Prediction of Live Body Weight for Thalli Sheep Using Chi-Square Automatic Interaction Detector and Multiple Linear Regression: A Comparative Study

1Govt. Degree College for Boys Makhdoom Rashid, Multan, Pakistan 2Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan 3Department of Livestock and Poultry Production, Bahauddin Zakariya University, Multan 4Govt. Degree College for boys Qadir Pur Raan, Multan, Pakistan Article Information Received 26 January 2021 Revised 03 July 2021 Accepted 10 August 2021 Available online 08 March 2022 (early access)


INTRODUCTION
I n recent years, small ruminants play a momentous role in developing economy of a country. Goat and sheep are well adapted to life and people are being farming these ruminants for multifactorial benefits such as, to fulfill the demands of meat, milk and wool. Different types of goat and sheep breeds are found in Pakistan. Thalli are one of the sheep breeds with massive potential in order to get the meat, milk, and wool. The main living places of Thalli breed is the desert regions of Muzaffargarh, Multan, Mianwalli, Jhang and Sargodha. One of the adaptive characteristics of Thalli breed is the remarkable tolerance of the temperature up to 50 o ; however, at this temperature other animals will suffer. The basic distinguishing features of the Thalli breed are relatively small head with pendulous ears. In the context of coloring, the black or brown head color is the exclusive characteristic of this animal. However, the other strains of this breed large heads with small ears. These two distinguish features make it more adaptive than other breeds. Medium sized body, romen nose and small tail are the other important characteristics of this breed. Genetically, the meat and wool production of Thalli is quite good as compared to other sheep breeds of Pakistan (Khan et al., 2003).
Predicting live body weight (BW) is an important topic to find out a proper feed amount, drug dose, and marketing for animal under rural condition without weighing instruments (Eyduran et al., 2013). In the literature, various reports found a great figure for the estimation of BW by using different body dimensions of different sheep breeds. Body dimensions are used to estimate BW quite well in the condition where weighbridges are not available (Berge, 1977;Buvanendran et al., 1980;Goonerwardene O n l i n e F i r s t A r t i c l e and Sahaayuraban, 1983). The predictive quality of the establishment in small ruminants is improved through fair and consecutive statistical techniques. Different researchers used various statistical techniques such as canonical correlation analysis (Yapark et al., 2008), path analysis (Yakubu, 2009), correlation analysis (Khan et al., 2006), use of factor scores in multiple regression (Tariq et al., 2012), simple regression (Chitra et al., 2012) and multiple linear regression (MLR) (Seifemichael., 2014) for BW prediction. By using the traditional statistical methods, the reliability of these methods can be harmfully affected by violation of the distributional assumptions, and it can lead to biased parameter estimation (Ruhil et al., 2013). Various studies have been carried out to reduce the problem of multicollinearity for prediction the BW from body parameters by means of Chi-square automatic interaction detector (CHAID) (Khan et al., 2014;Ali et al., 2015;Akin et al., 2017;Eyduran et al., 2017;Arsalan et al., 2020); Classification and regression tree diagram (CART) (Kovalchuk et al., 2017); Artificial neural network (ANN) (Behzadi and Aslaminejad, 2010;Ali et al., 2015;Eyduran et al., 2017;. Eyduran et al. (2017) predicted the BW of Pakistani Beetal goat based on six different traits (head girth, neck length, diagonal body length, belly sprung, shank circumference, and rump height) through CART, CHAID, ANN and MLR methods. In addition, Yakubu (2012) predicted BW through body parameters in UDA rams.
In Pakistan, numerous studies on BW prediction for Mengali, Balochi, Harnai, Beverigh and Rakhshani sheep are available (Mohammad et al., 2012;Khan et al., 2014;Ali et al., 2015). However, studies to predict the live BW for Thalli sheep found in Southern Punjab, Pakistan are scarce and are currently in need. This fact motivated us to carry out this study. The primary aim of this paper was to compare the predictive performances of CHAID and MLR for the prediction of live BW among Thalli sheep.

MATERIALS AND METHODS
The sample of 271 female sheep was obtained from different livestock experiment station (LES) of district Muzaffargarh and Multan. Random sampling approach was used for sheep selection. We considered only those healthy sheep who did not take any medication and physical disability. The required information was taken through self-administered questionnaire, comprised of age and morphologically measurements. Nine morphometrics traits i.e., body weight, withers height (WH), body length (BL), head length (HL), rump length (RL), head width (HW), rump width (RW), barrel depth (BD) and heart girth (HG) were measured on each sheep and were taken in standing position according to standard procedures. Data collection activity was made by the same person to avoid the between individual variation. Initially, descriptive analysis i.e., mean along with standard deviation (SD) and percentage co-efficient of variation (C.V %) of each quantitative variable were reported in Table I. Primarily, a CHAID method was used for the prediction of live BW of Thalli sheep. This algorithm usually used to categorize those subsets of predictors that best depict the dependent variable. A ten-fold cross validation criterion was used in the study. The basic objective of CHAID technique is to minimize variation within nodes to construct homogenous subgroups in the optimal regression tree diagram with significant predictors (Kass, 1980). In this study, minimum sheep numbers for parent and child nodes were set at 20 and 10 and p-value for splitting equal to 0.05. Moreover, the Bonferroni adjustment was utilized to correct for the p-values of the best predictor at each split in the CHAID algorithm. All the statistical analysis was performed by using SPSS 23.0 software program.
We also predict the live BW of Thalli sheep using MLR analysis. The MLR is a commonly used method for developing the relationship between a dependent variable and a set of predictors. The mathematical form of multiple linear regressions is as follows: Where, Live BW is a dependent variable, β 0 is an intercept, β i is the i th parameter, X i is the i th independent variable, and ε is a random error. To compare the predictive performance of CHAID and MLR, different model evaluation criteria i.e., co-efficient of determination (R 2 ),

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adjusted co-efficient of determination (adj-R 2 ), Pearson correlation coefficient (r), co-efficient of variation (CV), standard deviation ratio (SD ratio), relative approximation error (RAE), root mean square error (RMSE), mean absolute deviation (MAD) and akaike information criterion (AIC) were used. The details of mathematical equation and other relevant statistical measures can be seen in earlier published studies (Akaike, 1973;Sugiura, 1978;Salehi et al., 1998;Willmott and Matsuura, 2005;Takma et al., 2012;Eyduran et al., 2017).

RESULTS AND DISCUSSION
Sheep production has played a major role in animal production, particularly in rural development. One of the main targets of the breeders in sheep reproduction is to find out the relationship between body weight and the related traits. For predicting live BW of any sheep breed, linear body measurements can be used as indirect selection criteria. In this study, we also planned to predict BW of female Thalli sheep from linear body measurements.
In this study, predictive performance of CHAID and MLR used for predicting BW by means of some body measurements in sheep has been evaluated comparatively. Table II shows the performance of the CHAID and MLR methods to predict BW. The estimated value of r, R 2 and Adj-R 2 were significantly higher (P<0.05) for the CHAID algorithm compared with that for MLR. On the other hand, SD ratio, RMSE, RAE, MAD, CV% and AIC were lowest for the CHAID algorithm which indicates the better predictive capabilities in comparison with MLR. The worst performance in the current research work was recorded for the MLR method. A study by Khorshidi-Jalali et al. (2019) also obtained low R 2 (67%) for predicting body weight in Raini Cashmere goat by using the MLR method. In line with our results, some earlier reports highlighted the biological advantage of CHAID algorithm in BW prediction. e.g., Celik and Yilmaz (2017) found that CHAID was the ideal tree-based algorithm in the estimation of BW trait. Their results for different goodness-of-fit criteria were, r= 0.84, R 2 = 71.57, SD ratio = 0.53. Olfaz et al. (2019) published a study including 366 karayaka sheep in which they suggested that CHAID algorithm was the more useful method for body weight prediction as compared to the classification and regression tree (CART) method. We also compared the statistical results of different criterion with earlier reports. The present R 2 estimated for CHAID algorithm was highest while, Mohammad et al. (2012) estimated a lower R 2 value of 0.72 for CHAID algorithm in the body weight prediction through withers height, chest girth, body length, and breed in indigenous Pakistani sheep. However, in Harnai breed, Ali et al. (2015) presented better goodness-of-fit results (R 2 = 83.77, r=0.91, SD ratio= 0.40, RMSE= 1.50) for CHAID algorithm compared with the corresponding estimates in the present study. Another study used the exhaustive CHAID algorithm for BW estimation of Harnai sheep and the reported results (R 2 = 0.84) were also better than our results (Khan et al., 2014). Aksahan (2015) apply CHAID algorithm to get morphological measurements affecting final live weight (FLW) at fattening period of 103 young (Holstein, Simmental, Brown Swiss and crossbreed) bulls in Bolvadin district of Afyon province of Turkey, and detected a high predictive accuracy of % R 2 87.82 that the effect of BL, chest circumference, and back rump height, on FLW trait was important. The estimation of BW in indigenous beetal goat of Pakistan through head girth, neck length, diagonal body length, belly sprung, shank circumference and rump height input variables were reported by Eyduran et al. (2017) in the scope of CART, CHAID, RBF, MLP1, MLP2, MR modeling. We found better goodness of fit criteria (r, RMSE, AIC, MAD, SD ratio) in terms of CHAID algorithm in comparison with those recorded by Eyduran et al. (2017).
The difference in the results may be due the use of different sheep breeds, different body measurements, ages, environmental conditions, managerial factors, and the statistical techniques used in the study. However, it is recommended for further investigators that the predictive performances of the evaluated statistical methods should be used for different sheep breeds and studies with a large population, large number of sheep breeds and efficient factors in generalization of the results obtained from the current study.

CONCLUSION
In conclusion, we found that for prediction of live body weight in Thalli sheep, CHAID performed better and more accurate as compared to the MLR model due

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to the higher Pearson correlation coefficient, R 2 , Adj-R 2 and lower SD ratio, RMSE, RAE, MAD, CV%, and AIC. Although both CHAID and MLR models can remarkably predict live body weights very close to the actual values, performances of CHAID algorithm for prediction of live body weights applying body measurements of Thalli sheep was higher and more precise. Therefore, it is possible to apply CHAID algorithm, instead of traditional procedures for prediction of actual body weight using body measurements. The researchers may also use these results for comparison purposes and may be uses as a reference for next studies.

O n l i n e F i r s t A r t i c l e
Body Weight Prediction of Thalli Sheep