The extent and prevailing shape of spatial relationships in Polish variety testing trials on wheat

Pilarczyk, W.

doi:10.1111/j.1439-0523.2009.01660.x

Cited by 5 publications

(10 citation statements)

References 25 publications

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“…The model selections tend toward similar decisions insofar as the basic or random‐walk model is better suited to the small designs and nonlinear spatial models are better suited to the larger designs. There are other experimental situations in which the linear model ( r ) is also appropriate for experiments with higher treatment numbers, however, as Pilarczyk (2007) and Müller et al (2010) have reported. The idea that a particular covariance model is better suited than another for all subareas of the field or for a specific crop has been proven to be untenable.…”

Section: Discussionmentioning

confidence: 99%

Geostatistical Models in Agricultural Field Experiments: Investigations Based on Uniformity Trials

Richter

Kroschewski

2012

Agronomy Journal

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The probability of detecting treatment differences can often be increased by using geostatistical instead of classical statistical models. Geostatistical approaches require the selection of the best fitted model from a set of alternative models. This additional analysis effort could be reduced if the same model shows consistently the best fit for a given field or crop. To prove whether this reduction can be expected for designed on‐station trials, we analyzed five uniformity trials conducted on the same field. We studied whether different layouts of randomized complete block designs, the positions on the field, and the randomized plans influenced the model decision and analyzed the precision achieved. For this, the designs were shifted across the field, and 1000 randomized plans were projected onto each position. The model fit was evaluated using the corrected Akaike information criterion (AICC). The ranked AICC values were used for assessing model preference. In the means of all crops, designs, and models, the variation of the ranks depended on an individual decision for the combination of position and randomized plan by 62.6%. Therefore, the best fitted model was not predictable for a single experiment. As in the classical approach, the proper layout of a trial determines precision and unbiasedness of treatment differences. Randomization and blocking still should be the basic principles of experiment planning; however, their roles have partially changed. The detected bias of the Type I errors, both of the t‐test and F test, needs further investigation. Basic findings are also valid for on‐farm trials.

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Section: Discussionmentioning

confidence: 99%

Geostatistical Models in Agricultural Field Experiments: Investigations Based on Uniformity Trials

Richter

Kroschewski

2012

Agronomy Journal

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“…Each field experiment was conducted according to a two‐factor strip‐plot design with two replicates. The cultivars were randomly arranged in sub‐blocks (rows) and the two crop managements in perpendicular sub‐blocks (columns) (Pilarczyk, 2009). The area of a plot was 15 m 2 .…”

Section: Methodsmentioning

confidence: 99%

“…The FA structure uses multiplicative terms for approximation of the unstructured variance-covariance matrix (Piepho, 1997;So and Edwards, 2009;Beeck et al, 2010;Cullis et al, 2010). In many previous studies, FA structures were recommended to model cultivar two crop managements in perpendicular sub-blocks (columns) (Pilarczyk, 2009). The area of a plot was 15 m 2 .…”

Section: Multienvironment Trialmentioning

confidence: 99%

Prediction Accuracy and Consistency in Cultivar Ranking for Factor‐Analytic Linear Mixed Models for Winter Wheat Multienvironmental Trials

et al. 2017

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In the majority of research on models for multienvironment trials, evaluation of the prediction accuracy of models with different variance–covariance structures is focused on predicting the means for cultivar × location (C × L) combinations. In cultivar recommendation, however, it is often more important to evaluate prediction accuracy in modeling cultivar × region (C × R) combinations. The aim of this paper was to evaluate the prediction accuracy of two single‐stage linear mixed models (LMMs) with different variance–covariance structures, emphasizing factor‐analytic (FA) structures. One of the models was used to predict means for C × L combinations and the other one for C × R combinations. Additionally, we assessed implications of model choice for consistency in cultivar ranking. The data used for the analysis performed in this study were obtained from 42 locations and 47 winter wheat (Triticum aestivum L.) cultivars during three growing seasons within the Polish Post‐Registration Variety Testing System. The data were assigned to six agroecological regions. For evaluating the prediction accuracy of LMMs, we used cross validation based on a modified equation for the mean squared error of prediction. Yield rankings modeled by different variance–covariance structures were compared by Spearman's rank correlation. For each model with a different variance–covariance structure, we calculated the correlation coefficients between estimated and observed data. The model with the highest predictability for means of the C × L classification was the FA(2) variance–covariance structure. In the case of C × R means, the compound symmetry structure fared favorably, and using more complex variance–covariance structures (including heterogeneous covariances) did not increase prediction accuracy.

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“…For testing the global null hypothesis that all t treatments have equal mean, L′ will have t-1 linearly independent rows with pairwise contrasts. In general, the following problems occur with these tests (Kenward & Roger 1997, 2009Schabenberger & Pierce 2002):…”

Section: Introductionmentioning

confidence: 99%

“…For example, in split-plot and strip-plot designs, where treatment contrasts involve several variance components, it may be necessary to approximate the error degrees of freedom, particularly when missing data occur (Fai & Cornelius 1996;Spilke et al 2005). Studies by Kenward & Roger (1997, 2009, Gomez et al (2005) and Schaalje et al (2002) demonstrate that the validity of tests depends on the method chosen, the underlying covariance model and its parameter values, the parameterization of the model and the sample size. When using a spatial add-on component in the analysis of field trials, however, the data structures are not directly comparable, so that results of these studies do not apply.…”

Section: Introductionmentioning

confidence: 99%

Treatment comparisons in agricultural field trials accounting for spatial correlation

et al. 2014

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The classical analysis model for agricultural field trials is based on the principles of experimental designrandomization, replication and blocking -and it assumes independent residual effects. Accounting for any existent spatial correlation as an add-on component may be beneficial, but it requires selection of a suitable spatial model and modification of classical tests of treatment contrasts. Using a sugar beet trial laid out in complete blocks for illustration, it is shown that tests obtained with different modifications yield diverging results. Simulations were performed to decide whether different test modifications lead to valid statistical inferences. For the spherical, power and Gaussian models, each with six different values of the range parameter and without a nugget effect, the suitability of the following modifications was studied: a generalization of the Satterthwaite method (1941), the method of Kenward and Roger (1997), and the first-order corrected method described by Kenward and Roger (2009). A second-order method described by Kenward and Roger (2009) is also discussed and detailed results are provided as Supplemental Material (available at: http://journals.cambridge.org/AGS). Simulations were done for experiments with 10 or 30 treatments in complete and incomplete block designs. Model selection was performed using the corrected Akaike information criterion and likelihood-ratio tests. When simulation and analysis models were identical, at least one of the modifications for the t-test guaranteed control of the nominal Type I error rate in most cases. When the first-order method of Kenward and Roger was used, control of the t-test Type I error rate was poor for 10 treatments but on average very good for 30 treatments, when considering the best-fitting models for a given simulation setting. Results were not satisfactory for the F-test. The more pronounced the spatial correlation, the more substantial was the gain in power compared to classical analysis. For experiments with 20 treatments or more, the recommendation is to select the best-fitting model and then use the first-order method for t-tests. For F-tests, a randomization-based model with independent error effects should be used.

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The extent and prevailing shape of spatial relationships in Polish variety testing trials on wheat

Cited by 5 publications

References 25 publications

Geostatistical Models in Agricultural Field Experiments: Investigations Based on Uniformity Trials

Geostatistical Models in Agricultural Field Experiments: Investigations Based on Uniformity Trials

Prediction Accuracy and Consistency in Cultivar Ranking for Factor‐Analytic Linear Mixed Models for Winter Wheat Multienvironmental Trials

Treatment comparisons in agricultural field trials accounting for spatial correlation

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