Application of Regression Tree Method for Different Data from Animal Science
Application of Regression Tree Method for Different Data from Animal Science
Yusuf Koc1, Ecevit Eyduran1* and Omer Akbulut2
1Department of Animal Science, Agricultural Faculty, Igdir University, Igdir, Turkey
2Department of Actuarial Science, Faculty of Science, Ataturk University, Erzurum, Turkey
ABSTRACT
The aim of this study was to evaluate predictive performances of CHAID, Exhaustive CHAID, and CART regression tree methods for different combinations of parent node: child node in the data set regarding animal science. To achieve the aim, 1884 Mengali lambs were provided for predicting weaning weight from sex (male and female), birth type (single and twin), birth year (2005, 2006, 2007, 2008 and 2009), farm (Research station, Mastung, Quetta, and Noshki), birth weight, dam age, and dam weight. To choice the best regression tree method, goodness of fit criteria such as coefficient of determination (R2%), adjusted coefficient of determination (AdjR2%), coefficient of variation (%), SD ratio, relative approximation error (RAE), Root Mean Square Error (RMSE), Pearson correlation between actual and predicted weaning weights were estimated for each combination. It was determined that CHAID algorithm constructed more suitable tree structures, biologically in comparison to Exhaustive CHAID and CART data mining algorithms. Consequently, it is recommended that the biological suitability of the constructed tree structure should be taken account together with estimating model quality criteria.
Article Information
Received 27 July 2016
Revised 10 August 2016
Accepted 09 September 2016
Available online 25 March 2017
Authors’ Contributions
The article is summarized from the first author’s (YK) MSc Thesis. EE and OA interpreted the data, drafted and carefully revised the manuscript. All authors read and approved the final manuscript.
Key words
CART, CHAID, Exhaustive CHAID, Regression tree, Data Mining, Weaning weight
DOI: http://dx.doi.org/10.17582/journal.pjz/2017.49.2.599.607
* Corresponding author: ecevit.eyduran@gmail.com
00309923/2017/00020599 $ 9.00/0
Copyright 2017 Zoological Society of Pakistan
INTRODUCTION
In animal breeding, it is very prominent to survey the interrelationship between body morphological characteristics and yield characteristics viz. meat, milk and egg. On the other hand, it is essential to ascertain the effect of nongenetic factors affecting the examined yield characteristics, and in the scope of indirect selection, it is notable to exhibit causal relationship between economic yield characteristics and their related quantitative characteristics. Several examples for the causal relationship are the prediction of body weight from body and testicular characteristics, and the prediction of milk yield from udder traits, and the prediction of the spermatological traits from testicular traits, and so on. The main objective in the relational mechanism is to gain better offspring from parent generation in yield traits.
In animal science, the causal relationships can be revealed by several statistical approaches, simple linear regression analysis, multiple linear regression analysis, use of factor analysis scores in multiple regression analysis, use of principal component analysis scores in multiple regression analysis, Path Analysis and Regression Tree Analysis (Khan et al., 2014). However, general linear models have been widely used in the identification of significant factors on yield traits (Eyduran et al., 2008).
Regression tree analysis, one of the analysis methods for evaluating animal data, is thought as an alternative to the above mentioned methods (Eyduran et al., 2008) and it is a nonparametric analysis method partitioning the population into relationships among independent variables playing major role for homogenous subsets and identifying curve linear and interaction in the explanation of the variability in yield trait, a dependent variable (Kayri and Boysan, 2008). The preferability of the decision tree method is due to having more advantageous in multicollinearity, outliers and missing data without needing any assumption on the distribution of independent variables (Mendeş and Akkartal, 2009).
In the construction of the decision or regression tree diagram, CART, CHAID and Exhaustive CHAID algorithms are nonparametric techniques applied for performing the statistical analysis of nominal, ordinal and scale (continuous) variables (Ali et al., 2015). When the dependent variable is scale, the constructed tree is called regression tree, otherwise classification tree (Camdeviren et al., 2005). Regression tree analysis based on the algorithms is employable instead of multiple linear regression, ridge regression, use of factor analysis scores or principal component analysis scores in multiple linear regression analysis. The classification tree analysis on the basis of the algorithms is a good alternative to logistic regression analysis and discriminant analysis.
Regression tree analysis on the basis of some data mining algorithms, C4.5, CART, CHAID, and Exhaustive CHAID is a nonparametric method used mostly in medicinal, engineering and industrial fields. However, although its applications in animal science are increasing with each passing time (Dogan, 2003; Grzesiak et al., 2003; Eyduran et al., 2008; Mendes and Akkartal, 2009; Bakir et al., 2009, 2010; Topal et al., 2010; Yakubu, 2012; Grzesiak and Zaborski, 2012; Çak et al., 2013; Eyduran et al., 2013a, b, c; Yilmaz et al., 2013; Orhan et al., 2016), a satisfying stress on using goodness of fit criteria was rare in measuring predictive performance of the algorithms. Besides, there is very limited number of the studies on comparatively testing the data mining algorithms; playing a key role in future selection studies (Ali et al., 2015). But, the effect of various parent and child nodes on the predictive performance of the data mining algorithms has not been investigated, so far by taking a basis for goodness of fit criteria. With these reasons, the aim of this study was to evaluate predictive performances of CHAID, Exhaustive CHAID, and CART regression tree methods for different combinations of parent node: child node in the data set regarding animal science.
MATERIALS AND METHODS
Animal material
With the intention of comparatively surveying in CHAID, Exhaustive CHAID and CART data mining algorithms, the data on 1884 indigenous Mengali sheep (936 males and 948 females) reared at four different farms in Pakistan were used. The input (independent) variables in the data were sex (male and female), birth type (single and twin), lambing year (2005, 2006, 2007, 2008 and 2009), farm (Research Station, Mastung, Quetta and Noshki), dam age (20 to 78 months) and dam weight (25 to 48 kg), respectively in the prediction of weaning weight, a dependent (output) variable. In order to determine the effect of applying different number of animals in parent child nodes on the prediction performance, twenty six combinations from 500:250 to 10:5 were measured in the predictive ability of the algorithms, CART, CHAID and Exhaustive CHAID.
Method
The structure of independent variables can be nominal, ordinal and scale in regression tree method (Mendes and Akkartal, 2009). As in the present study, regression tree method with the specification of the CHAID, Exhaustive CHAID and CART data mining algorithms are the convenient method that informs about the relationship between each of quantitative traits (such as body weight, milk yield and fleece weight) and nominal, ordinal and scale variables more than one. The trees constructed for dependent variable taking limited values is called classification trees, otherwise the trees obtained by the outcome variable taking unlimited values are called regression trees.
Recursively, CART (Classification and Regression Tree) creates a binary regression tree dividing a subset into 2 small subsets by the time homogenous subsets are attained in the tree, but CHAID algorithms create a regression tree that establishes recursively multisplits until reaching up to maximum variance among subsets in the tree structure (Ali et al., 2015; Akin et al., 2016). Risk estimate is expressed as the variance within subsets in the regression tree construction.
Regression tree depths were adopted for the valued algorithms, CART (5) and CHAIDs (3). Examine the paper of Ali et al. (2015) for reaching more information concerning the algorithms.
Formulas of the goodness of fit (GOF) criteria measured for comparing predictive performance of the algorithms are below (Grzesiak and Zaborski, 2012):
Coefficient of Determination
Adjusted Coefficient of Determination
Standard Deviation Ratio
Relative Approximation Error (RAE)
Root Mean Square Error
Coefficient of Variation (%)
Where,
Yi, the actual or observed weaning weight (kg) of ith lamb; Ŷi, the predicted weaning weight value of ith lamb; Ȳ, average of the actual weaning weight values of the Mengali lambs; Ɛi, the residual value of ith lamb; Ɛi average of the residual values; k, number of significant independent variables in the model; and n, total lamb number. The residual value of each lamb is expressed as Ɛi= Yi  Ŷi.
The Pearson correlation coefficients between the observed and predicted weaning weight values were estimated by using each of the algorithms. The most predictive algorithm estimates the highest values in r, R2, R2Adj and the lowest values in CV(%), SDRATIO, RAE, and RMSE, respectively (Ali et al., 2015). The regression trees were constructed by using IBM SPSS 23 software SPSS Inc., 2015. We followed the command order,
Table I. Goodness of fit criteria for CHAID algorithm.
Parent node  Child node  RE 
R2 (%) 
RAE  RMSE  SDratio  r 
R2adj. (%) 
CV (%) 
500  250  0.992  50.176  0.249  0.996  0.706  0.708  50.128  6.222 
480  240  0.992  50.176  0.249  0.996  0.706  0.708  50.128  6.222 
460  230  0.992  50.176  0.249  0.996  0.706  0.708  50.128  6.222 
440  220  0.992  50.176  0.249  0.996  0.706  0.708  50.128  6.222 
420  210  0.992  50.176  0.249  0.996  0.706  0.708  50.128  6.222 
400  200  0.992  50.176  0.249  0.996  0.706  0.708  50.128  6.222 
380  190  0.992  50.176  0.249  0.996  0.706  0.708  50.128  6.222 
360  180  0.951  52.235  0.249  0.996  0.706  0.708  50.102  6.222 
340  170  0.976  52.979  0.244  0.975  0.691  0.723  52.184  6.092 
320  160  0.966  51.482  0.246  0.983  0.697  0.717  51.429  6.140 
300  150  0.955  52.034  0.244  0.977  0.693  0.721  51.981  6.105 
280  140  0.955  52.034  0.244  0.977  0.693  0.721  51.955  6.105 
260  130  0.953  52.135  0.244  0.976  0.692  0.722  52.071  6.098 
240  120  0.926  53.491  0.240  0.962  0.682  0.731  53.368  6.011 
220  110  0.926  53.491  0.240  0.962  0.682  0.731  53.401  6.011 
200  100  0.902  54.696  0.237  0.950  0.673  0.739  54.575  5.933 
180  90  0.814  59.116  0.225  0.902  0.640  0.769  59.015  5.636 
160  80  0.801  59.769  0.224  0.895  0.635  0.773  59.631  5.592 
140  70  0.791  60.271  0.222  0.889  0.630  0.776  60.156  5.555 
120  60  0.721  63.787  0.212  0.849  0.602  0.799  63.707 
5.303 
100  50  0.761  61.778  0.218  0.872  0.618  0.786  61.696  5.448 
80  40  0.687  65.495  0.207  0.829  0.588  0.809  65.397  5.178 
60  30  0.663  66.700  0.203  0.814  0.577  0.817  66.614  5.085 
40  20  0.571  71.321  0.189  0.756  0.536  0.844  71.222  4.721 
20  10  0.532  73.280  0.182  0.730  0.517  0.856  73.173  4.558 
10  5  0.510  74.385  0.178  0.714  0.506  0.863  74.320 
4.460 
Analyze > Classify > Tree…..in SPSS package program. Since our dependent variable (weaning weight) is scale, CART, CHAID and Exhaustive CHAID data mining algorithms are activated as growing methods in SPSS program to obtain a regression tree diagram. In the construction of the regression tree graph for each algorithm, the crossvalidation value of 10 was employed.
RESULTS AND DISCUSSION
Performance of CART and both CHAID algorithms according to different parent: child node proportions specified for the study were compared in order to appoint some environmental factors that impress weaning weight well and summary results of goodness of fit criteria estimated for the algorithms are given in Tables I, II and III, respectively. This information is novel in literature. With being decreased the proportion from 500:250 through 10:5, their goodness of fit criteria were found better. The regression tree structure generated by CHAID algorithm was more interpretable than those constructed by CART and Exhaustive CHAID algorithms, causing over branching.
Following are results of Goodness of fit criteria for weaning weight
CHAID algorithm
When minimum parent: child node proportion was reached from 500:250 to 10:5, RE (0.992 to 0.510),
Table II. Goodness of fit criteria for the Exhaustive CHAID algorithm.
Parent node  Child node  RE 
R2 (%) 
RAE  RMSE  SDratio  r 
R2adj. (%) 
CV (%) 
500  250  0.992  50.176  0.249  0.996  0.706  0.708  50.128  6.222 
480  240  0.992  50.176  0.249  0.996  0.706  0.708  50.128  6.222 
460  230  0.992  50.176  0.249  0.996  0.706  0.708  50.128  6.222 
440  220  0.992  50.176  0.249  0.996  0.706  0.708  50.128  6.222 
420  210  0.992  50.176  0.249  0.996  0.706  0.708  50.128  6.222 
400  200  0.992  50.176  0.249  0.996  0.706  0.708  50.128  6.222 
380  190  0.992  50.176  0.249  0.996  0.706  0.708  50.128  6.222 
360  180  0.951  52.235  0.244  0.975  0.691  0.723  52.158  6.092 
340  170  0.976  50.979  0.247  0.988  0.701  0.714  50.903  6.173 
320  160  0.966  51.482  0.246  0.983  0.697  0.717  51.429  6.140 
300  150  0.955  52.034  0.244  0.977  0.693  0.721  51.955  6.105 
280  140  0.955  52.034  0.244  0.977  0.693  0.721  51.955  6.105 
260  130  0.953  52.135  0.244  0.976  0.692  0.722  52.071  6.098 
240  120  0.926  53.491  0.240  0.962  0.682  0.731  53.368  6.011 
220  110  0.922  53.692  0.240  0.960  0.681  0.733  53.575  5.998 
200  100  0.877  55.952  0.234  0.937  0.664  0.748  55.812  5.852 
180  90  0.808  59.417  0.225  0.899  0.637  0.771  59.341  5.615 
160  80  0.795  60.070  0.223  0.892  0.632  0.775  59.979  5.570 
140  70  0.792  60.221  0.222  0.890  0.631  0.776  60.092  5.561 
120  60  0.746  62.531  0.216  0.864  0.612  0.791  62.442  5.395 
100  50  0.740  62.833  0.215  0.860  0.610  0.793  62.707  5.374 
80  40  0.706  64.540  0.210  0.840  0.596  0.803  64.442  5.248 
60  30  0.662  66.750  0.203  0.813  0.577  0.817  66.656  5.082 
40  20  0.565  71.622  0.188  0.752  0.533  0.846  71.535  4.695 
20  10  0.534  73.179  0.183  0.731  0.518  0.855  73.106  4.564 
10  5  0.511  74.335  0.179  0.715  0.507  0.862  74.273 
4.464 
SD ratio (0.706 to 0.506), RAE (0.249 to 0.178), RMSE (0.996 to 0.506) and CV (%) (6.222 to 4.460) reduced for CHAID algorithm, whereas the rest goodness of fit criteria ascended (Table I). It was drawn attention from the statistical evaluation that Pearson correlation coefficient between observed and predicted weaning weight values depictured an increment from 0.708 to 0.863, which is an indicator of reducing the variance within nodes forming in the tree diagram. From Table I, it is obvious that no alteration was found in goodness of fit criteria of CHAID algorithm between parent: child nodes 380:190 and 500:250.
A regression tree diagram was constructed by the CHAID algorithm for parent: child node proportions 500:250, 480:240, 460:230, 440:220, 420:210:400:200 and 380:190, respectively. The tree diagram is depicted in Figure 1. All lambs in the Mengali population were split into five subsubsets or populations (Nodes 15) as a result of significantly including birth weight, respectively. The heaviest lamb weaning weight of 17.614 kg was found for a subset of the lambs in Node 5 whose birth weight was greater than 3.800 kg.
The decision tree generated for only the parent: child node proportion 140:70 is illustrated in Figure 2. Node 0 was divided by birth weight (the most effective variable) into 8 subsets named Nodes 18, respectively. As birth weight increased from Node 1 to Node 8, weaning weight also increased (Fig. 2). Nodes 2, 3, 4 and 5 were effected by year factor (Adjusted P=0.000). Nodes 11 and 13 were divided by means of farm factor into two subsets (Nodes 1920 and Nodes 2122), respectively (Adjusted P=0.000). Node 9 was split by dam age into two subsets, respectively (Adjusted P=0.043). Node 15 was split by means of sex factor into two child subsets (Nodes 23 and 24), (Adjusted P=0.000).
Exhaustive CHAID algorithm
Table II demonstrated that RE (0.9920.511), RAE (0.2490.179), RMSE (0.9960.715) and SD ratio (0.7060.507), CV (%) (6.2224.464), R2 (50.17674.335%) and adjusted R2 (50.12874.273%) estimates of Exhaustive CHAID treebased algorithm from the parentchild node proportion 500250 to 10:5 were made, which means that its predictive performance in weaning weight improved as result of reducing the variance within nodes. However, higher coefficients of determination, and Pearson coefficients (0.7080.862) between actual and predicted weaning weight were obtained (Table II). For a good fit, an algorithm must have R2 greater than 70%. Goodness of fit criteria of the Exhaustive CHAID was found the definitely same with CHAID algorithm between the parentchild node proportions 500:250 and 380:190 (Tables I and II). But, at the proportions 300:150, 240:120 and 80:40, birth weight generated splits in succession in some branches of the regression tree diagram of Exhaustive CHAID algorithm. It could be suggested that use of CHAID and CART algorithms was better at the proportions. In agreement with our results, Tariq et al. (2012) determined
Table III. Goodness of fit criteria for CART algorithm.
Parent Node

Child Node  RE 
R2 (%) 
RAE  RMSE  SDratio  r 
R2adj (%) 
CV(%)  
500  250  1.022  48.667  0.253  1.011  0.719  0.697  48.593  6.463  
480  240  1.022  48.667  0.253  1.011  0.719  0.697  48.593  6.332  
460  230  1.022  48.667  0.253  1.011  0.719  0.697  48.593  6.332  
440  220  1.022  48.667  0.253  1.011  0.719  0.697  48.593  6.332  
420  210  1.022  48.667  0.253  1.011  0.719  0.697  48.593  6.332  
400  200  1.022  48.667  0.253  1.011  0.719  0.697  48.593  6.332  
380  190  1.022  48.667  0.253  1.011  0.719  0.697  48.593  6.332  
360  180  0.920  53.790  0.253  1.011  0.719  0.697  48.538  6.332  
340  170  0.920  53.790  0.240  0.959  0.680  0.733  53.701  5.991  
320  160  0.863  56.653  0.240  0.959  0.680  0.733  53.701  5.991  
300  150  0.863  56.653  0.232  0.929  0.659  0.753  56.553  5.803  
280  140  0.863  56.653  0.232  0.929  0.659  0.753  56.553  5.803  
260  130  0.863  56.653  0.232  0.929  0.659  0.753  56.553  5.803  
240  120  0.829  58.361  0.232  0.929  0.659  0.753  56.553  5.803  
220  110  0.829  58.361  0.227  0.910  0.645  0.764  58.292  5.686  
200  100  0.802  59.717  0.227  0.910  0.645  0.764  58.292  5.686  
180  90  0.802  59.717  0.224  0.895  0.635  0.773  59.622  5.593  
160  80  0.743  62.681  0.224  0.895  0.635  0.773  59.622  5.593  
140  70  0.732  63.233  0.215  0.862  0.611  0.792  62.575  5.385  
120  60  0.712  64.238  0.214  0.855  0.606  0.795  63.150  5.343  
100  50  0.693  65.192  0.211  0.844  0.598  0.802  64.154  5.270  
80  40  0.672  66.247  0.208  0.832  0.590  0.807  65.099  5.200  
60  30  0.637  68.005  0.205  0.820  0.581  0.814  66.166  5.120  
40  20  0.582  70.767  0.199  0.798  0.566  0.825  67.919  4.983  
20  10  0.572  71.270  0.191  0.763  0.541  0.841  70.676  4.764  
10  5  0.565  71.621  0.189  0.756  0.536  0.844  71.169  4.724 
that the Exhaustive CHAID algorithm had longer operation time compared to CHAID algorithm. However, all the algorithms succeeded in reducing the variance within nodes.
CART algorithm
When different parentchild node proportions were examined (Table III), it was concluded that RE (1.0220.565), RAE (0.2530.189), RMSE (1.0110.756) and SD ratio (0.7190.536) CV (6.4634.724%), R2 (48.66771.621%) and adjusted R2 (48.59371.169%) estimates of CART algorithm provided much better fit from 500:250 through 10:5 as also found in other algorithms. The result may be ascribed to reducing the variance within nodes (subsets) in weaning weight in the regression tree diagrams. Also, corresponding goodness of fit criteria such as coefficient of determination, adjusted coefficient of determination and Pearson correlation between predicted and actual weaning weight values increased under same conditions. It was found in the study that, in line with the other algorithms, CART reduced the variability within nodes or increased the variability among nodes in weaning weight, a response variable. In addition, some authors mentioned that SD ratio estimates of the data mining algorithms should be less than 0.40 for a good fit (Grzesiak et al., 2003; Grzesiak and Zaborski, 2012; Ali et al., 2015), which was in virtually agreement with those obtained for the algorithms in the study.
CONCLUSION
Weaning weight in farm animals played a considerable role on animal husbandry studies. In this respect, we intended in the study to comparatively examine the effect of different parent and child node proportions on predictive performance of CART, CHAID and Exhaustive CHAID data mining algorithms, and to observe the agreeableness of their tree constructions. All the algorithms had much better fit at parent and child node proportions from 500:250 to 10:5. For Mengali sheep data, CHAID algorithm generated more appropriate and deductive regression tree constructions. In literature, for example, the data mining algorithms can give more effective responses in the prediction of live body weight by morphological measurements, which are genetically correlated to the body weight (Khan et al., 2014; Ali et al., 2015).
As a result, it is expected that employing quantitative traits genetically correlated highly to a target trait like body weight with individual breeding coefficients and the data mining algorithms will serve a useful purpose in gaining superior animals for animal breeding studies. In other words, cutoff values of individual inbreeding coefficients in the regression tree diagrams formed by the treebased algorithms might release information on degree of inbreeding depression in a flock.
Acknowledgment
The authors would like to thank Prof. Mohammad Masood Tariq and Dr. Abdul Waheed for allowing us to use their data in the study.
Conflict of interest statement
We declare that we have no conflict of interest.
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