Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-23T10:09:26.787Z Has data issue: false hasContentIssue false
  • English
  • Français

Nonlinear Mixed-Model Regression to Analyze Herbicide Dose–Response Relationships

Published online by Cambridge University Press:  20 January 2017

Ole K. Nielsen ,
Christian Ritz  and
Jens. C. Streibig
Ole K. Nielsen*
Affiliation:
International Institute of Tropical Agriculture (IITA), Oyo Road, PMB. 5320 Ibadan, Nigeria
Christian Ritz
Affiliation:
Department of Mathematics and Physics, The Royal Veterinary and Agricultural University, Thorvaldsensvej 40, DK-1871 Frederiksberg C, Denmark
Jens. C. Streibig
Affiliation:
Department of Agricultural Sciences, The Royal Veterinary and Agricultural University, Thorvaldsensvej 40, DK-1871 Frederiksberg, Denmark
*
Corresponding author's E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Plant responses to various doses of herbicides usually follow a sigmoid model where the potency is given by the 50% inhibition (I 50) value. To assess the potency of a herbicide under a range of environmental conditions, a series of independent bioassays are necessary to account for assay-to-assay variation. Analysis has conventionally been done by separate analysis of the individual bioassays or by simply pooling data. Analyzing the individual bioassays separately throws up relevant information on interassay variation. Such a model becomes too complex because a full set of model parameters is needed for each data set. Pooling data instead, and analyzing the bioassay jointly, inflates parameter uncertainty because of oversimplification. Such a simple model would have too few variables, and the fixed-effect estimates would be more uncertain because they would be explaining the interassay random effects. This means that the underlying statistical model is not realistic. Therefore, we propose a new technique of intermediate complexity that outperforms either technique and provides biologically realistic estimates that allow us to compare herbicide potencies. With this technique, we simultaneously analyze independent experiments by using a combination of nonlinear regression and mixed models. The case study uses a group of independently run bioassays with two photosystem II–inhibiting herbicides, diuron and bentazon, by measuring the oxygen evolution of thylakoid membranes. The introduction of random elements in the nonlinear regression parameters reduces the uncertainty in the parameters of interest. We demonstrate that it is possible to pool data from independent experiments to assess which parameters can be assigned a random element, to conduct hypothesis testing, and to calculate stable confidence limits and thus obtain a more precise interpretation of the biologically relevant parameters, such as I 50, compared with the conventional nonlinear regression models of the individual bioassays.

Keywords

BentazondiuronBioassaylog-logistic analysismaximum likelihoodML, maximum likelihood
Type
Research
Information
Weed Technology , Volume 18 , Issue 1 , March 2004 , pp. 30 - 37
Copyright
Copyright © Weed Science Society of America 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Literature Cited

Armitage, P., Bailey, J. M., Petrie, A., Annable, L., and Stack-Dunne, M. P. 1974. Studies in the combination of bioassay results. Biometrics 30:1–9.Google Scholar
Bates, D. M. and Watts, D. G. 1988. Nonlinear Regression Analysis and its Applications. New York: J Wiley. Pp. 29–30.Google Scholar
Bellio, R., Jensen, J. E., and Seiden, P. 2000. Applications of likelihood asymptotics for nonlinear regression in herbicide bioassays. Biometrics 56:1204–1212.Google Scholar
Box, G. E. P. and Cox, D. R. 1964. An analysis of transformations. J. R. Stat. Soc 26:211–252.Google Scholar
Bray, I. 2002. Application of Markov chain Monte Carlo methods to projecting cancer incidence and mortality. J. R. Stat. Soc. Ser. C 51:151–164.CrossRefGoogle Scholar
Cook, R. D. and Weisberg, S. 1982. Residuals and Influence in Regression. London: Chapman & Hall. Pp. 37–43.Google Scholar
Davidian, M. and Giltinan, D. M. 1995. Nonlinear Models for Repeated Measurement Data. London: Chapman & Hall. Pp. 148–149.Google Scholar
Kho, R. M. 2000. On crop production and the balance of available resources. Agric. Ecosyst. Environ 80:71–85.CrossRefGoogle Scholar
Lindstrom, M. and Bates, D. M. 1990. Nonlinear mixed effects models for repeated measures data. Biometrics 46:673–687.CrossRefGoogle ScholarPubMed
Lotz, L. A. P., Kropff, M. J., and Groeneveld, R. M. W. 1990. Modelling weed competition and yield losses to study the effect of omission of herbicides in winter wheat. Neth. J. Agric. Sci 38:711–718.Google Scholar
McCulloch, C. E. and Searle, S. R. 2001. Generalized, Linear and Mixed Models. New York: Wiley. Pp. 79–94.Google Scholar
Oberg, A. and Davidian, M. 2000. Estimating data transformations in nonlinear mixed effects models. Biometrics 56:65–72.Google Scholar
Pinheiro, J. and Bates, D. 2000. Mixed-Effects Models in S and S-PLUS, Statistics and Computing Series. New York: Springer-Verlag. Pp. 83–84, 323.Google Scholar
Seefeldt, S. S., Jensen, J. E., and Fuerst, E. P. 1995. Log-logistic analysis of dose-response relationships. Weed Technol. 9:218–227.Google Scholar
Simonite, V. and Brown, W. J. 2003. Estimation of a large cross-classified multilevel model to study academic achievement in a modular degree course. J. R. Stat. Soc. Ser. A 166:119–133.Google Scholar
Spitters, C. J. T. 1983a. An alternative approach to the analysis of mixed cropping experiments. 1. Estimation of competition effects. Neth. J. Agric. Sci 31:1–11.Google Scholar
Spitters, C. J. T. 1983b. An alternative approach to the analysis of mixed cropping experiments. 2. Marketable yield. Neth. J. Agric. Sci 31:143–155.Google Scholar
Streibig, J. C., Dayan, F. E., Rimando, A. M., and Duke, S. O. 1999. Joint action of natural and synthetic photosystem II inhibitors. Pestic. Sci 55:137–146.Google Scholar
Streibig, J. C., Rudemo, M., and Jensen, J. E. 1993. Dose response curves and statistical models. in Streibig, J. C. and Kudsk, P., eds. Herbicide Bioassays. Boca Raton, FL: CRC. Pp. 29–55.Google Scholar
Streibig, J. C., Walker, A., and Blair, A. M. et al. 1995. Variability of bioassays with metsulfuron-methyl in soil. Weed Res 35:215–224.Google Scholar
Vleeshouwers, L. M., Streibig, J. C., and Skovgaard, I. 1989. Assessment of competition between crops and weeds. Weed Res 29:273–280.Google Scholar