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Dawn M. VanLeeuwen, Rolston St. Hilaire, and Emad Y. Bsoul

Statistical analysis of data from repeated measures experiments with missing factor combinations encounters multiple complications. Data from asynchronous cyclic drought experiments incorporate unequal numbers of drought cycles for different sources and provide an example of data both with repeated measures and missing factor combinations. Repeated measures data are problematic because typical analyses with PROC GLM do not allow the researcher to compare candidate covariance structures. In contrast, PROC MIXED allows comparison of covariance structures and several options for modeling serial correlation and variance heterogeneity. When there are missing factor combinations, the cross-classified model traditionally used for synchronized trials is inappropriate. For asynchronous data, some least squares means estimates for treatment and source main effects, and treatment by source interaction effects are inestimable. The objectives of this paper were to use an asynchronous drought cycle data set to 1) model an appropriate covariance structure using mixed models, and 2) compare the cross-classified fixed effects model to drought cycle nested within source models. We used a data set of midday water potential measurements taken during a cyclic drought study of 15 half-siblings of bigtooth maples (Acer grandidentatum Nutt.) indigenous to Arizona, New Mexico, Texas, and Utah. Data were analyzed using SAS PROC MIXED software. Information criteria lead to the selection of a model incorporating separate compound symmetric covariance structures for the two irrigation treatment groups. When using nested models in the fixed portion of the model, there are no missing factors because drought cycle is not treated as a crossed experimental factor. Nested models provided meaningful F tests and estimated all the least squares means, but the cross-classified model did not. Furthermore, the nested models adequately compared the treatment effect of sources subjected to asynchronous drought events. We conclude that researchers wishing to analyze data from asynchronous drought trials must consider using mixed models with nested fixed effects.

Open access

Jacob H. Shreckhise, James S. Owen Jr., Matthew J. Eick, Alexander X. Niemiera, James E. Altland, and Brian E. Jackson

analysis was accomplished via covariance structure modeling ( Wolfinger, 1993 ), in which the most appropriate covariance structure was selected by fitting data to various homogeneous and heterogenous covariance structures available in JMP Pro 14 (SAS

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Lingdi Dong, Waltram Ravelombola, Yuejin Weng, Jun Qin, Wei Zhou, Gehendra Bhattarai, Bazgha Zia, Wei Yang, Linqi Shi, Beiquan Mou, and Ainong Shi

.4 (SAS Institute Inc., Cary, NC). Before ANOVA, a covariance structure matrix was determined using SAS 9.4 (SAS Institute Inc.) because the analysis involved repeated measures ( Littell et al., 2000 ). ANOVA was performed using the covariance matrix

Free access

Timothy L. Righetti, David R. Sandrock, Bernadine Strik, and Anita Azarenko

conducted, the subplot factor (tissue type) was treated as a nonindependent correlated factor and a repeated-measures correction was performed in PROC MIXED. Four covariance structures were evaluated; unstructured (UN), compound symmetry (CS), Toeplitz, and

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Richard J. Heerema, Dawn VanLeeuwen, Marisa Y. Thompson, Joshua D. Sherman, Mary J. Comeau, and James L. Walworth

unstructured covariance structures were considered. Analysis proceeded using the covariance structure that produced the lowest Akaike information criteria (AICC) with a finite sample size correction value. Because comparing Zn treatments at each date was

Open access

Manoj Chhetri and Charles Fontanier

. The data were subjected to repeated-measures analysis of variance in R using the lmer function in the lme4 package ( Bates et al., 2015 ). Different variance–covariance structures were investigated to build the model, and the appropriate repeated

Free access

Barrett R. Gruber, Libby R.R. Davies, and Patricia S. McManus

and n = 4 in 2008 and 2009). The “tree (fungicide)” nested variable was used as the repeated effect in all models to accommodate the covariance of fruits per shoot, fresh weight, and SSC. A compound symmetry covariance structure was used in all years

Free access

Thomas E. Marler

SAS GLIMMIX procedure in Version 9.2 (SAS Institute, Inc., Cary, NC). The AR(1) covariance structure was selected as the best covariance structure between repeated measures based on the minimum AICC value criterion. Root extension, leaf area, and leaf

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Weijie Jiang, Jie Bai, Xueyong Yang, Hongjun Yu, and Yanpeng Liu

recorded at 485 nm. Statistical analyses. Each of the five physiological indices was analyzed using Proc Mixed in SAS (version 8.0; SAS Institute, Cary, NC) with a variance–covariance structure for the repeated measures analysis of variance. The variance–covariance

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Katrina J.M. Hodgson-Kratky, Olivier M. Stoffyn, and David J. Wolyn

distribution of error were tested using the Shapiro–Wilk statistic, Levene’s test, and by visual analysis of residual plots, respectively. For rubber yield and root dry weight per plant, a covariance structure which had heterogeneous error over site was