Comparison of connectionist and multiple regression approaches for prediction of body weight of goats

Abstract

The Attappady Black goat is a native goat breed of Kerala in India and is mainly known for its valuable meat and skin. In this work, a comparative study of connectionist network [also known as artificial neural network (ANN)] and multiple regression is made to predict the body weight from body measurements in Attappady Black goats. A multilayer feed forward network with backpropagation of error learning mechanism was used to predict the body weight. Data collected from 824 Attappady Black goats in the age group of 0–12 months consisting of 370 males and 454 females were used for the study. The whole data set was partitioned into two data sets, namely training data set comprising of 75 per cent data (277 and 340 records in males and females, respectively) to build the neural network model and test data set comprising of 25 per cent (93 and 114 records in males and females, respectively) to test the model. Three different morphometric measurements viz. chest girth, body length and height at withers were used as input variables, and body weight was considered as output variable. Multiple regression analysis (MRA) was also done using the same training and testing data sets. The prediction efficiency of both models was compared using the R ² value and root mean square error (RMSE). The correlation coefficients between the actual and predicted body weights in case of ANN were found to be positive and highly significant and ranged from 90.27 to 93.69%. The low value of RMSE and high value of R ² in case of connectionist network (RMSE: male—1.9005, female—1.8434; R ²: male—87.34, female—85.70) in comparison with MRA model (RMSE: male—2.0798, female—2.0836; R ²: male—84.84, female—81.74) show that connectionist network model is a better tool to predict body weight in goats than MRA.

Appendix

1.1 Root mean square error

$$ {\text{RMSE}} = \sqrt {\frac{1}{N}\left[ {\sum\limits_{1}^{N} {\left( {Q_{\exp } - Q_{\text{cal}} } \right)}^{2} } \right]} $$

where O _exp = observed value, Q _cal = predicted value, N = number of observations.

1.2 The SD ratio is the quotient of two standard deviations: errors and data

$$ {\text{SD}}\;{\text{ratio}} = \sqrt {\frac{{\sum {(E_{i} - \bar{E} )^{2} } }}{{\sum {(Y_{i} - \bar{Y} )^{2} } }}} $$

where E _i is the individual error of a data set, E is the mean error of data set, $\bar{Y}_{i}$ are actual values, and Y is the mean actual value.

1.3 R ² coefficient of determination

$$ R^{2} \,{\text{value}} = \frac{{{\text{Total}}\;{\text{sum}}\;{\text{of}}\;{\text{squares}} - {\text{Error}}\;{\text{sum}}\;{\text{of}}\;{\text{squares}}}}{{{\text{Total}}\;{\text{sum}}\;{\text{of}}\;{\text{squares}}}} \times 100 $$