COLLINEARITY DIAGNOSES AND CORRECTION IN PREDICTIVE MODELS OF NIGERIAN LOCAL CHICKEN OF TWO GENOTYPES USING PRINCIPAL COMPONENT ANALYSIS

Samuel Ter Vincent

Abstract


This paper was aimed at investigating the relationship between body weight and body measurements in normal feathered and naked neck genotypes so as to ascertain the existence or otherwise of collinearity instability. If detected, fix the problem using PCA. Body weight (BW) and seven linear body dimensions; chest circumference (CC), body length (BL), wing span (WS), thigh length (TL), shank length (SL), neck length (NL) and beak length (BkL) were taken from one-hundred and fifty-six matured local chickens comprising 97 normal feathered (57 males and 40 females) and 59 naked necks (24 males and 35 females). GLM was used to study genotype and sex effects. Naked neck birds (NNBs) had higher values for BW, CC, BL and TL compared to their normal feathered (NF) counterparts. Sexual dimorphism was observed in all the traits with higher values recorded for males. Phenotypic correlations among BW and biometric traits were positive and highly significant (r = 0.51-0.95 and 0.52-0.98; <0.01 for NFBs and NNBs). Collinearity diagnosis revealed two severe cases each in NFBs (VIF = 12.60 (CC) and 13.75 (BL)) and NNBs (VIF = 26.39 (CC) and 23.12 (BL)). Collinearity problems were further confirmed from the computations of the eigenvalues of the correlation matrix, condition indexes and variance proportion. Using varimax rotation of the transformation matrix, three Principal Components (PCs) were extracted each for NFB and NNB. The three extracted PCs accounted for 90.913% and 87.086% of the total variance for NFB and NNB respectively. Linear regression of extracted PCs against BW revealed that tolerance (T) = 1 for all the extracted components. This implies that no percentage of the variance in the PC1 of NFBs and NNBs could be explained by the other extracted PCs (PC2 and PC3) included in the model; this clearly shows that the collinearity has been fixed.  Further confirmation test with VIF shows that, VIF of PCFS equaled one which neatly shows that the variances of the estimated coefficient were no longer inflated.

  

Keywords


Collinearity, Principal component analysis, Normal feathered birds, Naked neck birds, Variance inflation factor

References


Adeleke, M. A., Peters, S. O., Ozoje, M. O., Ikeobi, C. O. N., Bamgbose, A. M., & Adebambo O. A. (2011). Genetic parameter estimates for body weight and linear body measurements in pure and crossbred progenies of Nigerian indigenous chickens. Livestock Research for Rural Development. 23 (1)

Afolayan R. A., Adeyinka, I. A. & Lakpini C. A. M. (2006). The estimation of live weight from body measurements in Yankasa sheep. Czech J. Anim. Sci. (8):343-348.

Ajayi, F. O.(2010). Nigerian indigenous chicken: A valuable genetic resource for meat and egg production. Asian Journal of Poultry Science. 4:164-172.

Ajayi, F.O. (2010). Nigerian indigenous chicken: A valuable genetic resource for meat and egg production. Asian Journal of Poultry Science. 4:164-172.

Alemayehu, T., Tikabo, G., & Gangwar, S. K. (2012). Application of linear body measurements for predicting body weight of Abergelle goat breed in Tigray region, Northern-Ethiopia. Global Journal of Bio-Science and Biotechnology. 1(2): 314-319.

Alin, A. (2010). Multicollinearity. - WIREs Computational Statistics

Bagui N.J.G., & Valdez, C.A. (2007). Live weight estimation of locally raised adult purebred Brahman cattle using external body measurements. Philippine Journal of Veterinary Medicine. 44, 36-42.

Belsley D.A., Kuh, E., & Welsch, R.E. (1980). Regression diagnostics: Identifying influential data sources of collinearity. 1 Edition, John Wiley and Sons, New York, pp. 292.

Blanckenhorn, W. U. (2005). Behavioral causes and consequences of sexual size dimorphism. Ethology 2005, 111: 977–1016.

Clutton-Brock, T. H., Albon, S. D., & Harvey, P. H. (1980). Antlers, body size, and breeding group size in the Cervidae. Nature (Lond.) 285: 565–567.

Clutton-Brock, T. H., Guinness, F. E., & Albon, S. D. (1982). Red deer: behavior and ecology of two sexes. University of Chicago, Chicago 1982.

Darwin, C. (1871). The descent of man, and selection in relation to sex. D. Appleton, New York.

Dascalu, C. G., & Cozma, C. D. (2009). Principal components analysis – method to reduce the collinearity in multiple linear regression models; application in medical studies. Proceedings of the 2nd WSEAS International Conference on Multivariate Analysis and its Application in Science and Engineering. Pp 140-145

Dormann, C. F., Elith J., Bacher, S., Buchmann C., Carré, G., Marquéz, J. R. G., Gruber, B., Carl, G., Lafourcade, B., Leitão, P. J., Münkemüller, T., McClean, C., Osborne, P. E., Reineking, B., Schröder, B., Skidmore, A. K., Zurell, D., & Lautenbach, S. (2013). Collinearity: a review of methods to deal with it and a simulation study evaluating their performance. Ecography. 36(1):027-046

Durosaro, S. O., Oyetade, M. S., Ilori, B. M., Adenaike, A. S., Olowofeso, O., Wheto, M., Amusan, S. A., Osho, S.O., & Ozoje, M.O. (2013). Estimation of body weight of Nigerian local turkeys from zoometric measurements at 4, 8 and 12 weeks of age. Global Journal of Science Frontier Research (Bio-Tech and Genetics). 2013,13(1)

Freund, R. J., & Wilson, W. J. (1998). Regression analysis: Statistical modeling of a response variable. Academic Press, San Diego, California, USA, pp444.

Galal, A. (2000). Pleiotropic effects of naked neck, frizzled and double segregation genes on some phenotypic and genetic parameters of chickens under hot environmental conditions. Egypt Poult. Sci. 20:945-960.

Gill J.L. (1986). Outliers and influence in multiple regression. J. Anim. Breeding and Genetics. 103: 161175.

IBM-SPSS 20.0.0 (2011). International Business Machines Corp-Statistical Package for Social Sciences. IBM Inc. and SPSS Inc., 444 Michigan Avenue, Chicago.

Kaiser HF (1974). An index to factorial simplicity. Psychometrika. 39(1): 13-36.

Khan, M. A., Tariq, M. M., Eydduran, E., Tatliyer, A., Rafeeq, M., Abbas, F., Rashid, N., Awan, M. A., & Javed, K. (2014). Estimating body weight from several body measurements in Harnai sheep without multicollinearity problem. The Journal of Animal & Plant Sciences. 24(1): 120-126.

LeBlanc, M., Festa-Bianchet, M., & Jorgenson, J.T. (2001). Sexual size dimorphism in bighorn sheep (Ovis Canadensis): effect of population density. Can. J. Zool. 2001, 79:1661-1670

Malau-Aduli A.E.O., Aziz, M.A., Kojina, T., Niibayashi, T., Oshima, K. & Komatsu, M. (2004). Fixing collinearity instability using principal component and ridge regression analyses in the relationship between body measurements and body weight in Japanese Black cattle. J. Anim. Vet. Adv. 3: 856-863.

McCracken, K.V., Paton D. C., & Afton, A. D. (2000). Sexual size dimorphism of the Musk duck. Wilson Bull. 112: 457- 466.

Momoh, O. M., Nwosu, C.C., & Adeyinka, I. A.(2010). Comparative evaluation of two Nigerian local chicken ecotypes and their crosses for growth traits. International Journal of Poultry Science 9: 738-743.

Mulyono, R. H., Gunawan. A., & Sumantri, C. (2009). Characteristics of size and shape of body dimension of Madura and Rote (Indonesia) Fat-Tailed Sheep using PCA. The 1st Int. Sem. on Anim. Indust., 253-258.

Nwagu, B. I.(2002) Production and Management of Indigenous Poultry Species.A Training Manual in National Training Workshop on Poultry Production at Nigerian National Animal Production Research Institute, Shika, Zaria. Pp. 10-26.

Patra, B.N., Bais, R.K.S., Prasad, R.B., & Singh, B.P. (2002). Performance of naked neck versus normally feathered coloured broilers for growth, carcass traits and blood biochemical parameters in tropical climates. Asian-Aust. J. Anim. Sci. 12: 560-563.

Pimentel E.C.G., Queiroz, S.A., & Carvalheiro, R. (2007). Fries, L.A, Use of ridge regression for prediction of early growth performance in crossbred calves. Genet. Mol. Biol. 30: 536-544.

Pinto, L. F. B., Dacker, I. U. De melo, C. M. R., Ledur, M. C., & Coutinho, L. L. (2006). Principal components analysis applied to performance and carcass traits in the chicken. Anim. Res. 55: 419-425

RIM (1992). Nigerian livestock resources. Vol. II. National synthesis. Annex Publ. Resource Inventor Management Ltd.

Rook A. J., Dhanoa, M.S., & M. Gill, 1990. Prediction of the voluntary intake of grass silages by beef cattle. 2. Principal component and ridge regression analyses. Anim. Prod., 50: 439 -454.

Roso V.M., Schenkel, F.S., Miller, S.P., & Schaeffer, L.R. (2005). Estimation of genetic effects in the presence of multicollinearity in multibreed beef cattle evaluation. J. Anim. Sci. 83: 1788-1800.

Salako AE (2006). Principal component factor analysis of morphostructure of immature sheep. Int. J. Morphol. 24:571-574

Semakula, J., Mutetikka, D., Kugonza, R. D., & Mpairwe, D. (2010). Variability in body morphometric measurements and their application in predicting live body weight of

Mubende and Small East African goat in Uganda. Middle-East J. Sci. Res. 5(2): 98-105.

Semakula, J., Lusembo, P., Kugonza, D. R., Mutetikka, D., Ssennyonjo, J., & Mwesigwa, M. (2011). Estimation of live body weight using zoometrical measurements for improved marketing of indigenous chicken in the Lake Victoria basin of Uganda. Livestock Research for Rural Development 2011, 23:170

Sri Rachma A. B., Hiroshi, H., Muh, I. A. D, Lellah, R., & Kusumandari, I. P. (2013). Study of body dimension of Gaga’s chicken, germ plasm of local chickens from south Sulawesi-Inddonesia. International Journal of Plant, Animal and Environmental Science. 3(4): 204-209.

Vincent, S. T., Araku, J. O., Ayongu, F., Chia, S. S., Momoh, O. M., & Yakubu, A. (2014). Redundancy Elimination from Morpho-Stuctures of Nigerian Uda Rams Using Principal Component Analysis. Journal of Animal Production Advances. 4(10): 520-526

Yakubu, a. (2010).Fixing multicollinearity instability in the prediction of body weight from morphometric traits of white Fulani cows. Journal of Central European Agriculture. 11(4): 487-492.

Yakubu, A., Kuje, D., & Okpeku, M. (2009). Principal Components as measures of size and shape in Nigerian indigenous chickens. Thai J. Agr. Sci., 42(3): 167-176.

Yamaki, M., Correa, G. S. S., Silva, M. A., Barbosa, L., & Torres, R. A. (2006). Evaluation of quail carcass traits using principal component analysis. Proceedings of the 8th World Congress on Genetics Applied to Livestock Production, August 13-18, Belo Horizonte, MG, Brazil.

Yilmaz, O., Cemal, I., & Karaca, O. (2013). Estimation of mature live weight using somebody measurements in Karya sheep. Trop. Anim. Heath Prod. 45: 397–403.

Yunusa, A. J., Salako, A. E., & Oladejo, O. A. (2013). Principal component analysis of the morphostructure of Uda and Balami sheep in Nigeria. International Journal of Agricultural Science. 1(3): 45-51.

Yamaki, M., Correa, G. S. S., Silva, M. A., Barbosa, L. and Torres, R. A. (2006). Evaluation of quail carcass traits using principal component analysis. Proceedings of the 8th World Congress on Genetics Applied to Livestock Production, August 13-18, Belo Horizonte, MG, Brazil.

Yunusa, A. J., Salako, A. E. and Oladejo, O. A. (2013). Principal component analysis of the morphostructure of Uda and balami sheep in Nigeria. International Journal of Agricultural Science. 1(3): 45-51.


Refbacks

  • There are currently no refbacks.


Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.