Register      Login
Crop and Pasture Science Crop and Pasture Science Society
Plant sciences, sustainable farming systems and food quality
Shopping Cart: ( empty )
You are here: Home > Journals > CP > CP23135
RESEARCH ARTICLE
Contents Vol 75(3)

Multivariate assumptions and effect of model parameters in path analysis in oat crop

Jaqueline Sgarbossa https://orcid.org/0000-0001-7541-090X A * , Alessandro Dal’Cól Lúcio https://orcid.org/0000-0003-0761-4200 A , José Antonio Gonzalez da Silva https://orcid.org/0000-0002-9335-2421 B , Braulio Otomar Caron https://orcid.org/0000-0002-6557-3294 C , Maria Inês Diel https://orcid.org/0000-0002-7905-2166 D , Tiago Olivoto https://orcid.org/0000-0002-0241-9636 E , Claiton Nardini https://orcid.org/0000-0001-5791-6720 F , Odenis Alessi https://orcid.org/0000-0002-3509-6984 B and Darlei Michalski Lambrecht https://orcid.org/0000-0002-1376-3504 A
+ Author Affiliations
- Author Affiliations

A Department of Plant Science, Federal University of Santa Maria, Santa Maria, Rio Grande do Sul, Brazil.

B Department of Agronomy, Regional University of Northwestern Rio Grande do Sul State, Ijuí, Rio Grande do Sul, Brazil.

C Department of Agronomy and Natural Sciences, Federal University of Santa Maria Campus Frederico Westphalen, Frederico Westphalen, Rio Grande do Sul, Brazil.

D Federal University of Pampa, Itaqui, Rio Grande do Sul, Brazil.

E Department of Plant Science, Federal University of Santa Catarina, Florianópolis, Santa Catarina, Brazil.

F Department of Forest Science, Federal University of Paraná, Curitiba, Paraná, Brazil.

* Correspondence to: sgarbossajs@yahoo.com

Handling Editor: Davide Cammarano

Crop & Pasture Science 75, CP23135 https://doi.org/10.1071/CP23135
Submitted: 12 May 2023  Accepted: 7 February 2024  Published: 1 March 2024

© 2024 The Author(s) (or their employer(s)). Published by CSIRO Publishing

Abstract

Context

Path analysis (PA) is a widely used multivariate statistical technique. When performing PA, the effects of the parameters of the mathematical model relating to the experimental design are disregarded, working only with the average effects of the treatments.

Aims

We aimed to analyse the implications of statistical assumptions, and of removing mathematical model parameters, on the PA results in oat.

Methods

A field study was conducted in southern Brazil in five crop years. The experimental design employed was a two-factor 22 × 5 randomised complete block design, characterised by 22 cultivars and five fungicide applications, with three repetitions. Six explanatory variables were measured, panicle length, panicle dry mass, panicle spikelet number, panicle grain number, panicle grain dry mass, and harvest index, and the primary variable yield. Initially, normality and multicollinearity diagnoses were carried out and correlation coefficients were calculated. The PA was performed in three ways: traditional, with measures to address multicollinearity (ridge), and traditional with eliminating variables.

Key results and conclusions

The occurrence of multicollinearity resulted in obtaining path coefficients without biological application. Removing the model’s parameters modifies the path coefficients, with average changes of 10.5% and 13.3% in the direction, and 24.7% and 23.0% in the magnitude, of the direct and indirect effects, respectively.

Implications

This new approach makes it possible to remove the influences of treatments and experimental design from observations and, consequently, from path coefficients and their interpretations. Therefore, the researcher will reduce possible bias in the coefficient estimates, highlighting the real relationship between the variables, and making the results and interpretations more reliable.

Keywords: Avena sativa, linear relationships, multicollinearity, multivariate analysis, parameter removal, simple correlation, variable elimination, yield components.

References

Alessi O, Dornelles EF, Mamann ÂTWd, Kraisig AR, Henrichsen L, Marolli A, Pansera V, Silva JAGd (2018) Aplicação de modelos de regressão e de adaptabilidade e estabilidade na identificação de cultivares de aveia branca com maior resistência genética a doenças foliares. Proceeding Series of the Brazilian Society of Computational and Applied Mathematics 6, 1-7.
| Crossref | Google Scholar |

Alvares CA, Stape JL, Sentelhas PC, de Moraes Gonçalves JL, Sparovek G (2013) Köppen’s climate classification map for Brazil. Meteorologische Zeitschrift 22, 711-728.
| Crossref | Google Scholar |

Benin G, Carvalho FIFd, Oliveira ACd, Marchioro VS, Lorencetti C, Kurek AJ, Silva JAG, Cargnin A, Simoni D (2003) Estimativas de correlações e coeficientes de trilha como critérios de seleção para rendimento de grãos em aveia. Revista Brasileira de Agrociência 9, 9-16.
| Google Scholar |

Bibi A, Shahzad AN, Sadaqat HA, Tahir MHN, Fatima B (2012) Genetic characterization and inheritance studies of oats (Avena sativa L.) for green fodder yield. International Journal of Biology, Pharmacy and Allied Sciences 1, 450-460.
| Google Scholar |

Borchers HW (2021) pracma: practical numerical math functions. CRAN. R-project. Available at https://cran.r-project.org/package=pracma

Bowman A, Crawford E, Alexander G, Bowman RW (2007) rpanel: simple interactive controls for R functions using the tcltk package. Journal of Statistical Software 17, 1-18.
| Crossref | Google Scholar |

Box GEP, Cox DR (1964) An analysis of transformations. Journal of the Royal Statistical Society: Series B (Methodological) 26, 211-243.
| Crossref | Google Scholar |

Caierão E, Carvalho FIFd, Pacheco MT, Lonrecetti C, Marchioro VS, Silva JG (2001) Seleção indireta em aveia para o incremento no rendimento de grãos. Ciência Rural 31, 231-236.
| Crossref | Google Scholar |

Caierão E, Carvalho FIFd, Floss EL (2006) Seleção indireta para o incremento do rendimento de grãos em aveia. Ciência Rural 36, 1126-1131.
| Crossref | Google Scholar |

Cargnelutti Filho A, Toebe M, Alves BM, Burin C, Santos GOd, Facco G, Neu IMM (2015) Relações lineares entre caracteres de aveia preta. Ciência Rural 45, 985-992.
| Crossref | Google Scholar |

Carvalho CGPd, Oliveira VR, Cruz CD, Casali VWD (1999) Análise de trilha sob multicolinearidade em pimentão. Pesquisa Agropecuária Brasileira 34, 603-613.
| Crossref | Google Scholar |

Cassol LC, Piva JT, Soares AB, Assmann AL (2011) Produtividade e composição estrutural de aveia e azevém submetidos a épocas de corte e adubação nitrogenada. Revista Ceres 58, 438-443.
| Crossref | Google Scholar |

Conab (2019) Acompanhamento da safra brasileira de grãos: safra 2019/20 - Terceiro levantamento. 3. v. 7. Companhia Nacional de Abastecimento, Brasília, DF. Available at https://www.conab.gov.br/info-agro/safras/graos/boletim-da-safra-de-graos?start=50 [accessed 21 January 2020]

Conab (2021) Acompanhamento da safra brasileira de grãos: safra 2021/22 - Segundo levantamento. 2. v. 9. Companhia Nacional de Abastecimento, Brasília, DF. Available at https://www.conab.gov.br/info-agro/safras/graos/boletim-da-safra-de-graos?start=20 [accessed 15 December 2021]

Couto MRM, Lúcio AD, Lopes SJ, Carpes RH (2009) Transformações de dados em experimentos com abobrinha italiana em ambiente protegido. Ciência Rural 39, 1701-1707.
| Crossref | Google Scholar |

Cruz CD (2005) ‘Princípios de Genética Quantitativa.’ (UFV: Viçosa - MG, Brazil)

Cruz CD, Regazzi AJ, Carneiro PCS (2012) ‘Modelos biométricos aplicados ao melhoramento genético.’ (UFV: Viçosa, Brazil)

Dornelles EF, Silva JAGd, Carvalho IR, Alessi O, Pansera V, Lautenchleger F, Stumm EMF, Carbonera R, Bárta RL, Tisott JV (2020) Resistance of oat cultivars to reduction in fungicide use and a longer interval from application to harvest to promote food security. Genetics and Molecular Research 19, 1-12.
| Crossref | Google Scholar |

Dumlupinar Z, Maral H, Kara R, Dokuyucu T, Akkaya A (2011) Evaluation of Turkish oat landraces based on grain yield, yield components and some quality traits. Turkish Journal of Field Crops 16, 190-196.
| Google Scholar |

Falconer DS, Mackay TF (1997) ‘Introduction to quantitative genetics.’ (Pearson Education India: London)

Faraway J (2016) faraway: functions and datasets for books by Julian Faraway. Cran. R-project. Available at https://cran.r-project.org/package=faraway

Ferreira DF (2009) ‘Estatística Básica.’ (UFLA: Lavras, Brazil)

Fox J, Weisberg S (2019) ‘An R companion to applied regression.’ (Sage)

Hair JF, Black WC, Babin BJ, Anderson RE, Tatham RL (2009) ‘Análise multivariada de dados.’ (Bookman)

Harrell FE (2021) Frank E Harrell. CRAN. R-project. Available at https://cran.r-project.org/package=Hmisc

Kaziu I, Kashta F, Celami A (2019) Estimation of grain yield, grain components and correlations between them in some oat cultivars. Albanian Journal of Agricultural Sciences 18, 13-19 Available at https://www.proquest.com/scholarly-journals/estimation-grain-yield-components-correlations/docview/2317872862/se-2.
| Google Scholar |

Korkmaz S, Goksuluk D, Zararsiz G (2014) MVN: an R package for assessing multivariate normality. The R Journal 6, 151-162.
| Crossref | Google Scholar |

Kraisig AR, Silva JAGd, Carvalho IR, Mamann ÂTWD, Corso JS, Norbert L (2020) Time of nitrogen supply in yield, industrial and chemical quality of oat grains. Revista Brasileira de Engenharia Agrícola e Ambiental 24, 700-706.
| Crossref | Google Scholar |

Kutner MH, Nachtsheim CJ, Neter J (2004) ‘Applied linear regression models.’ (McGraw-Hill: Boston, MA, USA)

Leite JGDB, Federizzi LC, Bergamaschi H (2012) Mudanças climáticas e seus possíveis impactos aos sistemas agrícolas no Sul do Brasil. Agrária 7, 337-343 Available at http://www.agraria.pro.br/ojs32/index.php/RBCA/article/view/v5i3a1239/993.
| Google Scholar |

Lúcio AD, Storck L, Krause W, Gonçalves RQ, Nied AH (2013) Relações entre os caracteres de maracujazeiro-azedo. Ciência Rural 43, 225-232.
| Crossref | Google Scholar |

Mantai RD, Silva JAGd, Marolli A, Mamann ÂTWd, Sawicki S, Krüger CAMB (2017) Simulation of oat development cycle by photoperiod and temperature. Revista Brasileira de Engenharia Agrícola e Ambiental 21, 3-8.
| Crossref | Google Scholar |

Mantai RD, Silva JAGd, Binelo MO, Sausen ATZR, Rossi DS, Corso JS (2020a) Nitrogen management in the relationships between oat inflorescence components and productivity. Revista Brasileira de Engenharia Agrícola e Ambiental 24, 385-393.
| Crossref | Google Scholar |

Mantai RD, Silva JAGd, Scremin OB, Carvalho IR, Magano DA, Fachinetto JM, Lautenchleger F, Rosa JAd, Peter CL, Berlezi JD, Babeski CM (2020b) Nitrogen levels in oat grains and its relation to productivity. Genetics and Molecular Research 19, 1-13.
| Crossref | Google Scholar |

Meira D, Meier C, Olivoto T, Follmann DN, Rigatti A, Lunkes A, Marchioro VS, Souza VQd (2019a) Multivariate analysis reveals genetic divergence and promising traits for indirect selection in black oat. Revista Brasileira de Ciências Agrárias 14, 1-7.
| Crossref | Google Scholar |

Meira D, Meier C, Olivoto T, Nardino M, Klein LA, Moro ED, Fassini F, Marchioro VS, Souza VQd (2019b) Estimates of genetic parameters between and within black oat populations. Bragantia 78, 43-51.
| Crossref | Google Scholar |

Meira D, Meier C, Olivoto T, Nardino M, Rigatti A, Klein LA, Caron BO, Marchioro VS, Souza VQD (2019c) Phenotypic variance of black oat growing in crop seasons reveals genetic effects predominance. Anais Da Academia Brasileira De Ciências 91, e20180036.
| Crossref | Google Scholar |

Montgomery DC, Peck EA (1982) ‘Introduction to linear regression analysis.’ (John Wiley and Sons, Inc.: New York, NY, USA)

Moradi M, Rezai A, Arzani A (2005) Path analysis for yield and related traits in oats. Journal of Science and Technology of Agriculture and Natural Resources 9, 173-180.
| Google Scholar |

Moreira FB, Cecato U, Prado INd, Wada FY, Rêgo FCdA, Nascimento WGd (2008) Avaliação de aveia preta cv Iapar 61 submetida a níveis crescentes de nitrogênio em área proveniente de cultura de soja. Acta Scientiarum. Animal Sciences 23, 815-821.
| Crossref | Google Scholar |

Moreira SO, Gonçalves LSA, Rodrigues R, Sudré CP, Júnior ATdA, Medeiros AM (2022) Correlações e análise de trilha sob multicolinearidade em linhas recombinadas de pimenta (Capsicum annuum L.). Revista Brasileira de Ciências Agrárias 8, 15-20.
| Crossref | Google Scholar |

Olivoto T, de Souza VQ, Nardino M, Carvalho IR, Ferrari M, de Pelegrin AJ, Szareski VJ, Schmidt D (2017) Multicollinearity in path analysis: a simple method to reduce its effects. Agronomy Journal 109, 131-142.
| Crossref | Google Scholar |

R Core Team (2021) R: a language and environment for statistical computing. Available at https://www.r-project.org/

Rodrigues GB, Marim BG, Silva DJHd, Mattedi AP, Almeida VdS (2010) Análise de trilha de componentes de produção primários e secundários em tomateiro do grupo Salada. Pesquisa Agropecuária Brasileira 45, 155-162.
| Crossref | Google Scholar |

Royston JP (1983) Some techniques for assessing multivariate normality based on the Shapiro-Wilk W. Journal of the Royal Statistical Society Series C (Applied Statistics) 32, 121-133.
| Crossref | Google Scholar |

Salla VP, Danner MA, Citadin I, Sasso SAZ, Donazzolo J, Gil BV (2015) Análise de trilha em caracteres de frutos de jabuticabeira. Pesquisa Agropecuária Brasileira 50, 218-223.
| Crossref | Google Scholar |

Sari BG, Lúcio AD, Santana CS, Lopes SJ (2017) Linear relationships between cherry tomato traits. Ciência Rural 47, e20160666.
| Crossref | Google Scholar |

Sari BG, Lúcio AD, Olivoto T, Krysczun DK, Tischler AL, Drebes L (2018) Interference of sample size on multicollinearity diagnosis in path analysis. Pesquisa Agropecuária Brasileira 53, 769-773.
| Crossref | Google Scholar |

Shapiro SS, Wilk MB (1965) An analysis of variance test for normality (complete samples). Biometrika 52, 591-611.
| Crossref | Google Scholar |

Silva ARd, Malafaia G, Menezes IPP (2017) biotools: an R function to predict spatial gene diversity via an individual-based approach. Genetics and Molecular Research 16, 1-6.
| Crossref | Google Scholar |

Silva JAGd, Mamann ÂTWd, Scremin OB, Carvalho IR, Pereira LM, Lima ARCd, Lautenchleger F, Basso NCF, Argenta CV, Berlezi JD, Porazzi FU, Matter EM, Norbert L (2020) Biostimulants in the indicators of yield and industrial and chemical quality of oat grains. Journal of Agricultural Studies 8, 68-87.
| Crossref | Google Scholar |

Steel RGD, Torrie JH, Dickey DA (1997) ‘Principles and procedures of statistics: a biometrical approach.’ (MH Book: New York, NY, USA)

Tedesco MJ, Gianello C, Bissani CA, Bohnen H, Volkweiss SJ (1995) ‘Análise de solo, plantas e outros materiais.’ (UFRGS: Porto Alegre, Brazil)

Tierney L (2021) tkrplot: TK Rplot. CRAN. R-project. Available at https://cran.r-project.org/package=tkrplot

Toebe M, Cargnelutti Filho A (2013a) Não normalidade multivariada e multicolinearidade na análise de trilha em milho. Pesquisa Agropecuária Brasileira 48, 466-477.
| Crossref | Google Scholar |

Toebe M, Cargnelutti Filho A (2013b) Multicollinearity in path analysis of maize (Zea mays L.). Journal of Cereal Science 57, 453-462.
| Crossref | Google Scholar |

Toebe M, Cargnelutti Filho A, Storck L, Lúcio AD (2017a) Sample size for estimation of direct effects in path analysis of corn. Genetics and Molecular Research 16, 1-23.
| Crossref | Google Scholar |

Toebe M, Cargnelutti Filho A, Storck L, Lúcio AD (2017b) Direct effects on scenarios and types of path analyses in corn hybrids. Genetics and Molecular Research 16, 1-15.
| Crossref | Google Scholar |

Vencovski R, Barriga P (1992) ‘Genética biométrica no fitomelhoramento.’ (Sociedade Brasileira de Genética: Ribeirão Preto - SP, Brazil)