Comparing Predictive Performances of Tree-Based Data Mining Algorithms and MARS Algorithm in the Prediction of Live Body Weight from Body Traits in Pakistan Goats

Senol Celik

Department of Animal Science, Faculty of Agriculture, Bingol University, Bingol, Turkey

ABSTRACT

The main purpose of this investigation was to comparatively evaluate predictive performances of multivariate adaptive regression splines (MARS), chi-squared automatic interaction detector (CHAID), exhaustive CHAID and classification and regression trees (CART) data mining algorithms in predicting live body weight as a continuous response variable by means of morphological measurements i.e. live body weight (LBW), body length (BL), withers height (WH), rump height (RH), belly girth (BG) and chest girth (CG) as continuous predictors from 130 Pakistan goats. Also, sex factor was included as a possible nominal predictor in the current study. To measure predictive performances of the tested algorithms, model evaluation criteria such as the correlation coefficient between actual and predicted LBW values (r), Akaike’s and corrected Akaike information criterion (AIC and AICc), root-mean-square error (RMSE), mean absolute deviation (MAD), standard deviation ratio (SDratio), and mean absolute percentage error (MAPE) were estimated. According to these criteria, MARS produced better predictive accuracy in explaining the variability in LBW compared with others. MARS produced the best fit for 3rd interaction order on the basis of the smallest generalized cross validation (GCV). In the MARS algorithm, BL and CG were the predictors that had the highest relative importance (100%) in the prediction of live body weight and these two predictors could be considered as indirect selection criteria for breeding schemes. It could be suggested that the CART, the CHAID, the Exhaustive CHAID and especially MARS algorithms in the prediction of live body weight were significant statistical tools in sophistically describing the studied breed standards for breeding purposes.

Article Information

Received 07 September 2018

Revised 01 December 2018

Accepted 20 December 2018

Available online 13 May 2019

Key words

Data Mining, CHAID, Exhaustive CHAID, CART, MARS, Body measurement.

DOI: http://dx.doi.org/10.17582/journal.pjz/2019.51.4.1447.1456

* Corresponding author: senolcelik@bingol.edu.tr

0030-9923/2019/0004-1447 $ 9.00/0

Copyright 2019 Zoological Society of Pakistan

Introduction

Goats are well adapted to life in the dry parts of the tropics where there is usually a shortage of food for humans and animals (Egwu et al., 1995). It is well-known that small ruminants play a main role in developing national economy and meeting basic requirements of people (Karabacak et al., 2017).

Predicting live body weight (LBW) is a noteworthy topic to find out proper drug dose, feed amount, and marketing for an animal under rural conditions without weighing instrument (Eyduran et al., 2013). The prediction of LBW and its causal relationships with other body measurements for ideal breeding studies is imperative to increase meat production per animal. In other words, determination of the body measurements connected with live body weight is indispensable for gaining superior offspring in the goat selection strategies and experimental studies (Lawrence and Fowler, 2002; Cam et al., 2010). An effectual characterization of the studied breed standards in goats is desired for conserving gene sources and producing elite populations. The predictive power of the characterization is possible through selecting effective statistical approaches (Eyduran et al., 2017) and influent predictors.

Eyduran et al. (2016) highlighted that usage of data mining algorithms in predicting live body weight from morphological traits in small ruminants was more informative for developing better breeding strategies. Although multiple regression models seriously affected by multicollinearity problems were adopted for predicting LBW (Pesmen and Yardimci, 2008; Coronado et al., 2015; Moaeen-ud-Din et al., 2016), much more robust studies have been conducted in predicting live body weight by morphological measurements through the CART (Ali et al., 2015; Yordanova et al., 2015; Celik et al., 2018), the CHAID (Ali et al., 2015; Koç et al., 2017), the MARS (Eyduran et al., 2017a; Celik et al., 2018; Erturk, 2018; Aytekin et al., 2018) and the artificial neural networks (ANNs) (Ali et al., 2015; Celik et al., 2018) in various farm animal species. To illustrate, Eyduran et al. (2017) captured the best one among the CART, the CHAID, and the ANNs algorithms in the prediction of live body weight (LBW) by body measurements taken from Beetal goat reared under Pakistan harsh conditions. However, the MARS application is seldom in literature (Aytekin et al., 2018). To date, an implementation of CART, CHAID tree-based algorithms and especially MARS algorithm (with/without interaction effect) were present in the prediction of LBW using morphological traits in the Pakistan goat. Use of the powerful data mining algorithms with the purpose of attaining more accurate outcomes is unavoidable for regression type problems like the LBW prediction (Celik et al., 2018) and may be gained more importance.

Hence, the goal of the present study was to comparatively evaluate predictive performances of the CART, the CHAID, the Exhaustive CHAID and the MARS algorithms in the prediction of LBW from several body measurements in the Pakistan goats.

 

Materials and methods

The data were collected from 130 goats reared at the Experimental Station, University of Balochistan, Quetta, Pakistan. The available data were taken partially from the former study conducted by Eyduran et al. (2013) in order to evaluate predictive performances of the CART (Ali et al., 2015), the CHAID (Akin et al., 2018; Gozuacik et al., 2018; Kovalchuk et al., 2017), the Exhaustive CHAID and the MARS algorithms (Celik et al., 2018).

To predict the live body weight (LBW), body length (BL), withers height (WH), rump height (RH), belly girth (BG) and chest girth (CG) were measured at varying ages (24 to 48 months) as suggested by Abegaz and Awgichew (2009). Descriptive statistics of morphological measurements of the Pakistan goats are presented in Table I.

CHAID is graphical algorithms that create regression tree structures and analyze qualitative and quantitative data, simultaneously. CHAID proposed by Kass (1980) has three stages (merging, partitioning and stopping) and is a tree-based algorithm that recursively uses multi-way splitting to form homogenous subsets on by taking a basis of Bonferroni adjustment until obtaining the least differences between the actual and predicted values in a response variable (Orhan et al., 2016; Akin et al., 2016; Eyduran et al., 2016). A quantitative input variable in the CHAID algorithms is converted into an ordinal variable (Orhan et al., 2016).

CHAID is a non-parametric analysis for a criterion variable with two or more categories. This permits researchers to perform the segmentation with respect to that variable and in agreement with the combination of a range of predictors (Díaz-Pérez et al., 2005; Legohérel et al., 2015).

The Exhaustive CHAID, as a modification of the tree-based CHAID algorithm, applies a more detailed merging and testing of predictor variables, and requires more computing time (Tang et al., 2005).

The CART algorithm is proposed by Breiman et al. (1984). The CART is a binary decision tree algorithm made by splitting a node into two child nodes repeatedly, beginning with the root node that contains the whole learning sample. Some earlier studies reported for more detailed information on the CART and CHAID algorithms were reported (Akin et al., 2017a, b, c, 2018).

The MARS algorithm developed by Jerome Friedman in the year 1991 (Friedman, 1991) is a nonparametric regression technique specifying piecewise basis functions for revealing the complex relationship between a response variable and a set of predictors, and it automatically choices knot locations. Prediction equation of the MARS algorithm can be written below:

Where, βo and βm are the basis function parameters of the MARS algorithm used on the basis of the least squares criterion. The spline basis function Bm(x), can be implemented as:

 

Table I.- Descriptive statistics of some morphological characteristics of Pakistan goats .

Body measurements	Variables	n	Minimum	Maximum	Mean	Std. Error	Std. Deviation
Live weight (cm)	LBW	130	20.00	85.00	35.90	0.97	11.05
Body length (cm)	BL	130	48.26	106.00	71.65	1.20	13.64
Withers height (cm)	WH	130	58.00	103.00	75.33	0.89	10.15
Rump height (cm)	RH	130	58.42	101.00	78.01	0.86	9.85
Belly girth (cm)	BG	130	62.00	114.30	85.92	0.96	10.96
Chest girth (cm)	CG	130	54.00	99.00	76.84	0.77	8.82

Where, km is the number of knots, skm takes either 1 or -1 and presents the right/left regions of the related step function, v(k, m) is the label of the input variable and tk, m is the knot location (Friedman, 1991).

The generalized cross validation (GCV) is approved to eliminate the redundant basis functions (Friedman and Silverman, 1989; Kornacki and Ćwik, 2005).

Where, N is the number of data and C(B) is a complexity penalty increasing with the number of basis function in the model and which is expressed as:

Where, d is a penalty for each basis function entered into the model and number of the basis functions (Friedman, 1991).

To comparatively the predictive performances of the MARS, the CART, the CHAID and the exhaustive CHAID in the 10-fold cross-validation, the following model evaluation criteria were calculated (Willmott and Matsuura, 2005; Liddle, 2007; Takma et al., 2012):

1. Pearson correlation coefficient (r) between the actual and predicted LBW values:

2. Coefficient of determination

3. Adjusted coefficient of determination

4. Root-mean-square error (RMSE) expressed by the following formula:

5. Standard deviation ratio (SDratio):

6. Mean absolute percentage error (MAPE):

7. Mean absolute deviation (MAD):

8. Akaike Information Criteria (AIC):

9. Corrected Akaike Information Criteria AIC:

Where, 2k(k+1) / n – k – 1 bias-correction term. This term is used when n / k <40 or the sample size is small (Hu, 2007). n is the number of cases in a set, k is the number of model parameters (number of the selected terms in the MARS), Yi is the actual (observed) value of a response variable (LBW), Yip is the predicted value of a response variable(LBW), sm is the standard deviation of model errors, sd is the standard deviation of a response variable (LBW), RSS: Residual sum square (RSS is the sum of the squares of residuals (deviations predicted from actual values of data).

In addition, a two-tailed t-test (with the Bonferroni adjustment) of the significance of the differences between correlation coefficients (r) among prediction models was carried out, whose test statistic was presented by the following formula (Kenny, 1987; Eyduran et al., 2017b):

Where, r13 is a correlation coefficient between observed and predicted values for the first model, r23 is a correlation coefficient between observed and predicted values for the second model, r12 is a correlation coefficient between the values predicted by the first and the second model, n is a sample size.

In the CHAID, the Exhaustive CHAID and the CART algorithms, minimum parent-child node ratio 4:2 is taken for the best predictive solution. MARS algorithm used order interaction of 3 to achieve the best solution fpr the smallest GCV error.

 

Statistical evaluations on the CHAID, the Exhaustive CHAID, and the CART tree-based algorithms were made using IBM SPSS version 23, whereas MARS algorithm was specified by the earth package of R Studio program (Milborrow, 2011, 2018). The MARS model with the smallest GCV, SDRATIO, RMSE, MAPE, MAD, AIC, AICc and the highest coefficient of determination (R2) and Pearson coefficient (r) between observed and predicted values of LBW was appropriated as the best one. All the statistical calculations were implemented through the package `earth` of R Studio software (R Core Team, 2014). The R commands written for the present study were presented in Appendix section for the future works to be conducted for regression type problems.

 

Results

We aimed here to find morphological linear measurements connected with LBW in the goats using robust statistical techniques. In that, predictive performances of the CHAID, the Exhaustive CHAID, the CART and the MARS algorithms were measured as part of predicting LBW. Their goodness-of-fit-criteria outcomes are summarized in Table II. The superiority order in the predictive accuracy of the declared algorithms was MARS > CHAID > Exhaustive CHAID > CART in relation to the estimated model evaluation criteria. Because the criteria of goodness of fit of the first algorithm were found better. The predictive performance of the MARS algorithm was recorded better.

CHAID algorithm formed a decision tree structure, and its visual outcome is shown in Figure 1. Exhaustive CHAID algorithm formed a decision tree structure, and its outcome is displayed in Figure 2. CART algorithm formed a regression tree structure, and its outcome is depicted in Figure 3.

 

Table II.- Predictive performance of CHAID, Exhaustive CHAID, CART and MARS algorithms.

	r	R2	Adj. R2	RMSE	SD ratio	MAPE	MAD	RAE	AIC	AICc
CHAID	0.80	0.64	0.63	6.60	0.60	13.24	4.59	0.18	501	501
Exh. CHAID	0.77	0.59	0.58	7.02	0.64	13.96	4.95	0.19	517	517
CART	0.67	0.45	0.43	8.15	0.74	15.34	5.43	0.22	554	554
MARS	0.95	0.91	0.86	3.32	0.30	8.49	2.67	0.09	402	451

 

Table III.- Results of the MARS algorithm for Pakistan goats.

Basic functions		Coefficients
Intercept		-23.524
SexM	BF1	-108.508
max(0, 60.96-BL)	BF2	-3.152
max(0, BL-60.96)	BF3	2.180
max(0, WH-87)	BF4	1.788
max(0, 88-WH)	BF5	1.692
max(0, 73.66-RH)	BF6	3.121
max(0, RH-83.82)	BF7	4.855
max(0, RH-86.36)	BF8	-6.877
max(0, BG-86)	BF9	1.324
max(0, CG-83.82)	BF10	-2.635
BG * SexM	BF11	1.361
max(0, BL-63.5) * max(0, 88-WH)	BF12	-0.078
max(0, BL-73) * max(0, RH-73.66)	BF13	-0.087
max(0, BL-60.96) * max(0, CG-76.2)	BF14	-0.259
max(0, BL-63.5) * max(0, CG-81.28)	BF15	0.385
max(0, BL-63.5) * max(0, 86-CG)	BF16	0.817
max(0, 70-BL) * max(0, 86-CG)	BF17	0.142
max(0, BL-71.12) * max(0, 86-CG)	BF18	0.764
max(0, WH-66.04) * max(0, 102-BG)	BF19	-0.423
max(0, WH-68.58) * max(0, 102-BG)	BF20	0.641
max(0, WH-71.12) * max(0, 102-BG)	BF21	0.198
max(0, WH-76.2) * max(0, 102-BG)	BF22	-0.254
max(0, 88-WH) * max(0, BG-88.9)	BF23	-0.121
max(0, 88-WH) * max(0, CG-81)	BF24	0.380
max(0, 88-WH) * max(0, 81-CG)	BF25	-0.059
max(0, RH-71.12) * max(0, 102-BG)	BF26	0.818
max(0, RH-73.66) * max(0, BG-81.28)	BF27	0.075
max(0, RH-73.66) * max(0, 81.28-BG)	BF28	-0.493
max(0, RH-74.93) * max(0, 102-BG)	BF29	-1.527
max(0, RH-76.2) * max(0, 102-BG)	BF30	1.093
max(0, 71.12-RH) * max(0, 86-CG)	BF31	-0.216
max(0, RH-71.12) * max(0, 86-CG)	BF32	-0.158
max(0, 102-BG) * max(0, 76.2-CG)	BF33	0.017
max(0, 73-BL) * max(0, RH-73.66) *SexM	BF34	-0.296
max(0, BL-64) * max(0, WH-68.58) *max(0, 86-CG)	BF35	-0.279
max(0, BL-64) * max(0, 68.58-WH) *max(0, 86-CG)	BF36	-0.068
max(0, BL-64) * max(0, WH-71.12) *max(0, 86-CG)	BF37	0.271
max(0, BL-70) * max(0, WH-71.12) *max(0, 86-CG)	BF38	-0.269
max(0, BL-70) * max(0, 71.12-WH) *max(0, 86-CG)	BF39	-0.157
max(0, BL-70) * max(0, WH-74) *max(0, 86-CG)	BF40	0.287
max(0, 71.12-BL) * max(0, RH-76.2) *max(0, 102-BG)	BF41	0.030
max(0, BL-64) * max(0, 78-RH) *max(0, 86-CG)	BF42	-0.032
max(0, WH-66.04) * max(0, RH-71.12) *max(0, 102-BG)	BF43	-0.054
max(0, WH-71.12) * max(0, RH-73.66) *max(0, 102-BG)	BF44	0.051

BL, body length; WH, withers height; RH, rump height; BG, belly girth; CG, chest girth; BF, basic functions.

 

In relation to CART algorithm results, the goats with BL ≤ 77.500 cm produced the average LBW of 32.510 kg, whereas those with BL > 77.500 provided the average LBW of 47.690 kg.

Results of the MARS algorithm for Pakistan goat are reported in Table III. The GCV value of the MARS model was 10.99. For the Pakistan goats, the observed LBW values of the MARS model with the interaction order of 3 exhibited much better fit.

The relative importance of the significant predictors in Table IV is given.

 

Table IV.- Relative importance of model independent variables.

Variables	GCV	No. of subsets
BL	100.0	44
CG	100.0	44
RH	72.9	43
BG	63.9	42
SEX	63.9	42
WH	58.0	38

 

Discussion

Use of the data mining algorithms is still not adequate for predicting LBW by means of morphological measurements and environmental factors as predictors in small ruminant literature (Ali et al., 2015). Eyduran et al. (2016) underlined significance of these sophistical approaches. Therefore, the present work was considered to fill the gap in the literature. The worst performance in the current work was recorded in the CART tree-based algorithm. Yakubu (2012) also obtained low R2 for predicting LBW of Uda rams. The CART R2 estimate reported by Yakubu (2012) was much lower than the estimates of MARS and both CHAID algorithms stated here.

With the scope of multivariate linear regression models, Coronado et al. (2015) predicted LBW by means of BL, TL, HG, RL and width, HL, and EL for local Amatepec (0.82 R2) and Tejupilco (0.76 R2) goats in Southern México, which was almost in agreement with the corresponding R2 estimates for both CHAID algorithms, but lower than the estimate of the MARS algorithm. Perez et al. (2016) predicted LBW through a special prediction equation, LBW= ((2*RH+4*BL+6*HG)/10)-53 where Rump height (RH), Body Length (BL) and Heart Girth (HG), and reported Pearson correlation coefficient of 0.899 between the actual and predicted LBW values of the goats reared in Philippines. The previous estimate was found lower than that (0.95) obtained for only MARS in the Pakistan goats (Table II). The present results were found much better in comparison with those reported by Moaeen-ud-Din et al. (2016) with 0.210 and 0.124 R2 in predicting LBW of Beetal (LBW = 24.39 + 0.45HG+0.42BL) and Crossbred (LBW = 35.51 – 0.054 WH + 0.424 HG) goats in Pakistan. We could say that the multiple regression model built by Moaeen-ud-Din et al. (2016) was inadequate in predicting LBW. This means that the used models in the earlier study were insufficient or the influential predictors were unavailable in explaining the variability in LBW.

Pesmen and Yardimci (2008) had a bit higher R2 of 0.95 in the Saanen goats through the following prediction equation; LBW= - 146.313 + 1.081*HG + 0.679*BL + 3.013*SC than the present MARS modeling. However, the fact that the present MARS model included interaction effects could be considered as an advantage for breeding purposes. Benyi (1997) found higher R2 for linear (0.87 to 0.92 R2) and geometric functions (0.97 to 0.99 R2) in the West African goats and Sahel x West African Dwarf goats, whereas the present R2 estimates for other algorithms except for CART were found much better than regression results of Chitra et al. (2012).

Eyduran et al. (2017b) obtained a lower R2 of 0.75 in multiple linear regression model (Ordinary Least Squares Method) for the LBW prediction in Beetal goats and they found that sex, BL, SC (Shank circumference) and RH (Rump height) (P<0.01) compared with the present estimates of MARS and both CHAID algorithms (Table II). Also, Eyduran et al. (2017b) obtained for SD ratio the range from 0.5030 (RBF algorithm) to 0.5727 (MLP), which was better than those found for the-tree-based CART and CHAID algorithms as expected, but these two ANN algorithms were much worse than that obtained for MARS (0.30) in the present study. Similarly, Celik et al. (2018), Aytekin et al. (2018) and Ertürk (2018) also emphasized the superiority of the MARS algorithms.

The wide variation may be ascribed to the variability in breed, age, gender, rearing systems, predictors and interaction degrees and effects, as well as especially statistical techniques. However, it is suggested that efficiently revealing predictive performances of the evaluated algorithms should be used for different goat breeds and much wider populations to generalize the achieved results.

 

Conclusions

The MARS algorithm outperformed tree-based data mining algorithms in predictive accuracy and effectively revealed interaction effects between significant predictors. In conclusion, the CART, the CHAID, and especially the MARS algorithms in the predicting LBW from morphological traits were significant statistical tools in sophistically describing the breed standards and establishing indirect selection criteria in practice for breeding purposes.

 

Supplementary material

There is supplementary material associated with this article. Access the material online at: http://dx.doi.org/10.17582/journal.pjz/2019.51.4.1447.1456

 

Statement of conflict of interest

The authors declare no conflict of interest.

 

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