Categorical variables belonging to Honamli and Hair goats in the study are presented in Table 2. Descriptive statistics of continuous variables obtained from Honamli and Hair goats are given in Table 3. Honamli females had higher values compared to males because females are older (Table 2). In other words, young billy goats are preferred in the herd to shorten the time between generations.
Table 2
Categorical variables belonging to Honamli and Hair goats
Factors
|
Levels
|
N
|
Percentage (%)
|
Sex
|
Female
|
118
|
79.73%
|
Male
|
30
|
20.27%
|
Breeds
|
Honamli
|
83
|
56.08%
|
Hair
|
65
|
43.92%
|
Age
|
1
|
48
|
32.43%
|
2
|
8
|
5.41%
|
3
|
18
|
12.16%
|
4
|
10
|
6.76%
|
5
|
4
|
2.70%
|
6
|
60
|
40.54%
|
Ear
|
Comuk (native terms)
|
48
|
32.43%
|
Lop
|
100
|
67.57%
|
Table 3
Descriptive statistics on live weight and some body measurements in Honamli and Hair goats of different age
Traits
|
Breed
|
Sex
|
N
|
Minimum
|
Maximum
|
Mean±SE
|
StDev
|
CoefVar
|
LW
|
Honamli
|
Female
|
73
|
27.10
|
84.70
|
60.76±1.54
|
13.13
|
21.60
|
Male
|
10
|
37.20
|
63.10
|
48.02±2.77
|
8.76
|
18.24
|
Hair
|
Female
|
45
|
27.30
|
72.20
|
48.40±1.76
|
11.77
|
24.33
|
Male
|
20
|
29.00
|
43.60
|
36.15±0.95
|
4.25
|
11.74
|
WH
|
Honamli
|
Female
|
73
|
51.90
|
89.50
|
75.78±1.04
|
8.90
|
11.75
|
Male
|
10
|
66.00
|
87.00
|
76.25±2.37
|
7.51
|
9.84
|
Hair
|
Female
|
45
|
51.70
|
85.00
|
70.63±1.20
|
8.05
|
11.39
|
Male
|
20
|
63.50
|
77.50
|
68.70±0.94
|
4.22
|
6.15
|
BH
|
Honamli
|
Female
|
73
|
64.50
|
90.50
|
79.14±0.71
|
6.05
|
7.65
|
Male
|
10
|
66.50
|
86.00
|
76.60±1.97
|
6.23
|
8.13
|
Hair
|
Female
|
45
|
60.00
|
79.50
|
71.09±0.69
|
4.66
|
6.55
|
Male
|
20
|
61.00
|
75.50
|
68.40±1.01
|
4.50
|
6.58
|
RH
|
Honamli
|
Female
|
73
|
65.50
|
89.00
|
79.14±0.66
|
5.63
|
7.12
|
Male
|
10
|
70.00
|
86.50
|
77.45±1.69
|
5.36
|
6.92
|
Hair
|
Female
|
45
|
60.50
|
81.00
|
71.82±0.72
|
4.80
|
6.68
|
Male
|
20
|
61.00
|
77.00
|
68.08±0.98
|
4.39
|
6.45
|
CD
|
Honamli
|
Female
|
73
|
16.50
|
29.50
|
24.66±0.29
|
2.47
|
10.00
|
Male
|
10
|
20.50
|
27.50
|
24.45±0.76
|
2.41
|
9.85
|
Hair
|
Female
|
45
|
18.50
|
27.50
|
22.36±0.28
|
1.86
|
8.31
|
Male
|
20
|
18.50
|
23.50
|
21.13±0.32
|
1.44
|
6.82
|
BL
|
Honamli
|
Female
|
73
|
46.00
|
91.50
|
80.57±0.97
|
8.25
|
10.24
|
Male
|
10
|
62.50
|
88.00
|
75.65±2.70
|
8.54
|
11.29
|
Hair
|
Female
|
45
|
60.00
|
92.00
|
74.63±1.12
|
7.50
|
10.05
|
Male
|
20
|
58.00
|
76.50
|
68.30±0.83
|
3.69
|
5.41
|
CG
|
Honamli
|
Female
|
73
|
70.00
|
104.00
|
91.04±0.82
|
6.96
|
7.65
|
Male
|
10
|
81.00
|
95.00
|
86.25±1.36
|
4.30
|
4.99
|
Hair
|
Female
|
45
|
73.00
|
102.50
|
86.64±1.05
|
7.02
|
8.11
|
Male
|
20
|
72.50
|
90.50
|
81.50±0.98
|
4.38
|
5.37
|
LG
|
Honamli
|
Female
|
73
|
35.00
|
67.00
|
51.21±0.74
|
6.29
|
12.28
|
Male
|
10
|
46.00
|
65.00
|
55.90±2.05
|
6.48
|
11.59
|
Hair
|
Female
|
45
|
39.00
|
77.50
|
50.87±1.13
|
7.58
|
14.90
|
Male
|
20
|
46.50
|
61.00
|
55.00±0.75
|
3.35
|
6.09
|
HL
|
Honamli
|
Female
|
73
|
17.00
|
24.00
|
21.23±0.18
|
1.49
|
7.03
|
Male
|
10
|
19.50
|
22.50
|
20.80±0.31
|
0.98
|
4.70
|
Hair
|
Female
|
45
|
17.00
|
23.00
|
19.67±0.22
|
1.45
|
7.39
|
Male
|
20
|
17.50
|
22.50
|
20.13±0.29
|
1.30
|
6.44
|
FH
|
Honamli
|
Female
|
73
|
11.00
|
21.00
|
14.26±0.25
|
2.13
|
14.95
|
Male
|
10
|
12.00
|
16.00
|
13.95±0.46
|
1.46
|
10.48
|
Hair
|
Female
|
45
|
11.00
|
17.00
|
13.37±0.24
|
1.58
|
11.79
|
Male
|
20
|
11.50
|
23.00
|
14.03±0.53
|
2.37
|
16.86
|
EL
|
Honamli
|
Female
|
73
|
8.00
|
22.50
|
16.97±0.44
|
3.74
|
22.02
|
Male
|
10
|
9.50
|
21.00
|
15.50±1.34
|
4.22
|
27.24
|
Hair
|
Female
|
45
|
13.00
|
28.00
|
17.79±0.45
|
3.00
|
16.88
|
Male
|
20
|
7.00
|
20.50
|
14.68±0.86
|
3.86
|
26.31
|
TL
|
Honamli
|
Female
|
73
|
13.00
|
27.50
|
19.11±0.39
|
3.37
|
17.61
|
Male
|
10
|
15.00
|
29.00
|
20.35±1.35
|
4.28
|
21.04
|
Hair
|
Female
|
45
|
11.00
|
22.00
|
15.97±0.35
|
2.31
|
14.50
|
Male
|
20
|
14.00
|
20.00
|
16.43±0.42
|
1.88
|
11.44
|
Live weight (LW), Withers height (WH), Back height (BH), Rump height (RH), Chest Depth (CD), Body length (BL), Chest girth (CG), Leg girth (LG), Head lenght (HL), Fore head (FH), Ear lenght (EL), and Tail lenght (TL)
|
The MARS algorithm, which provides the best classification of Honamli and Hair goats, takes the form of body features "LW", "BH", "CD", "HG" and "HL" as independent variables in the prediction model. In addition, the model also includes "Age" and "Sex Male" variables that do not have body features.
GLMHONAMLI = -0.5232799 - 3.033782 * SexMale + 1.5192 * max(0, 4 - Age) - 1.068315 * max(0, 35.4 - LW) + 0.4609831 * max(0, BH - 72) + 25.86152 * max(0, BH - 82) - 0.6795643 * max(0, 25 - CD) + 1.559002 * max(0, 77.5 - HG) - 0.5741605 * max(0, 21.5 - HL)
The probability of any goat being Honamli can be estimated with the help of the PHONAMLI = expGLMHONAMLI / (1+ exp GLMHONAMLI ) equation. The "exp" value used in the equation refers to the base of the natural logarithm of 2.718. Using the basic MARS model, it is possible to derive a new prediction equation used in the classification of females. If the goats used in breed discrimination estimation are female animals older than 4 years old, the following equation can be used.
GLMHONAMLI = -0.5232799 - 1.068315 * max(0, 35.4 - LW) + 0.4609831 * max(0, BH - 72) + 25.86152 * max(0, BH - 82) - 0.6795643 * max(0, 25 - CD) + 1.559002 * max(0, 77.5 - HG) - 0.5741605 * max(0, 21.5 - HL)
For example, if the body characteristics of a 4-year-old female goat are LW = 40 kg, BH = 78 cm, CD = 25 cm, HG = 75 cm and HL = 20 cm, the breed could be estimated using the equation as follows;
GLMHONAMLI = -0.5232799 - 3.033782 * SexMale (Female=0) + 1.5192 * max(0, 4 - 4) - 1.068315 * max(0, 35.4 - 40) + 0.4609831 * max(0, 78 - 72) + 25.86152 * max(0, 78 - 82) - 0.6795643 * max(0, 25 - 25) + 1.559002 * max(0, 77.5 - 75) - 0.5741605 * max(0, 21.5 - 20)
GLMHONAMLI = -0.5232799 + 0.4609831 * max(0, 78 - 72) + 1.559002 * max(0, 77.5 - 75) - 0.5741605 * max(0, 21.5 - 20)
GLMHONAMLI = -0.5232799 + 0.4609831 *6 + 1.559002 * 2.5 - 0.5741605 * 1.5GLMHONAMLI = 5.27888295PHONAMLI = expGLMHONAMLI / (1+ exp GLMHONAMLI )PHONAMLI = 2.7185.27888295/ (1+ 2.7185.27888295)PHONAMLI = 0.994924974 probably the goat belongs to the Honamli breed.Classification performances of data mining algorithms used for race discrimination are shown in Table 4. The areas under ROC (AUC) were statistically significant for all algorithms that made breed discrimination (P <0.01).Among the algorithms used for breed discrimination, the best classification performance is the MARS algorithm in terms of sensitivity (0.916), specificity (0.846), and general accuracy rate (0.937). The MARS algorithm was able to correctly classify 75 of 83 Honamli goats, 55 of 65 Hair goats and 88.50 (%) of all goats. In addition, the MARS algorithm was found to have the largest area in the breed discrimination diagnostic test with the area under the ROC curve of 0.942. Using the morphological characteristics of Honamli and Hair goats, the best performing algorithms for breed discrimination are MARS and CART. By using the morphological characteristics of Honamli and Hair goats, it was determined that the performances of the discrimination made by the CHAID algorithm had the values of sensitivity, specificity and accuracy repectively as 0.911, 0.841, and 0.878. The CHAID algorithm, which is used to classify goat breeds correctly, allocated 11 of 83 Honamli incorrectly and 72 correctly, while it separated 58 of 65 Hair goats correctly. CHAID has the area under the largest ROC with a value of 0.880 after the MARS algorithm.In the study, performance results of CART were determined as 0,849, 0,927, and 0,848 for sensitivity, specificity, and accuracy rate respectively. The CART algorithm estimated 79 of 83 Honamli goats, 51 of 65 Hair goats and 87.80 (%) of all goats by classifying them correctly. In addition, the CART algorithm was found to have the third largest AUC (0.868) value in the diagnostic test used for breed discrimination. Although the results are similar to the CHAID algorithm, the performance value of the Exhaustive CHAID algorithm is lower. The Exhaustive CHAID algorithm used to distinguish Honamli and Hair goats has performance values such as sensitivity (0.861), specificity (0.855), and accuracy rate (0.858). While Exhaustive CHAID algorithm classified 74 of 83 Honamli goats correctly, 9 of them were classified incorrectly. While this algorithm allocated 12 of 65 Hair goats incorrectly, 53 of them were classified correctly. The area under ROC, which is one of the diagnostic test performance criteria in racial discrimination, was determined as (0.853). In this study, in which the breed discrimination was made by using the morphological characteristics of Honamli and Hair goats, performance values of the QUEST algorithm, which is one of the data mining algorithms, were determined as sensitivity (0.889), specificity (0.682), and accuracy (0.770) rate, respectively. The QUEST algorithm, which has the worst performance among the algorithms, classified only 56 of the 83 Honamli goats correctly, while 27 of them were incorrectly classified. Although the QUEST algorithm failed to classify Honamli goats, it classified 58 of 65 Hair goats correctly and seven of them incorrectly.The fact that the sensitivity and specificity values of the model performance value criteria are close to each other and that the AUC value is close to one is an indication of the correct classification. Models compared in terms of AUC can be mathematically expressed as MARS = CHAID = CART> = Exhaustive CHAID> = QUEST. When all data mining algorithms are compared among themselves in terms of performance criteria, it was determined that the most successful algorithm used in breed discrimination is MARS. Among the classification tree algorithms, it was determined that the CHAID algorithm has the best diagnostic test performance. Although the CART algorithm correctly classified Honamli goats with a high rate (95.20%), the percentage of correctly classifying Hair goats (78.50%) remained low. Although the Exhaustive CHAID algorithm correctly separated both breeds in close percentages, their performance values were insufficient compared to other algorithms (MARS, CHAID, and CART). The QUEST algorithm made the worst classification according to the model performance criteria. While QUEST algorithm correctly separated Hair goats with a high rate (89.20%), the separation percentage of Honamli goats (67.50%) remained quite low.
Table 4
Classification performances of the data mining algorithms for each diagnosis test
Algorithm
|
Sensitivity
|
Specificity
|
AUC±SE
|
Accuracy of Model
|
Correctly Classify of Honamli breed
|
Correctly Classify of Hair breed
|
P-value
|
MARS
|
0.916
|
0.846
|
0.942±0.028a
|
0.885
|
0.894
|
0.892
|
<0.001
|
CHAID
|
0.911
|
0.841
|
0.880±0.027a
|
0.878
|
0.867
|
0.892
|
<0.001
|
CART
|
0.849
|
0.927
|
0.868±0.023a
|
0.878
|
0.952
|
0.785
|
<0.001
|
Exhaustive CHAID
|
0.861
|
0.855
|
0.853±0.030ab
|
0.858
|
0.892
|
0.815
|
<0.001
|
QUEST
|
0.889
|
0.682
|
0.784±0.032b
|
0.770
|
0.675
|
0.892
|
<0.001
|
a, ab, b The difference between AUC with letter in any data mining algorithm column is significant (P<0.05).
|
CHAID was chosen as the best classifier among the classification trees for the distinction of Honamli Hair goats (Table 4). In the root node of the CHAID diagram, 83 (56.10 %) of the 148 goats were classified as Honamli 65 (43.90 %) and as Hair (Figure 2). When the CHAID diagram is examined, it was determined that the first order effective independent variable on breed discrimination is RH (Adj. P-value = 0.000, χ2 = 59.332), second order is Age (Adj. P-value = 0.014, χ2 = 9.981), and BH (Adj. P-value = 0.036, χ2 = 6.313), and third-order independent variables were LG (Adj. P-value = 0.045, χ2 = 13.362) and CD (Adj. P-value = 0.003, χ2 = 12.577). Branches generated by independent variables in the entire tree structure are statistically significant (P<0.05).
All goats (Node 0) considered in the study were divided into 3 sub-groups (nodes) in terms of RH variable. In the first node, 39 (83%) of the goats with RH = <71.00 cm shorter were Hair and 8 (17%) of them were Honamli. In the second node, 25 Hair (43.1%) and 33 Honamli (56.9%) of 58 goats were classified in a range of 71.0 <RH = <79.0. In the third node, it was determined that 42 of the goats (71.9 <RH) with RH trait more than 79 cm were Honamli (97.7%) and only one of them was Hair goat.
Goats (Node 3rd) with RH characteristics greater than 79 cm formed nodes 6th and 7th in terms of GH characteristics. In the 6th Node, 83.30% of the goats with the BH trait less than 79.50 cm or equal value are classified as Honamli and 16.70% as Hair goat. All of the goats with the BH trait values greater than 79.50 belong to the Honamli breed (Node 7th).
While the 3rd and 4th nodes of the CHAID algorithm diagram showed a division according to the age variable, it did not have a direct but indirect effect on breed discrimination. Accordingly, it was determined that 13 of the goats aged 3 and under are Honamli (92.9%) and one of them is Hair goat (7.1%) (LG = <53.50) in terms of LG (Node 8th). In Node 9, the goats with a value between 53.50 <LG = <59.50 were classified as 2 Honamli (28.6%) and 5 as Hair (71.4%). At node 10, 100% of all goats with the LG trait larger than 79 cm (71.90 <LG) belong to the Honamli breed. In node 11, when CD characteristics of goats older than 3 years are less than and equal to 23.50 cm, (CD = <23.50), 93.30% of goats are classified as Hair and 6.7% as Honamli. If the CD trait is greater than 23.50 cm (23.50 <CD), the probability of finding Honamli goat is 68.80% and 31.20% is Hair goat (Node 12th).