Agricultural experiments with repeated measures over time: analysis strategies comparison
DOI:
https://doi.org/10.15517/am.v34i2.52634Keywords:
biometry, statistical models, analysis of variance, multivariate analysis, statistical analysisAbstract
Introduction. Several modeling techniques have been used to analyze experiments with repeated measures over time; however, some of these are no longer relevant. Objective. To compare four analysis strategies that are used to analyze agricultural experiments with evaluations over time. Materials and methods. Data from an experiment in which the effect of different nitrogen fertilizer sources on chlorophyll content in a forage grass at different harvest ages was used. These data were analyzed using four strategies: the area under the curve index (AUC), multivariate analysis of variance (MANOVA), random effect of the experimental unit, and temporal correlation modeling. The lasts two strategies were performed under the theory of mixed linear models; in these different models were fitted, all with the same fixed effects structure, but with different random effects, residual correlation structure, or residual variance structure. Using penalized likelihood criteria [Akaike information criterion (AIC) and Bayesian information criterion (BIC)], the best fitting model was chosen, with which inferences were made about the means of the significant fixed effects, and compared with the results obtained from the AUC and MANOVA strategies. Results. The best fitting mixed linear had a compound symmetry correlation structure and heteroscedastic variances. This model allowed for the analysis of the treatment × time interaction; on the other hand, both the MANOVA and the AUC allowed for the analysis of temporal trends of the treatments. Conclusion. The best fitting mixed linear model made it possible to select the best treatment based on the evaluation time. On the other hand, both the MANOVA and the AUC led to the selection of treatments that were not the best at all evaluation times.
Downloads
References
Arnau, J., & Bono, R. (2008). Estudios longitudinales: modelos de diseño y análisis. Escritos de Psicología, 2(1), 32–14.
Barrios Maestre, R., & Silva-Acuña, R. (2019). Pertinencia de uso del análisis estadístico de medidas repetidas en la investigación agrícola. Agronomía Tropical, 69, 9–17.
Beale, C. M., Lennon, J. J., Yearsley, J. M., Brewer, M. J., & Elston, D. A. (2010). Regression analysis of spatial data. Ecology Letters, 13, 246–264. https://doi.org/10.1111/J.1461-0248.2009.01422.X
Bell, M. L., King, M. T., & Fairclough, D. L. (2014). Bias in area under the curve for longitudinal clinical trials with missing patient reported outcome data: Summary measures versus summary statistics. SAGE Open, 4(2). https://doi.org/10.1177/2158244014534858
Dale, M. R. T., & Fortin, M. J. (2014). Spatial analysis. A guide for ecologists (2nd ed.). Cambridge University Press.
Demidenko, E. (2013). Mixed models: Theory and applications with R (2nd ed.). Wiley.
Di Rienzo, J. A., Casanoves, F., Balzarini, M. G., Gonzalez, L., Tablada, M., & Robledo, C. W. (2020). Infostat (Versión 2020) [programa de computadora]. Centro de Transferencia InfoStat. https://www.infostat.com.ar/index.php?mod=page&id=15
Di Rienzo, J. A., Casanoves, F., Gonzalez, L., Tablada, E., Díaz, M., Robledo, C., & Balzarini, M. (2005). Diseño de experimentos. In J. Di Rienzo., & F. Casanoves (Eds.), Estadística para las ciencias agropecuarias (7ª ed., pp. 245–274). Editorial Brujas.
Di Rienzo, J. A., Guzmán, A. W., & Casanoves, F. (2002). A multiple-comparisons method based on the distribution of the root node distance of a binary tree. Journal of Agricultural, Biological, and Environmental Statistics, 7(2), 129–142. https://doi.org/10.1198/10857110260141193
Gómez, S., Torres, V., García, Y., & Navarro, J. A. (2012). Procedimientos estadísticos más utilizados en el análisis de medidas repetidas en el tiempo en el sector agropecuario. Revista Cubana de Ciencia Agrícola, 46(1), 1–7.
Gueorguieva, R., & Krystal, J. H. (2004). Move over ANOVA: progress in analyzing repeated-measures data and its reflection in papers published in the Archives of General Psychiatry. Archives of General Psychiatry, 61(3), 310–317. https://doi.org/10.1001/ARCHPSYC.61.3.310
Lawal, B. (2014). Applied statistical methods in agriculture, health and life sciences. Springer Cham. https://doi.org/10.1007/978-3-319-05555-8
Legendre, P., & Fortin, M. J. (1989). Spatial pattern and ecological analysis. Vegetatio, 80(2), 107–138. https://doi.org/10.1007/BF00048036
Littell, R. C., Milliken, G. A., Stroup, W. W., Wolfinger, R. D., & Schabenberger, O. (2006). SAS for mixed models (2nd ed.). SAS Institute Inc.
Mets, K. D., Armenteras, D., & Dávalos, L. M. (2017). Spatial autocorrelation reduces model precision and predictive power in deforestation analyses. Ecosphere, 8(5), Article e01824. https://doi.org/10.1002/ECS2.1824
Montgomery, D. C. (2020). Design and analysis of experiments (10th ed.). John Wiley & Sons, Inc.
Navarro Flores, J. R. (2012). La técnica del área bajo la curva. Centro de Protección de Cultivos. https://www.kerwa.ucr.ac.cr/handle/10669/585
Peterson, T. A., Blackmer, T. M., Francis, D. D., & Schepers, J. S. (1993). G93-1171 using a chlorophyll meter to improve N management. University of Nebraska. https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=2349&context=extensionhist
Pinheiro, J. C., & Bates, D. M. (2000). Mixed-effects models in S and S-PLUS. Springer-Verlag.
Powers, S. J., & Kozak, M. (2019). Repeated measures: There’s added value in modelling over time. Annals of Applied Biology, 175(2), 129–135. https://doi.org/10.1111/aab.12534
R Core Team. (2020). R: A language and environment for statistical computing. R Foundation for Statistical Computing. https://www.R-project.org/
Rosopa, P. J., Schaffer, M. M., & Schroeder, A. N. (2013). Managing heteroscedasticity in general linear models. Psychological Methods, 18(3), 335–351. https://doi.org/10.1037/A0032553
Shi, L., Hatsukami, D. K., Koopmeiners, J. S., Le, C. T., Benowitz, N. L., Donny, E. C., & Luo, X. (2021). A mixed effects model for analyzing area under the curve of longitudinally measured biomarkers with missing data. Pharmaceutical Statistics, 20(6), 1249–1264. https://doi.org/10.1002/pst.2146
Signorell, A. (2022). Tools for descriptive statistics and exploratory data analysis (Version 0.99.44) [Computer software]. R Core Team. https://cran.r-project.org/package=DescTools
Stroup, W. W., Milliken, G. A., Claassen, E. A., & Wolfinger, R. D. (2018). SAS for Mixed models: Introduction and basic applications (2nd ed.). SAS Institute Inc.
Verbeke, G., & Molenberghs, G. (2000). Linear mixed models for longitudinal data. Springer. https://doi.org/10.1007/978-1-4419-0300-6
West, B. T., Welch, K. B., & Gałecki, A. T. (2015). Linear mixed models. A practical guide using statistical Software (2nd ed.). CRC Press.
Wilcox, R. R. (1986). Controlling power in a heteroscedastic ANOVA procedure. British Journal of Mathematical and Statistical Psychology, 39(1), 65–68. https://doi.org/10.1111/J.2044-8317.1986.TB00845.X
Zea, J. F., Murcia, M. A., & Poveda, F. E. (2014). Modelos mixtos aplicados a la productividad de hojarasca. Comunicaciones En Estadística, 7(2), 173–189. https://doi.org/10.15332/S2027-3355.2014.0002.04
Zuur, A. F., Ieno, E. N., Walker, N., Saveliev, A. A., & Smith, G. M. (2009). Dealing with heterogeneity. In M. Gail., K. Krickeberg., J. M. Samet., A. Tsiatis., & W. Wong (Eds.), Mixed effects models and extensions in ecology with R. Springer. https://doi.org/10.1007/978-0-387-87458-6
Downloads
Additional Files
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 Jorge Claudio Vargas-Rojas, Alejandro Vargas-Martínez, Eduardo Corrales-Brenes
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
1. Proposed policy for open access journals
Authors who publish in this journal accept the following conditions:
a. Authors retain the copyright and assign to the journal the right to the first publication, with the work registered under the attribution, non-commercial and no-derivative license from Creative Commons, which allows third parties to use what has been published as long as they mention the authorship of the work and upon first publication in this journal, the work may not be used for commercial purposes and the publications may not be used to remix, transform or create another work.
b. Authors may enter into additional independent contractual arrangements for the non-exclusive distribution of the version of the article published in this journal (e.g., including it in an institutional repository or publishing it in a book) provided that they clearly indicate that the work was first published in this journal.
c. Authors are permitted and encouraged to publish their work on the Internet (e.g. on institutional or personal pages) before and during the review and publication process, as it may lead to productive exchanges and faster and wider dissemination of published work (see The Effect of Open Access).
