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Allowing for the structure of a designed experiment when estimating and testing trait correlations

Published online by Cambridge University Press:  22 February 2018

Hans-Peter Piepho
Hans-Peter Piepho*
Affiliation:
Biostatistics Unit, University of Hohenheim, 70593 Stuttgart, Germany
*
Author for correspondence: Hans-Peter Piepho, E-mail: [email protected]
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Abstract

Crop scientists occasionally compute sample correlations between traits based on observed data from designed experiments, and this is often accompanied by significance tests of the null hypothesis that traits are uncorrelated. This simple approach does not account for effects due to the randomization layout and treatment structure of the experiments and hence statistical inference based on standard procedures is not appropriate. The present paper describes how valid inferences accounting for all relevant effects can be obtained using bivariate mixed linear model procedures. A salient feature of the approach is that the bivariate model is commensurate with the model used for univariate analysis of individual traits and allows bivariate correlations to be computed at the level of effects. Heterogeneity of correlations between effects can be assessed by likelihood ratio tests or by graphical inspection of bivariate scatter plots of effect estimates. if heterogeneity is found to be substantial, it is crucial to focus on the correlation of effects, and usually, the main interest will be in the treatment effects. If heterogeneity is judged to be negligible, the marginal correlation can be estimated from the bivariate model for an overall assessment of association. The proposed methods are illustrated using four examples. Hints are given to alternative routes of analysis accounting for all treatment and design effects such as regression with groups and analysis of covariance.

Keywords

Analysis of variancebivariate mixed modelblock effectsdesigned experimentlikelihood ratio testresidual maximum likelihoodtreatment effectsvariance components
Type
Crops and Soils Research Paper
Information
The Journal of Agricultural Science , Volume 156 , Issue 1 , January 2018 , pp. 59 - 70
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Copyright
Copyright © Cambridge University Press 2018 

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References

Anderson, TW (1971) The Statistical Analysis of Time Series. New York: John Wiley & Sons.Google Scholar
Andrews, DF and Herzberg, AM (1985) Data: A Collection of Problems From Many Fields for the Student and Research Worker. New York: Springer.CrossRefGoogle Scholar
Booth, JG, Federer, WT, Wells, MT and Wolfinger, RD (2009) A multivariate variance components model for analysis of covariance in designed experiments. Statistical Science 24, 223–237.Google Scholar
Casella, G and Berger, RL (1990) Statistical Inference. Belmont: Duxbury Press.Google Scholar
De Faveri, J, Verbyla, AP, Cullis, BR, Pitchford, WS and Thompson, R (2017) Residual variance–covariance modelling in analysis of multivariate data from variety selection trials. Journal of Agricultural, Biological, and Environmental Statistics 22, 1–22.Google Scholar
Dixon, P (2016) Should blocks be fixed or random? In Annual Conference on Applied Statistics in Agriculture. Manhattan, KS: Kansas State University. Available at http://newprairiepress.org/agstatconference/2016/proceedings/4 (Accessed 24 January 2018).Google Scholar
Falconer, DS and Mackay, TFC (1996) Introduction to Quantitative Genetics, 4th edn. Harlow, UK: Longmans Green.Google Scholar
Forkman, J and Piepho, HP (2013) Performance of empirical BLUP and Bayesian prediction in small randomized complete block experiments. Journal of Agricultural Science, Cambridge 151, 381–395.Google Scholar
Ganesalingam, A, Smith, AB, Beeck, CP, Cowling, WA, Thompson, R and Cullis, BR (2013) A bivariate mixed model approach for the analysis of plant survival data. Euphytica 190, 371–383.Google Scholar
Gelman, A (2005) Analysis of variance: why is it more important than ever. Annals of Statistics 33, 1–53.CrossRefGoogle Scholar
Giesbrecht, FG and Gumpertz, ML (2004) Planning, Construction, and Statistical Analysis of Comparative Experiments. Wiley Series in Probability and Statistics. New York: Wiley.Google Scholar
Gomez, KA and Gomez, AA (1984) Statistical Procedures for Agricultural Research. New York: John Wiley and Sons.Google Scholar
Hill, WG and Thompson, R (1978) Probabilities of nonpositive definite between group or genetic covariance matrices. Biometrics 34, 429–439.Google Scholar
Holland, JB (2006) Estimating genotypic correlations and their standard errors using multivariate restricted maximum likelihood estimation with SAS proc MIXED. Crop Science 46, 642–654.CrossRefGoogle Scholar
James, W and Stein, C (1961) Estimation with quadratic loss. In Neyman, J (ed.). Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Contributions to the Theory of Statistics. Berkeley, CA: University of California Press, pp. 361–379.Google Scholar
Lee, Y, Nelder, JA and Pawitan, Y (2006) Generalized Linear Models with Random Effects. Unified Analysis via H-Likelihood. Boca Raton, FL: Chapman & Hall/CRC.Google Scholar
Littell, RC, Milliken, GA, Stroup, WW, Wolfinger, R and Schabenberger, O (2006) SAS System for Mixed Models, 2nd edn. Cary, NC: SAS Institute.Google Scholar
Mack, L, Capezzone, F, Munz, S, Piepho, HP, Claupein, W, Phillips, T and Graeff-Hönninger, S (2017) Nondestructive leaf area estimation for chia. Agronomy Journal 109, 1960–1969.CrossRefGoogle Scholar
Mead, R, Curnow, RN and Hasted, AM (1993) Statistical Methods in Agriculture and Experimental Biology, 2nd edn. London, UK: Chapman & Hall.Google Scholar
Milliken, GA and Johnson, DE (2002) Analysis of Messy Data. Volume III: Analysis of Covariance. Boca Raton, FL: CRC Press.Google Scholar
Nelder, JA (1965) The analysis of randomized experiments with orthogonal block structure. I. Block structure and the null analysis of variance. II. Treatment structure and the general analysis of variance. Proceedings of the Royal Society of London A 283, 147–178.Google Scholar
Patterson, HD and Thompson, R (1971) Recovery of inter-block information when block sizes are unequal. Biometrika 58, 545–554.Google Scholar
Pearce, SC (2006) Analysis of covariance. In Kotz, S, Balakrishnan, N, Read, CB and Vidakovic, B (eds). Encyclopedia of Statistical Sciences 1, 2nd edn. New York: Wiley, pp. 126–132.Google Scholar
Piepho, HP and Möhring, J (2011) On estimation of genotypic correlations and their standard errors by multivariate REML using the MIXED procedure of the SAS system. Crop Science 51, 2449–2454.CrossRefGoogle Scholar
Piepho, HP, Williams, ER and Fleck, M (2006) A note on the analysis of designed experiments with complex treatment structure. HortScience 41, 446–452.Google Scholar
Piepho, HP, Müller, BU and Jansen, C (2014) Analysis of a complex trait with missing data on the component traits. Communications in Biometry and Crop Science 9, 26–40.Google Scholar
Schabenberger, O and Pierce, PJ (2002) Contemporary Statistical Models for the Plant and Soil Sciences. Boca Raton, FL: CRC Press.Google Scholar
Searle, SR, Casella, G and McCulloch, CE (1992) Variance Components. New York: John Wiley & Sons.CrossRefGoogle Scholar
Singh, M and El-Bizri, KS (1992) Phenotypic correlation: its estimation and testing significance. Biometrical Journal 34, 165–171.CrossRefGoogle Scholar
Thimm, NH (2002) Applied Multivariate Analysis. New York: Springer.Google Scholar
Winer, BJ, Brown, DR and Michels, KM (1991) Statistical Principles in Experimental Design, 3rd edn. New York: McGraw-Hill.Google Scholar
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