README.md

In nsantantonio/Bilinear: Fits bilinear models for multi environment trial data

Bilinear package for fitting bilinear models (AMMI, GGE, etc.)

v0.2 release

The new release allows for missing data to be imputed with an EM algorithm within bilinear(). I have fixed a few other issues, and will continue to update and fix any bugs that arise. Please post issues to the issue board here on this github page. I will get to them as soon as I can.

Package formatting

To install, first install devtools by entering an R environment and typing.

install.packages("devtools")

Load the devtools library with

library(devtools)

Then install bilinear by typing

install_github("nsantantonio/Bilinear")

You can now load the library as you would any other R package

library(Bilinear)

I highly reccomend that you do not download these files directly! Follow the installation instructions above.

Microsoft R open

I have had issues using devtools with Microsoft R open https://mran.microsoft.com/open. I have supplied a source tarball, Bilinear_0.2.1.tar.gz for those who use MRAN, which can be found in the v0.2.1 release. You can also just clone the repo and build on your own machine.

git clone https://github.com/nsantantonio/Bilinear

R CMD build Bilinear

R CMD INSTALL Bilinear

Missing cells are now allowed!

Missing genotype/environment combinations are now allowed, and are imputed with an expectation maximization algorithm within bilinear(). There is also functionality to allow the user to determine the accuracy of imputation, using the em() function (although this function is not required to be called by the user under typical circumstances). While I have imposed no limit on the degree of missingness, I would suggest avoiding data sets with poor interconnectivity (i.e. poor overlap of genotype/environment information). An extreme example would be one set of lines evaluated in one set of environments and another set of genotypes evaluated in another set of environments put together and connected with missing values.

Bilinear

Fit bilinear models using AMMI (Additive Main effects Multiplicative Interaction) or GGE/SREG (Genotype and Genotype by Environment /Sites REGression) and make 2D and 3D biplots. Also tests for the number of significant dimensions of GxE using a parameteric bootstrap test method suggested by Forkman and Piepho (2014). An additional test for significant multiplicative terms, the FR test from Piepho (1995), has been also been implemented in version 0.1.

type ?bilinear for some examples. Bilinear version 0.1 contains the relevant functions, namely bilinear() to fit model and run statistical tests for signficant dimensions, BBplot() to plot 2D and 3D biplots, and AMMIplot() to produce linear and winner plots for AMMI models such as those in Gauch & Zobel (1997).

Plant Breeders Disclaimer

It is this author's opinion that GGE type models are more difficult to interpret than AMMI type models, as the genotypic main effect will be present in one or more of the remaining dimensions of the residual matrix, but not necessarily the first (largest) dimension (e.g. when Var(GxE) > Var(G)). Therefore, I recommend using AMMI type models, as both genotype and environment main effects are removed from the residuals before GxE effects are assessed. However, GGE type models are provided here as a freely available resource for those who want to use them. The decorateGGE option of BBplot will draw the mega-environment delineations suggested by Yan et al. (2000).

Proceed with Caution

This software is in development and bugs may (almost certainly) be present. I have tried to make the package flexible to different data inputs, but this leads to difficulties in testing all the possible ways one might try to input data. See known bugs below.

Known issues that have been fixed

• Unbalanced data is now allowed! Missing genotype/environment cells are imputed using an expectation maximization algorithm.

• ANOVA table for replicated data is now correct. The SS and MS were previously incorrectly calculated for the ANOVA table when the data were replicated, but the model fit, effects, p-values, and other results were unaffected.

Known issues to be addressed

• The plotting functions will be updated to allow more flexibility to the user to add certain line names, change colors etc.

Soy data

The soy.Rdata included here is from Zobel, Wright and Gauch (1988) and is subset from the gauch.soy dataset included in the agridat package. This was included to show the equivalence between using within environment means and raw data.

Ontario data

The ontario.Rdata included here is the Onterio wheat data containing 18 genotypes evaluated in 9 environments from from Yan et al. (2000) transcribed directly from the Yan et al. (2007) paper.

References

Imputation using expectation maximization

• Gauch, H. G., & Zobel, R. W. (1990). Imputing missing yield trial data. Theoretical and Applied Genetics, 79(6), 753-761.

Bootstrap test

• Forkman, J., & Piepho, H. P. (2014). Parametric bootstrap methods for testing multiplicative terms in GGE and AMMI models. Biometrics, 70(3), 639-647.

F test

• Piepho, H.P., 1995. Robustness of statistical tests for multiplicative terms in the additive main effects and multiplicative interaction model for cultivar trials. Theoretical and Applied Genetics, 90(3-4), pp.438-443.

SVD sign ambiguity (might not be relevant for centered matrices...)

• Bro, Rasmus, Evrim Acar, and Tamara G. Kolda. "Resolving the sign ambiguity in the singular value decomposition." Journal of Chemometrics 22, no. 2 (2008): 135-140.

selected background

AMMI

• Zobel, R. W., Wright, M. J., & Gauch, H. G. (1988). Statistical analysis of a yield trial. Agronomy Journal, 80(3), 388-393.
• Gauch, H., & Zobel, R. W. (1997). Identifying mega-environments and targeting genotypes. Crop Science, 37(2), 311-326.
• Gauch, H. G. (2013). A simple protocol for AMMI analysis of yield trials. Crop Science, 53(5), 1860-1869.

GGE

• Yan, W., Hunt, L. A., Sheng, Q., & Szlavnics, Z. (2000). Cultivar evaluation and mega-environment investigation based on the GGE biplot. Crop Science, 40(3), 597-605.

EM for unbalanced data

• Gauch Jr, H. G., & Zobel, R. W. (1990). Imputing missing yield trial data. Theoretical and Applied Genetics, 79(6), 753-761.

Discussion of bilinear models and biplot interpretation. I highly recommend reading them in the order shown here:

• Gauch, H. G. (2006). Statistical analysis of yield trials by AMMI and GGE. Crop science, 46(4), 1488-1500.
• Yan, W., Kang, M. S., Ma, B., Woods, S., & Cornelius, P. L. (2007). GGE biplot vs. AMMI analysis of genotype-by-environment data. Crop science, 47(2), 643-653.
• Gauch, H. G., Piepho, H. P., & Annicchiarico, P. (2008). Statistical analysis of yield trials by AMMI and GGE: Further considerations. Crop Science, 48(3), 866-889.
• Yang, R. C., Crossa, J., Cornelius, P. L., & Burgueño, J. (2009). Biplot analysis of genotype × environment interaction: Proceed with caution. Crop Science, 49(5), 1564-1576.

nsantantonio/Bilinear documentation built on Aug. 18, 2020, 2:31 p.m.