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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.

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William Terry Kelley

Statistical analysis of agricultural research has traditionally been via the use of fixed model methods. However, recent advances in statistical software have made analysts through random or mixed model methods more practical. Errant or inappropriate use of statistical programs to analyze data has been a recurring problem in the reporting of agricultural research findings. Often variables are all considered to be fixed in order to facilitate analysis, when in reality some variables in field research are nearly always random. Proper selection of error terms and calculation of standard errors are also frequently done incorrectly when statistical analysts packages are not used correctly. Unbalanced data is also quite normal in field research due to unforseen circumstances that result in lost information. Most of these situations can be more early handled with a mixed model approach. In this work, a broccoli field trial involving tillage and planting dates was analyzed using the General Smear Models procedure in SAS and the General Elmer Mixed Models Procedure in GLMM. Comparison of the analyses revealed that conclusions would differ somewhat with balanced data and even more with unbalanced data. Since variance components from all random effects are used to calculate standard errors in GLMM, standard errors in the mixed model were larger, but likely more accurate Inference space was also broader and allowed prediction space to include the entire population of experimental units which were sampled in the experiment. The mixed model procedure was more efficient and thus more sensitive to differences in treatments.

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Hiroshi Iwanami, Shigeki Moriya, Nobuhiro Kotoda, Sae Takahashi, and Kazuyuki Abe

estimations ( Durel et al., 1998 ). Genetic parameter estimates have begun to be generated in apple for fruit traits, following developments in statistical tools and methods for analyzing unbalanced data, including REML and BLUP. For example, GCA and SCA

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Mark E. Herrington, Craig Hardner, Malcolm Wegener, Louella Woolcock, and Mark J. Dieters

et al. (1998) who, in the absence of a well-structured formal crossing design, used pedigree information to estimate genetic parameters from large unbalanced data sets in apple ( Malus × sylvestris var. domestica ) comprising 213 families, Silva

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Steven J. McKay, James M. Bradeen, and James J. Luby

Utilization of pedigree information to estimate genetic parameters from large unbalanced data sets in apple Theor. Appl. Genet. 96 1077 1085 Food and Agricultural Organization of the United Nations 2010 FAOSTAT 8 Apr. 2011. < >. Green, B

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Arthur Villordon, Christopher Clark, Don LaBonte, and Nurit Firon

, respectively, to normalize the residuals. The unbalanced data sets were analyzed using SAS Proc Mixed (SAS Version 9.1; SAS Inc., Cary, NC). Results and Discussion ‘Beauregard’ and ‘Evangeline’ cuttings treated with 1-MCP showed variable AR emergence and length

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Arthur Villordon and Christopher Clark

main roots. Thus, only galls on LRs were counted each time an AR image was analyzed. Statistical analyses. Root length and counts were transformed using log 10 and square root transformation, respectively. The unbalanced data set was analyzed using SAS

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George C.J. Fernandez

conducted by horticultural scientists often give rise to several random sources of variation. Relevant examples are split plot designs, multiyear and multisite yield trials, and repeated measurements taken on the same field plot. Unbalanced data are a common

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Brian S. Yandell

typically unable to handle unbalanced data or data with multiple factors, nesting, or blocking. Experiments of any complexity tend to need tools found in a full-featured statistical package. Although many statistical packages can embed menus in spreadsheets

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Jonathan M. Bokmeyer, Stacy A. Bonos, and William A. Meyer

variance. The analysis of variance was generated by PROC GLM (SAS Institute, Cary, NC) as a result of an unbalanced data set. Broad-sense heritability estimates were determined from restricted maximum likelihood variance and covariance components using the