
[1]
y = a2 + b2x + e, for s1 < x ≤ s2, and [2] y = a3 + b3x + e, for x > s2,
[3]
where x is the independent and y is the dependent variable. The parameters ai (i = 1 to 3) and bi (i = 1 to 3) denote, respectively, the intercept
449
and the slope of the regression lines, and e is the error term. The parameters s1 and s2 are called the change points or break points. Equation 1 was fitted to all data points equal to or smaller than the first change point, s1; equation 2 was fitted to all data points larger than s1 but equal to or smaller than s2; and equation 3 was fitted to all data points larger than s2. The program fit the model under the assumption that the 2 change
Three-phase segmented linear regression Week Training set 26 27 28 31 34 35 38 39 40 42 44 45 46 48 49 50 52 53 55 56 58 59 62 63 64 Validation set 29 30 32 33 36 37 41 43 47 51 54 57 60 61
Artificial neural network
Observed
Predicted
Residuals
Relative error, %
Predicted
Residuals
Relative error, %
52.6 67.55 77.63 85.73 85.9 86.4 86.23 85.8 84.9 83.83 82.7 81.9 80.6 78 77.07 75.73 73.67 73.93 72.1 71.00 71.23 69.53 66.3 64.27 63.3
79.26 80.20 81.14 83.95 86.76 87.47 89.62 90.33 89.40 87.53 85.66 84.73 83.80 81.93 81.00 80.06 78.20 77.26 75.40 77.47 72.60 71.67 68.87 67.93 67.00
−26.66 −12.65 −3.51 1.78 −0.86 −1.07 −3.39 −4.53 −4.50 −3.70 −2.96 −2.83 −3.20 −3.93 −3.93 −4.33 −4.53 −3.33 −3.30 −3.47 −1.37 −2.14 −2.57 −3.66 −3.70
50.69 18.73 4.52 −2.08 1.00 1.24 3.93 5.28 5.30 4.41 3.58 3.46 3.97 5.04 5.10 5.72 6.15 4.51 4.57 4.88 1.92 3.07 3.87 5.70 5.84
52.71 67.1 78.31 85.35 85.96 86.41 86.34 85.58 84.87 84.05 82.37 81.83 81.03 77.79 76.9 76.03 73.94 73.56 72.14 71.11 70.47 70.26 66.05 64.56 63.19
−0.11 0.45 −0.68 0.38 −0.06 −0.01 −0.11 0.22 0.03 −0.22 0.33 0.07 −0.43 0.21 0.17 −0.3 −0.27 0.37 −0.04 −0.11 0.76 −0.73 0.25 −0.29 −0.11
−0.002 0.007 −0.009 0.004 −0.001 0.000 −0.001 0.003 0.000 −0.003 0.004 0.001 −0.005 0.003 0.002 −0.004 −0.004 0.005 −0.001 −0.002 0.011 −0.010 0.4 −0.5 −0.18
83.73 84.8 85.5 86.17 86.27 86 84.37 83.5 79.1 74.73 72.13 71.1 68.7 67.93
82.07 83.01 84.89 85.82 88.19 88.90 88.46 86.60 82.86 79.13 76.33 73.53 70.73 69.80
1.66 1.79 0.61 0.35 −1.92 −2.90 −4.09 −3.10 −3.76 −4.40 −4.20 −2.43 −2.03 −1.87
−1.98 −2.11 −0.72 −0.40 2.22 3.37 4.85 3.71 4.76 5.89 5.83 3.42 2.96 2.75
83.25 84.87 85.51 85.65 86.67 86.66 84.49 83.21 79.41 74.79 73.11 70.64 69.64 68.1
0.48 −0.07 −0.01 0.52 −0.4 −0.66 −0.12 0.29 −0.31 −0.06 −0.98 0.46 −0.94 −0.17
0.6 −0.1 −0.1 0.6 −0.5 −0.8 −0.1 0.3 −0.4 −0.1 −1.4 0.6 −1.4 −0.3
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Table 1. Observed and predicted values for the weekly percentage of hatchability with the 3-phase segmented linear regression and artificial neural network models
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Table 2. Statistical information on the 3-phase linear segmented regression and artificial neural network models Three-phase linear segmented regression model Statistic 2
r MSE Bias
Training
Validation
Training
Validation
0.4003 45.0221 −4.3331
0.8320 7.8293 −1.8788
0.9984 0.1162 −0.0002
0.9601 0.2424 0.1401
2
n
∑ yt − yˆt t =1
MSE =
;
n
Bias: n
Bias =
∑ yt −yˆt t =1
,
n
where yt is the observed value, yˆt is the estimated value, and n is the number of observations; and Difference coefficient (Thiel’s U): 2
r=
∑ (yˆi1 − yi ) i
∑( i
yˆi2 − yi
2
)
,
where yˆi1 is the value estimated by the first model, yi is the observed value, and yˆi2 is the value estimated by the second model. The ratio r,
known as Theil’s U or the difference coefficient, was calculated to determine the relative efficiency of the prediction model.
RESULTS AND DISCUSSION In previous studies, under commercial hatchery conditions and practices, hatchability was significantly affected only by breeder age [1, 2]. Hatchability as a function of age was described by the 3-phase segmented linear regression and ANN models. As observed previously, the strain and sex ratio for all flocks was the same. With the 3-phase segmented linear regression model, hatchability increased at 0.937%/wk to 85.9% at 34 wk of age. Thereafter, hatchability decreased gradually at 0.223%/wk until a break point was reached at 39 wk of age. At the break point, there was an abrupt increase in the rate of decline in hatchability. After the break point, the rate of decline in hatchability was 1.6472%/wk, which represented a 7× increase over the previous segment. Table 1 presents the observed and predicted hatchability values from the training and validation sets for the models. A summary of statistical results for the models is presented in Table 2. The forecasting error measurement was based on the difference between the observed and predicted values. There was a difference in these forecasting error measurements between the 3-phase segmented linear regression model and the ANN model. A more efficient prediction of hatchability was generated by the ANN model as compared with the 3-phase segmented linear regression model, based on the statistical test (in terms of r2, MSE, and bias). The r2 and MSE values of the 3-phase segmented linear regression model for the training data set were 0.4003 and 45.02, respectively. The r2 and MSE values of the ANN model for the training data set were 0.9984 and 0.1162, respectively. The ANN model improved the r2 and MSE values of
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points, s1 and s2, were unknown and thus had to be estimated. The modeling by the 3-phase segmented linear regression method was performed with SAS software [9]. The performance of the models was compared by using error-measured indices, which are commonly used to investigate forecasting models. The following parameters were computed to evaluate the performance and accuracy of the models: r2 value (correlation coefficient between the predicted and observed values), mean squared error (MSE), bias, and Theil’s U [10]. These parameters were calculated with the following equations: MSE:
Artificial neural network model
Chamsaz et al.: MODELING OF HATCHABILITY
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Downloaded from http://japr.oxfordjournals.org/ at University of New Orleans on June 6, 2015 Figure 1. a) Comparison of the observed hatchability values and the 3-phase segmented linear regression-predicted hatchability values obtained from the training and validation sets. b) Comparison of the observed hatchability values and the artificial neural network-predicted hatchability values obtained from the training and validation sets.
the 3-phase segmented linear regression model by 149 and 99.7%, respectively. As measured by bias, the ANN model produced very little underestimation of the observed hatchability
values. Plots of observed vs. predicted hatchability values for the training and validation data sets and distribution of the residual values about the zero mean (observed hatchability −
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Figure 2. a) Residuals vs. flock age (week) for both the training and validation sets in the 3-phase segmented linear regression model. b) Residuals vs. flock age (week) for both the training and validation sets in the artificial neural network model.
predicted hatchability) obtained by the 3-phase segmented linear regression and ANN models are shown in Figure 1a and b and Figure 2a and
b, respectively. The agreement between the observed and predicted values and the randomized distribution of residuals about the zero mean
Chamsaz et al.: MODELING OF HATCHABILITY
CONCLUSIONS AND APPLICATIONS
1. Under commercial hatchery conditions and practices, hatchability was significantly affected only by flock age. 2. The ANN model produced very little underestimation of the observed hatchability values and had a higher predictive capacity than the 3-phase segmented linear regression model.
REFERENCES AND NOTES 1. Mauldin, J. M. 1989. An analysis of reproductive efficiency in Georgia hatcheries. General Rep. No. 113. Department of Poultry Science, University of Georgia, Athens. 2. Creel, L. H., D. Maurice, W. C. Bridges, and L. W. Grimes. 1998. A model to describe and predict post-peak changes in broiler hatchability. J. Appl. Poult. Res. 7:85– 89. 3. Roush, W. B., R. F. Wideman Jr., A. Cahaner, N. Deeb, and T. L. Cravener. 2001. Minimal number of chicken daily growth velocities for artificial neural network detection of pulmonary hypertension syndrome (PHS). Poult. Sci. 80:254–259. 4. Roush, W. B., W. A. Dozier III, and S. L. Branton. 2006. Comparison of Gompertz and neural network models of broiler growth. Poult. Sci. 85:794–797. 5. Roush, W. B., and T. L. Cravener. 1997. Artificial neural network prediction of amino acid levels in feed ingredients. Poult. Sci. 76:721–727. 6. Perai, A. H., H. Nassiri Moghaddam, S. Asadpour, J. Bahrampour, and Gh. Mansoori. 2010. A comparison of artificial neural networks with other statistical approaches for the prediction of true metabolizable energy of meat and bone meal. Poult. Sci. 89:1562–1568. 7. Simorgh Company, Mashhad, Iran. 8. MATLAB, version 7.5, Mathworks Inc., Natick, MA. 9. Version 9.1, SAS Institute Inc., Cary, NC. 10. Bolzan, A. C., R. A. F. Machado, and J. C. Z. Piaia. 2008. Egg hatchability prediction by multiple linear regression and artificial neural networks. Braz. J. Poult. Sci. 10:97–102.
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demonstrated the higher predictive capacity of the ANN model as compared with the 3-phase segmented regression model. To determine which model obtained the best prediction, we used the r ratio, as described in the text. According to the prediction model of Perai et al. [6] with Theil’s U, values equal to or less than 0.55 were considered reliable. The r ratio for the ANN model relative to the 3-phase segmented linear regression model was 0.05. The main finding of this study was that in commercial broiler breeder flocks, hatchability was a function of age, and the relationship could be described by an ANN model.
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Comparison of the 3-phase segmented linear regression and artificial neural network models to predict broiler hatchability M. Chamsaz,* A. H. Perai,† S. Asadpour,*1 and R. Hosseini Shahidi‡2
Primary Audience: Breeder Farms, Hatchery Managers, Researchers SUMMARY The objective of this study was to compare the performance of an artificial neural network (ANN) model and a 3-phase segmented linear regression model to describe the relationship between flock age and hatchability in broiler breeder flocks. The predictive quality of these models was tested for an external validation set of 14 wk, randomly chosen from 39 wk. The accuracy of the models was determined by the r2 value, mean square error, bias, and Theil’s Ustatistic parameters. The r2 values of the 3-phase segmented linear regression and ANN models were 0.4003 and 0.9984, respectively. Therefore, the ANN produced more accurate predictions of hatchability than the 3-phase segmented linear regression model. We conclude, based on the results of this study in commercial broiler breeder flocks, that hatchability is a function of flock age and that the relationship can be described by an ANN model. Key words: age, artificial neural network, broiler breeder, hatchability, 3-phase segmented linear regression model 2011 J. Appl. Poult. Res. 20:447–453 doi:10.3382/japr.2010-00249
DESCRIPTION OF PROBLEM The production of first-quality chicks depends on the breeding and hatching performance of the parent flocks. An increase of 1 unit in the hatchability of total eggs, which is considered a primary criterion of productivity on broiler breeder farms, would significantly increase cost effectiveness. Numerous factors affect egg
1 2
hatchability, including 1) breeding; 2) management decisions in the preincubation and incubation periods, such as the nutritional feeding program, cockerel-to-hen ratio, length of fertile egg storage, and provision of appropriate conditions during the incubation period; and 3) the physiological condition of the male and female broiler breeders in relation to their age (egg production, egg weight). Mauldin [1] analyzed the records
Corresponding author: [email protected] Present address: Faculty of Veterinary Medicine, Ferdowsi University of Mashhad, PO Box 9177948974, Mashhad, Iran.
Downloaded from http://japr.oxfordjournals.org/ at University of New Orleans on June 6, 2015
*Department of Chemistry, Faculty of Sciences, Ferdowsi University of Mashhad, PO Box 91735-654, Mashhad, Iran; †Excellence Center for Animal Science Research and Department of Animal Science, Faculty of Agriculture, Ferdowsi University of Mashhad, PO Box 91775-1163, Mashhad, Iran; and ‡Department of Veterinary Medicine, Islamic Azad University–Garmsar Branch, PO Box 144/35815, Garmsar, Iran
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MATERIALS AND METHODS Data Set The data set used to describe the relationship between hatchability and age was composed of weekly hatchability records for 3 Ross broiler breeder flocks from 1 commercial hatchery [7]. Hatchability was defined as the ratio of the total number of hatched eggs to the total number of incubated fertile eggs, expressed as a percentage. The sex ratio for all flocks was the same. All the flock records were from the same integrated operation, which applied standard procedures in housing, photoschedules, prophylactic measures, spiking, hatching egg collection and storage, and dietetic and incubation practices.
The original data were partitioned randomly into 2 subsets for modeling purposes. The first subset was the training set (n = 25), which was used for developing the 3-phase segmented linear regression and ANN models. The second subset was the validation set (n = 14), which was not used during the training and was used to validate the performance of the models. Development of the ANN Model The ANN used in this study was a multilayer feed-forward network that consisted of 3 layers: an input layer, a hidden layer, and an output layer. The network was trained using an error back-propagation training algorithm. When a multilayer ANN with a back-propagation training algorithm was used, the signals were transferred from the input neurons through the hidden layer to the output neurons. The difference between the predicted output and the observed data was calculated. The error was propagated backward through the hidden layer to the input layer to iteratively adjust weights and was biased to minimize the error in prediction. To avoid overtraining and consequent deterioration of the generalization ability of the ANN, the predictive performance of the ANN after each weight adjustment was checked on the validation data. The number of neurons in the hidden layer was determined by a trial-and-error process, always seeking networks with few hidden neurons and a good generalization capacity. The input, hidden, and output layers consisted of 1, 9, and 1 neurons, respectively. The neural network toolbox of MATLAB [8] was used to construct the ANN model. Development of the 3-Phase Segmented Linear Regression Model The 3-phase segmented linear regression model contained 2 change points. More specifically, the program estimated 3 regression equations that held for different ranges of the independent variable and estimated the change points for each subject separately. The relationship between the dependent variable (hatchability) and its independent variable (age) is described by 3 regression equations, which hold for different ranges of the independent variable. The 3-phase segmented linear regression model can be described as follows:
Downloaded from http://japr.oxfordjournals.org/ at University of New Orleans on June 6, 2015
of different integrated broiler breeder farms and observed that even on different commercial farms with variations in management decisions and dietetic practices, hatchability was essentially a function of age. Mauldin suggested a curvilinear model to describe the relationship between broiler breeder age and hatchability. The model developed assumed a steep increase to the peak of hatchability, followed by a constant decrease during the latter part of the production cycle. Analyzing the hatchability records of 51 broiler breeder flocks from 4 strains, Creel et al. [2] suggested that under commercial conditions and hatchery practices, hatchability was essentially a function of age [2]. They approached the relationship between age and hatchability by using a 3-phase segmented linear regression model with 7 parameters and concluded that this model had better predictive ability than the model by Mauldin [1] for hatchability and the management of broiler breeder flocks. Artificial neural networks (ANN) are inspired by the neurological structures and processing functions of the human brain. As described in the poultry science literature, ANN models are applicable in diagnosing ascites [3], modeling broiler growth [4], predicting amino acid levels [5], and determining the TMEn value [6] of feedstuffs. In this study, we evaluated the application of the 3-phase segmented linear regression and ANN models to describe the relationship between age and hatchability in broiler breeder flocks and then compared the predictive ability of these models.
Chamsaz et al.: MODELING OF HATCHABILITY
y = a1 + b1x + e, for x ≤ s1,
[1]
y = a2 + b2x + e, for s1 < x ≤ s2, and [2] y = a3 + b3x + e, for x > s2,
[3]
where x is the independent and y is the dependent variable. The parameters ai (i = 1 to 3) and bi (i = 1 to 3) denote, respectively, the intercept
449
and the slope of the regression lines, and e is the error term. The parameters s1 and s2 are called the change points or break points. Equation 1 was fitted to all data points equal to or smaller than the first change point, s1; equation 2 was fitted to all data points larger than s1 but equal to or smaller than s2; and equation 3 was fitted to all data points larger than s2. The program fit the model under the assumption that the 2 change
Three-phase segmented linear regression Week Training set 26 27 28 31 34 35 38 39 40 42 44 45 46 48 49 50 52 53 55 56 58 59 62 63 64 Validation set 29 30 32 33 36 37 41 43 47 51 54 57 60 61
Artificial neural network
Observed
Predicted
Residuals
Relative error, %
Predicted
Residuals
Relative error, %
52.6 67.55 77.63 85.73 85.9 86.4 86.23 85.8 84.9 83.83 82.7 81.9 80.6 78 77.07 75.73 73.67 73.93 72.1 71.00 71.23 69.53 66.3 64.27 63.3
79.26 80.20 81.14 83.95 86.76 87.47 89.62 90.33 89.40 87.53 85.66 84.73 83.80 81.93 81.00 80.06 78.20 77.26 75.40 77.47 72.60 71.67 68.87 67.93 67.00
−26.66 −12.65 −3.51 1.78 −0.86 −1.07 −3.39 −4.53 −4.50 −3.70 −2.96 −2.83 −3.20 −3.93 −3.93 −4.33 −4.53 −3.33 −3.30 −3.47 −1.37 −2.14 −2.57 −3.66 −3.70
50.69 18.73 4.52 −2.08 1.00 1.24 3.93 5.28 5.30 4.41 3.58 3.46 3.97 5.04 5.10 5.72 6.15 4.51 4.57 4.88 1.92 3.07 3.87 5.70 5.84
52.71 67.1 78.31 85.35 85.96 86.41 86.34 85.58 84.87 84.05 82.37 81.83 81.03 77.79 76.9 76.03 73.94 73.56 72.14 71.11 70.47 70.26 66.05 64.56 63.19
−0.11 0.45 −0.68 0.38 −0.06 −0.01 −0.11 0.22 0.03 −0.22 0.33 0.07 −0.43 0.21 0.17 −0.3 −0.27 0.37 −0.04 −0.11 0.76 −0.73 0.25 −0.29 −0.11
−0.002 0.007 −0.009 0.004 −0.001 0.000 −0.001 0.003 0.000 −0.003 0.004 0.001 −0.005 0.003 0.002 −0.004 −0.004 0.005 −0.001 −0.002 0.011 −0.010 0.4 −0.5 −0.18
83.73 84.8 85.5 86.17 86.27 86 84.37 83.5 79.1 74.73 72.13 71.1 68.7 67.93
82.07 83.01 84.89 85.82 88.19 88.90 88.46 86.60 82.86 79.13 76.33 73.53 70.73 69.80
1.66 1.79 0.61 0.35 −1.92 −2.90 −4.09 −3.10 −3.76 −4.40 −4.20 −2.43 −2.03 −1.87
−1.98 −2.11 −0.72 −0.40 2.22 3.37 4.85 3.71 4.76 5.89 5.83 3.42 2.96 2.75
83.25 84.87 85.51 85.65 86.67 86.66 84.49 83.21 79.41 74.79 73.11 70.64 69.64 68.1
0.48 −0.07 −0.01 0.52 −0.4 −0.66 −0.12 0.29 −0.31 −0.06 −0.98 0.46 −0.94 −0.17
0.6 −0.1 −0.1 0.6 −0.5 −0.8 −0.1 0.3 −0.4 −0.1 −1.4 0.6 −1.4 −0.3
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Table 1. Observed and predicted values for the weekly percentage of hatchability with the 3-phase segmented linear regression and artificial neural network models
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Table 2. Statistical information on the 3-phase linear segmented regression and artificial neural network models Three-phase linear segmented regression model Statistic 2
r MSE Bias
Training
Validation
Training
Validation
0.4003 45.0221 −4.3331
0.8320 7.8293 −1.8788
0.9984 0.1162 −0.0002
0.9601 0.2424 0.1401
2
n
∑ yt − yˆt t =1
MSE =
;
n
Bias: n
Bias =
∑ yt −yˆt t =1
,
n
where yt is the observed value, yˆt is the estimated value, and n is the number of observations; and Difference coefficient (Thiel’s U): 2
r=
∑ (yˆi1 − yi ) i
∑( i
yˆi2 − yi
2
)
,
where yˆi1 is the value estimated by the first model, yi is the observed value, and yˆi2 is the value estimated by the second model. The ratio r,
known as Theil’s U or the difference coefficient, was calculated to determine the relative efficiency of the prediction model.
RESULTS AND DISCUSSION In previous studies, under commercial hatchery conditions and practices, hatchability was significantly affected only by breeder age [1, 2]. Hatchability as a function of age was described by the 3-phase segmented linear regression and ANN models. As observed previously, the strain and sex ratio for all flocks was the same. With the 3-phase segmented linear regression model, hatchability increased at 0.937%/wk to 85.9% at 34 wk of age. Thereafter, hatchability decreased gradually at 0.223%/wk until a break point was reached at 39 wk of age. At the break point, there was an abrupt increase in the rate of decline in hatchability. After the break point, the rate of decline in hatchability was 1.6472%/wk, which represented a 7× increase over the previous segment. Table 1 presents the observed and predicted hatchability values from the training and validation sets for the models. A summary of statistical results for the models is presented in Table 2. The forecasting error measurement was based on the difference between the observed and predicted values. There was a difference in these forecasting error measurements between the 3-phase segmented linear regression model and the ANN model. A more efficient prediction of hatchability was generated by the ANN model as compared with the 3-phase segmented linear regression model, based on the statistical test (in terms of r2, MSE, and bias). The r2 and MSE values of the 3-phase segmented linear regression model for the training data set were 0.4003 and 45.02, respectively. The r2 and MSE values of the ANN model for the training data set were 0.9984 and 0.1162, respectively. The ANN model improved the r2 and MSE values of
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points, s1 and s2, were unknown and thus had to be estimated. The modeling by the 3-phase segmented linear regression method was performed with SAS software [9]. The performance of the models was compared by using error-measured indices, which are commonly used to investigate forecasting models. The following parameters were computed to evaluate the performance and accuracy of the models: r2 value (correlation coefficient between the predicted and observed values), mean squared error (MSE), bias, and Theil’s U [10]. These parameters were calculated with the following equations: MSE:
Artificial neural network model
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Downloaded from http://japr.oxfordjournals.org/ at University of New Orleans on June 6, 2015 Figure 1. a) Comparison of the observed hatchability values and the 3-phase segmented linear regression-predicted hatchability values obtained from the training and validation sets. b) Comparison of the observed hatchability values and the artificial neural network-predicted hatchability values obtained from the training and validation sets.
the 3-phase segmented linear regression model by 149 and 99.7%, respectively. As measured by bias, the ANN model produced very little underestimation of the observed hatchability
values. Plots of observed vs. predicted hatchability values for the training and validation data sets and distribution of the residual values about the zero mean (observed hatchability −
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Figure 2. a) Residuals vs. flock age (week) for both the training and validation sets in the 3-phase segmented linear regression model. b) Residuals vs. flock age (week) for both the training and validation sets in the artificial neural network model.
predicted hatchability) obtained by the 3-phase segmented linear regression and ANN models are shown in Figure 1a and b and Figure 2a and
b, respectively. The agreement between the observed and predicted values and the randomized distribution of residuals about the zero mean
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CONCLUSIONS AND APPLICATIONS
1. Under commercial hatchery conditions and practices, hatchability was significantly affected only by flock age. 2. The ANN model produced very little underestimation of the observed hatchability values and had a higher predictive capacity than the 3-phase segmented linear regression model.
REFERENCES AND NOTES 1. Mauldin, J. M. 1989. An analysis of reproductive efficiency in Georgia hatcheries. General Rep. No. 113. Department of Poultry Science, University of Georgia, Athens. 2. Creel, L. H., D. Maurice, W. C. Bridges, and L. W. Grimes. 1998. A model to describe and predict post-peak changes in broiler hatchability. J. Appl. Poult. Res. 7:85– 89. 3. Roush, W. B., R. F. Wideman Jr., A. Cahaner, N. Deeb, and T. L. Cravener. 2001. Minimal number of chicken daily growth velocities for artificial neural network detection of pulmonary hypertension syndrome (PHS). Poult. Sci. 80:254–259. 4. Roush, W. B., W. A. Dozier III, and S. L. Branton. 2006. Comparison of Gompertz and neural network models of broiler growth. Poult. Sci. 85:794–797. 5. Roush, W. B., and T. L. Cravener. 1997. Artificial neural network prediction of amino acid levels in feed ingredients. Poult. Sci. 76:721–727. 6. Perai, A. H., H. Nassiri Moghaddam, S. Asadpour, J. Bahrampour, and Gh. Mansoori. 2010. A comparison of artificial neural networks with other statistical approaches for the prediction of true metabolizable energy of meat and bone meal. Poult. Sci. 89:1562–1568. 7. Simorgh Company, Mashhad, Iran. 8. MATLAB, version 7.5, Mathworks Inc., Natick, MA. 9. Version 9.1, SAS Institute Inc., Cary, NC. 10. Bolzan, A. C., R. A. F. Machado, and J. C. Z. Piaia. 2008. Egg hatchability prediction by multiple linear regression and artificial neural networks. Braz. J. Poult. Sci. 10:97–102.
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demonstrated the higher predictive capacity of the ANN model as compared with the 3-phase segmented regression model. To determine which model obtained the best prediction, we used the r ratio, as described in the text. According to the prediction model of Perai et al. [6] with Theil’s U, values equal to or less than 0.55 were considered reliable. The r ratio for the ANN model relative to the 3-phase segmented linear regression model was 0.05. The main finding of this study was that in commercial broiler breeder flocks, hatchability was a function of age, and the relationship could be described by an ANN model.
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