In this (modest) study, we developed artificial neural network (ANN) models for predicting body weight using various independent (input) variables in eight-week old New Zealand white purebred and crossbred rabbits. From the whole data sets of similar age groups, 75 percent were used to train the neural network model and 25 percent were used to test the effectiveness of the model. Five predictor variables were used viz, breed, sex, heart girth, body length and height at wither as input variables and body weight was considered as dependent variable from the model. The ANN used was multilayer feed forward network with back propagation of error for efficient learning. Our ANN models (with <i>R</i><sup>2</sup> = 0.68 at ten thousand iterations, and <i>R</i><sup>2</sup> = 0.71 one million iterations) performed better than traditional multivariate linear regression (MLR) models (<i>R</i><sup>2</sup> = 0.66) indicating that the ANN models were able to more accurately capture how the variations in input variables explained the variations in body weight. It is concluded that ANN models are more powerful than MLR models in predicting animals’ body weight. Nonetheless, we recognize that fitting an ANN model requires more computation resources than fitting a tradition MLR model but the benefits of its accuracy outweigh any demerit from the associated computation overhead.
Traditional statistical prediction and classification methods (such as linear regression, logistic regression, principal component analysis, discriminant analysis, k-nearest neighbor classification, etc.) have a number of limitations (such as the assumptions upon which they are based [
We used 144 F1 eight-week-old rabbits (74 New Zealand White purebred and 70 New Zealand White × California rabbits, crossbred in rabbit unit of National Animal Production Research Institute (NAPRI), Shika, Kaduna State, Nigeria) in this study. The animals were intensively managed under air conditioned building to minimize heat stress. They were fed a pelletized diet in the mornings and green grasses such as guinea grass (Panicum maximum) were given in the evenings.
Body weight was taken by digital weighing scale (Mettler Toledo, Top Pan Sensitive Balance, J. Liang Int. Ltd. UK). The measurements were taken while the animals were held in a standing position. Three biometric traits were determined using a tape measure on each animal. The anatomical reference points were in accordance with standard zoometrical procedures [
Body length (BL): Diagonal distance from the points of shoulder to points of hip or first thoracic vertebrae to base of tail or to hip bone. This is also described as the distance between the most cranial palpable spinosus process of the thoracic vertebrae and either sciatic tubers or distance between the tops of the pelvic bone.
Heart girth (HG): This refers to the body circumference and was measured just behind the fore-legs.
Height at withers (HW): This was taken using a graduated measuring stick.
All biometric traits were measured in centimetres.
We implemented a three-layer ANN with backpropagation in Python programming language (
The entire dataset was randomly divided into two subset viz, the training set (consisting of 75 percent of the entire dataset) and testing subset (comprising of 25 percent of the entire dataset). The network was tested in 1 and 2 hidden layers with 3 to 25 neurons in each hidden layer. Initial weights and bias matrix were randomly initialized between −1 to 1. A nonlinear transformation (or activation) function tangent sigmoid (Equation (1)) were used to compute the output from summation of weighted inputs of neurons in each hidden layer. A pure linear transformation functions were used as output layer for getting network response.
where, x is weighted sum of inputs and α = constant
Neural network showing input nodes (breed, sex, HG, BL, and HW) at the input layer, hidden nodes at the hidden layer, and output node (body weight) at the output layer
To have a fine training of the artificial neural network model, we set the learning rate to as low as 0.005 and the momentum factor to as low as 0.001. We first ran 10 thousand iterations of training, using the obtained model (i.e. the neural network weights) for predicting the body weights, and saved the results. For the sake of comparison, we fitted a multivariate linear regression (MLR) model (and made sure the model passed various model diagnoses such as normal distribution of regression residuals shown in
Qexp = Observed value.
Qcal = Predicted value.
N = Number of observation.
We show the summary statistics of the observed weights and the predicted weights at ten thousand, and at one million training iterations of the ANN in
Notably, our implemented artificial neural network (ANN) and the results are encouraging as it outperforms multivariate linear regression (MLR). The coefficient of determination (R2) from each of our ANN models’ results (0.679 for ten thousand iterations,
ANN satisfactorily (R2= 0.679) predicted the observed weight after ten thousand training iterations
This figure shows how well the ANN predicted the observed weight after one million training iterations. Note that the R2(0.71) shows an improvement over ten thousand training iterations (shown in Figure 2)
Relationship between the predictions from one million training iterations and the predictions from ten thousand training iterations. The high R2(0.939) suggests that ANN’s results are highly consistent and should be reliable
. Summary statistics of the observed weights and the predicted weights at ten thousand, and at one million training iterations of the ANN
Minimum | Maximum | Mean | Std. Deviation | |
---|---|---|---|---|
Observed Body Weight | 470 | 1860 | 1313.25 | 285.628 |
Predicted Body Weight From ten thousand Iterations of ANN | 379.097218 | 1613.263 | 1274.32910 | 240.5847255 |
Predicted Body Weight From million Iterations of ANN | 426.691676 | 1658.181 | 1282.11313 | 254.5992157 |
. Comparison of ANN (at ten thousand, and at one million training iterations) and MLR of the observed weights and predicted weights
MLR | ANN after 10,000 training iterations | ANN after 1,000,000 training iterations | |
---|---|---|---|
Coefficient of determination (R2) | 0.659 | 0.679 | 0.710 |
Pearson correlation between observed and predicted weights | 0.812*** | 0.824*** | 0.843*** |
Prediction sum of squares | 5536677.167 | 5833084.503 | 6309725.164 |
***p < 0.001.
. Pearson correlation between the predicted weights at ten thousand, and the predicted weights at one million training iterations of the ANN
Predicted body weight from one million iterations of ANN | ||
---|---|---|
Predicted body weight from ten thousand iterations of ANN | Pearson correlation | 0.969*** |
Sum of squares and cross-products | 6114879.253 | |
Covariance | 59367.760 |
***p < 0.001.
Overall, our artificial neural network (even with just ten thousand iterations) considerably outperforms a multivariate linear regression model (