Determination of best-fitted regression model for estimation of body weight in Kanni Adu kids under farmer's management system

A K Thiruvenkadan

Assistant Professor, Department of Animal Genetics and Breeding, Veterinary College and Research Institute,
Namakkal-637 001,Tamil Nadu, India
drthirusiva@yahoo.com

Abstract

Data on body weight and body measurements were individually collected from Kanni Adu kids (114 males and 214 females) from its breeding tract.

The correlation coefficients between body weights and body measurements at different ages were positive and strongly correlated (P<0.01). The correlation coefficient for different body measurements ranged between 0.506 and 0.968. Simple and multiple regression models were fitted with body weight as dependant variable and height at withers, chest girth and body length as independent variables. The coefficient of determination indicated that body measurements succeed to describe more variation in live weight. The chest girth accounted maximum of 80.4 to 93.6 per cent of total variation in body weight. The model constructed with pooled data from birth-12 months of age was the best fitted multiple regression models with chest girth, body length and height at withers as an independent variables (R² = 0.913, MS_E = 1.82 for males and R² = 0.948, MS_E = 1.195 for females). In all age groups the highest R² was obtained, if we include all the body measurements in the regression equation. This suggests that weight could be estimated more accurately by combination of two or more measurements. However, a study of different criteria revealed that model having a larger R² with a smaller MS_E and SD_E produced a better goodness of fit.

It was concluded that the body weight of Kanni Adu kids could be estimated accurately in farmer's field condition using morphometric measurements taken with a tape.

Key words: body weight, correlation, Kanni Adu, prediction, regression

Introduction

Goat rearing is of great importance in Indian households and plays major role for the sustenance of small and marginal farmers and landless agricultural labourers. Kanni Adu goats are found in the southern part of India especially in Tamil Nadu. They are valuable for meat and for their skin (Acharya  1982 and Thiruvenkadan et al 2000a  2000b). Measurements of various body conformations are of value in judging the quantity characteristics of meat and also helpful in developing suitable selection criteria (Bose and Basu  1984;Sarma et al 1984; Sharaby and Suleiman  1987; Islam et al 1991). Knowing the body weight of a goat is important for a number of reasons, related to breeding (selection), feeding and health care. However this fundamental knowledge is often unavailable to those working with goats in the small scale farming sector, due to unavailability of scales. Hence, farmers have to rely on questionable estimates of the body weight of their goats, leading to inaccuracies in decision-making and husbandry. The chief method of weighing animals without scales is to regress body weight on a certain number of body characteristics, which can be measured readily. Body measurements have been used to predict body weight by several authors in many breeds of Indian goats (Tandon  1965; Das et al 1990; Prasad et al 1990; Ulaganathan et al 1992; Singh and Mishra  2004), Sahel goats of Nigeria (Mohammed and Amin  1996; Slippers et al 2000), West African Dwarf goats (Mayaka et al 1995) and Nguni goats (Slippers et al 2000). Such procedures are almost non existent for Kanni Adu goats. Enevoldsen and Kristensen (1997) reported that different models might be needed to predict body weight in different environmental conditions and breeds. Hence, this study has been made to determine the best fitted regression model for prediction of live weight of Kanni Adu goats under field conditions and also to identify the criteria to be applied to investigate fitting state of simple and multiple models to actual data for estimation of body weight.

Material and Methods

Study site and Breed

The study was carried out in Tamil Nadu in the southern part of India. The breed under study, is commonly known as Kanni Adu goats and a detailed description of it may be found elsewhere (Acharya 1982; Thiruvenkadan et al 2000a  2000b).

Data collection

Data were collected from a total of 328 (114 males and 214 females) Kanni Adu goats in its breeding tract. Measurements recorded were live body weight, height at withers, body length and chest girth as per Sasimowski (1987) and as indicated in Photo 1.

Within each group, weight was regressed on body measurements using least square by stepwise regression analysis (Harvey 1990) to determine the combination of body dimensions for each sex that explains variation in the dependent variable (Sharaby and Suleiman 1987). Separate prediction equations were developed for male and female kids. The comparison amongst actual body weight and predicted body weight was made by paired 't' test (Slippers et al 2000). In addition, the prediction bias was estimated using sample average (D_i = W_i - Ŵ_i (i = 1 to n), i.e. D_i - Proportion difference, W_i - Actual weight and Ŵ_i - Predicted weight) and standard deviation (Mayaka et al 1995). Pearson's correlation coefficients were estimated between body weight and all body measurements. To determine the best fitted regression equation the criteria viz., coefficient multiple determination (R²), residual mean square (MS_E) of Snedecor and Cochran (1989) and error standard deviation (SD_E) and range observed in predicted weight were also used for evaluating and comparing different regressions models.

Results and Discussion

Body measurements and body weight

Means and standard errors of live weight and body measurements are presented in Table 1. In all the age groups, among the body measurements, height at withers was highest followed by chest girth and body length. Males had higher values than females of all the traits studied and they were not significantly different.

Correlation coefficient

The correlation coefficients between body weight and body measurements for males and females are presented in Table 2.

Positive and highly significant (P<0.01) correlations were observed. The correlations coefficients observed in Kanni Adu kids was comparable to the reported values of Mukherjee et al  1981, 1986; Singh et al 1987; Das and Sharma  1994; Topal et al 2003 and Topal and Macit  2004. The high correlation coefficients between body weight and body measurements for all age groups suggest that either of these variables or their combination could provide a good estimate for predicting live weight of Kanni Adu kids. Among these three body measurements, chest girth had the highest correlation coefficient in males at 0-3 months and in females at >3-6 months and in both sexes at 0-12 month age groups. The body length had the highest correlation coefficient in males of >3-6 months and in females of >6-9 and >9-12 months. The height at withers had high correlation with body weight in males of >6-9 and >9-12 months and in females of 0-3 months age groups. This tends to infer that at different ages different conformational traits may be more successfully used for selection. The correlations between body weights and body measurements in pooled data from 0-12 months of age were higher than those at different age groups. This might be due to more or less similar environmental influence at different age groups. Looking at the values of the correlation coefficients, in general, females showed a higher tendency of relationship than that of male kids. This agrees to the report of Singh (1975). Since body measurements had high correlation with body weight, this may be used as selection criteria, Bhattacharya et al. (1984) and Bose and Basu (1984) also reported that selection based on body measurements should improve meat production in goats.

Fitted regressions

Table 3 details the regression output including the fitted functions and coefficient of determinations. It shows the seven final models for the estimation of body weight in each age groups of both sexes.

The coefficient of determination (R²) indicated that the body measurements succeed to describe more variation in live weight. The variation of body weight due to body measurements differed between sexes and age groups. Thus chest girth accounted maximum of 80.4 to 93.6 per cent of the total variation in body weight, together with ease of measurement, justifies the use of chest girth as a foremost weight predictor. The higher association of body weight with chest girth was possibly due to relatively larger contribution in body weight by chest girth (consisting of bones, muscles and viscera). It is in concert with findings of Mayaka et al 1995; Mohammed and Amin 1996; Benyi 1997; Myeni and Slippers 1997; Nesamvuni et al 2000; Slippers et al 2000; Topal et al 2003 and Topal and Macit 2004.

Using of chest girth was less reliable in predicting the body weight at >6-9 and >9-12 months age groups. In these age groups height at withers and body length accounted for the greatest amount of variation in body weight for males and females respectively. This result is similar to the report of Mukherjee et al 1981, 1983; Prasad et al1990 and Ulaganathan et al 1992. In general, the analysis of R² at different age groups in both sexes revealed that a comparatively lower relationship between body weight and body height was observed. This is mainly due to the fact that the height is due to growth of bones, whose function of increase in weight is probably not proportionate to increase in general body weight. The results are supported by other research (Singh et al 1979a; Mukherjee et al 1983; Bhattacharya et al 1984, Das et al 1990 and Ulaganathan et al 1992). As the age advances, the coefficient of determination for all characteristics decreased. This indicated that body measurements could predict 0-6 months body weight more accurately than >6-12 months body weight. On the contrary, Das and Sharma (1994) reported lower R² values for weaning than those of yearling weight. However, highest variation of body weight was accounted for by combination of height at withers, chest girth and body length than individually of all the age groups in both sexes. These results are also supported by Bose and Basu  (1984); Bhattacharya et al (1984); Prasad et al (1990); Das and Sharma  (1994); Topal et al (2003) and Topal and Macit  (2004). Since in all the age groups the highest R² was obtained when all the body measurements were included in the regression equations, this suggests that weight could be estimated more accurately by combination of two or more measurements than by girth alone.

The coefficient of determination (R²) was highest (89.1 per cent in males and 93.6 per cent in females) in a regression model constructed using pooled data, within sexes, from 0-12 months of age, when compared to equations constructed at different age groups. Hence, this regression equation alone may be used to predict the body weight of Kanni Adu goats at different age groups. Mayaka et al (1995) reported similar findings.

Prediction accuracy

Table 4 shows the statistical parameters viz.  R², MS_E , F value, C.V and SD_E for all the regression equations investigated. In a multiple regression analysis the important thing to be considered was which independent variables were most considered in determining the dependent variable.

As a criterion, the value of R² always increased as more independent variables were added to the regression. So, R² was not suitable for comparing the different equations. Hence, the criterion that was free from this disadvantage viz., residual mean square (MS_E) as per Snedecor and Cochran (1989) was used. Inclusion of chest girth and body length at 0-3 and >3-6 months in males, all the three body measurements at 0-3 months in females and at 0-12 months in both sexes, height at withers and body length at >6-9 months of both sexes, height at withers and chest girth at >3-6 months of females, height at withers alone at >9-12 months in males and body length at >9-12 months in females produced higher R² with the smallest MS_E and SD_E. Hence, at different age groups, the regression equation with the above combinations may be used for estimating the body weight of Kanni Adu kids at respective age groups. Selection of criteria for prediction indicated that the independent variables with the smallest residual mean square might be selected. Since the decrease of residual mean square (MS_E) resulted in decrease of error standard deviation (SD_E), the same may also be used as a criterion. This is similar to the report of Topal et al (2003), Topal and Macit (2004). Ulaganathan et al (1992) who reported that larger R² and smaller MS_E produced better goodness of fit.

The coefficient of variation for males (residual standard deviation/ mean of the dependent variable) was 6.1 to 19.7 per cent for males and 8.1 to 18.9 per cent for females. The F values were highly significant in both males and females of all age groups except at >6-9 months and >9-12 months in males. These results are similar to the report of Singh et al 1979a, 1979b; Bhattacharya et al 1984.

The predicted weight, difference between actual weight in proportions and the range for actual and predicted weight in different equations of both sexes is presented in Table 5.

In all the age groups of both sexes there was no significant difference between actual weight and predicted weight. But there was a difference in range values in each equation and the approximation to the actual was observed in equations with high R² and lower MS_E and SD_E. Cross validation was performed for males and females for different equations and in most cases the prediction bias did not differ from zero. The equations with larger R² with smallest MS_E and SD_E showed a range similar to the range observed in actual weight category. Lower R² showed wide variation of range, which was, much higher than those observed in actual weight of both sexes.

Conclusions

• Body weight and the three body measurements were significantly correlated with each other.

• Body weight had higher association with heart girth than with length or height.

• Correlations and coefficient of determination between 0-12 months age groups were higher than between weight at 0-3, >3-6, >6-9 and >9-12 months age group separately.

• Instead of using separate equations for different age groups, the regression equation of 0-12 months may be used for predicting the body weight of Kanni Adu goats at different ages.

• The chest girth alone or combinations of three measurements, may be used for predicting the body weight.

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