Canonical correlations in agricultural research: Method of interpretation used leads to greater reliability of results


  • Maria Inês Diel Universidade Federal de Santa Maria
  • Alessandro Dal'Col Lúcio Universidade Federal de Santa Maria
  • Darlei Michalski Lambrecht Universidade Federal de Santa Maria
  • Marcos Vinícius Marques Pinheiro Universidade Federal de Viçosa
  • Bruno Giacomini Sari Universidade Federal de Santa Maria
  • Tiago Olivoto Universidade Federal de Santa Maria
  • Oscar Valeriano Sánchez Valera Instituto Nacional do México
  • Patrícia Jesus de Melo Universidade Federal de Santa Maria
  • Francieli de Lima Tartaglia Federal University of Santa Maria
  • André Luis Tischler Federal University of Santa Maria
  • Denise Schmidt Universidade Federal de Santa Maria



Canonical weights, Canonical loadings, Cross-loadings, Multicollinearity, Methods


Canonical correlations analyzes are being used in the agrarian sciences and constitute an important tool in the interpretation of results. This analysis is performed by complicated mathematical equations and it is only possible to use it thanks to the development of computational software, which allow different interpretations of results, and it is up to the researcher to choose according to his knowledge. Canonical correlations can be interpreted using canonical weights, canonical loadings, or canonical cross-loadings. In Brazil, most of the works that use these analyzes interpret the canonical weights. Therefore, this study aims to show, through an analysis of canonical correlations, the best way to interpret the results, so that they are presented in the most reliable way possible. Data from an experiment with two cultivars of biquinho pepper seeded in 5 light spectrums were performed. The variables were root length and volume, plant height, number of leaves, fresh shoot and root mass, shoot dry mass. Two groups of variables were organized, the multicollinearity was determined through the condition number and the inflation factor of the variance. Canonical correlations analysis was carried out, and weights, loadings, and canonical cross-loadings were estimated for the interpretation of the results. After the interpretations, it was defined that the canonical cross-loadings should be preferred for the interpretation of the canonical correlations. Weights or canonical coefficients provide dubious results of relationships between groups of characters and should be avoided.


Download data is not yet available.

Author Biographies

Francieli de Lima Tartaglia, Federal University of Santa Maria

Department of Plant Science

André Luis Tischler, Federal University of Santa Maria

Department of Plant Science


Akbas Y. and Takma C. (2005). Canonical correlation analysis for studying the relationship between egg production traits and body weight, egg weight and age at sexual maturity in layers, Czech Journal of Animal Science, 50, 163–168.

Alves B.M., Cargnelutti Filho A. and Burin C. (2017). Multicollinearity in canonical correlation analysis in maize., Genetics and Molecular Research 16, gmr16019546.

Alves B.M., Cargnelutti Filho A., Toebe M. and Burin C. (2016). Linear relations among phenological, morphological, productive and protein-nutritional traits in early maturing and super-early maturing maize genotypes, Journal of Cereal Science 70, 229–239.

Alves B.M., Filho A.C., Burin C. and Toebe M. (2017). Linear associations among phenological, morphological, productive, and energetic-nutritional traits in corn, Pesquisa Agropecuaria Brasileira, 52, 26–35.

Bandinelli M.G., Bisognin D.A., Storck L., Gnocato F.S., Kielse P., Ascoli C., (2017). Correlação de caracteres de planta e tubérculo nas primeiras gerações de seleção de batata, Horticultura Brasileira, Associação Brasileira de Horticultura, 35, 82–88.

Basu A. and Mandal A. (2010). Canonical Correlation, International Encyclopedia of Education, 52–57.

Blalock H.M. (1963). Correlated Independent Variables: The Problem of Multicollinearity, Social Forces, 42, 233–237.

Borchers H.W. (2018). pracma: Practical Numerical Math Functions.

Brum B., Lopes S.J., Storck L., Lucio A.D., de Oliveira P.H. and Milani M. (2011). Canonical correlation between variables seed, seedling, plant and grain yield in castor bean, Ciencia Rural, 41 , 404–411.

Butts C.T. (2018). yacca: Yet Another Canonical Correlation Analysis Package.

Cocozzelli C. (1990). Understanding Canonical Correlation Analysis : Describing Underlying Relations Between Sets of Variables, Journal of Social Service Research, 13, 19–42.

Cruz C.D., Regazzi A.J. and Carneiro P.C.S. (2012). Modelos Biométricos Aplicados Ao Melhoramento Genético, 4th ed., Editora UFV, Viçosa.

Hair J.F., Black W.C., Babin B.J. and Anderson R.E. (1998). Multivariate Data Analysis, Prentice-Hall, Inc, 1,

Hair J.F., Black W.C., Babin B.J., Anderson R.E. and Tatham R.L. (2009). Análise Multivariada de Dados, 6th ed., Bookman, Porto Alegre.

Hotelling H. (1936). Relations Between Two Sets of Variates, Biometrika, 28 3/4, p. 321.

Kazmi R.H., Willems L.A.J., Joosen R.V.L., Khan N., Ligterink W. and Hilhorst H.W.M. (2017), Metabolomic analysis of tomato seed germination, Metabolomics 13 12, p. 145.

Lambert Z. V. and Durand R.M. (1975). Some Precautions in Using Canonical Analysis, Journal of Marketing Research, 12, 468–475.

Marubayashi Hidalgo A., Pinheiro da Silva L., Reis Mota R. and Nunes Martins E. (2014). Canonical-correlation analysis applied to selection-index methodology in quails, Livestock Science 169, 35–41.

Meredith W. (1964). Canonical correlations with fallible data, Psychometrika, 29 1, p. .

Montgomery D.C. and Peck E.A. (1982). Introduction to Linear Regression Analysis, John Wiley & Sons, Ltd., New York.

Nimon K., Henson R.K. and Gates M.S. (2010). Revisiting interpretation of canonical correlation analysis: A tutorial and demonstration of canonical commonality analysis, Multivariate Behavioral Research 45, 702–724.

Protasio T. de P., Guimarães Neto R.M., Santana J. de D.P. de, Guimarães Júnior J.B. and Trugilho P.F. (2014), Canonical correlation analysis of the characteristics of charcoal from Qualea parviflora Mart., Revista Cerne 20, 81–88.

Rigão M.H., Storck L., Bisognin D.A. and LopesS.J. (2009). Correlação canônica entre caracteres de tubérculos para seleção precoce de clones de batata, Ciência Rural 39, 2347–2353.

Takada K., Lowe A.A. and Freund V.K. (1984). Canonical correlations between masticatory muscle orientation and dentoskeletal morphology in children, Am. J. Orthod., 86, 331–341.




How to Cite

Diel, M. I. ., Lúcio, A. D. ., Michalski Lambrecht, D., Pinheiro, M. V. M. ., Sari, B. G. ., Olivoto, T. ., Valera, O. V. S. ., Melo, P. J. de ., Tartaglia, F. de L. ., Tischler, A. L. ., & Schmidt, D. . (2020). Canonical correlations in agricultural research: Method of interpretation used leads to greater reliability of results. International Journal for Innovation Education and Research, 8(7), 171–181.

Most read articles by the same author(s)