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Bayesian model for multi-environment trials

Source: R/bayes_met.R
bayes_met.Rd

Fits a Bayesian multi-environment model using rstan, the R interface to Stan.

Usage

bayes_met(
  data,
  gen,
  loc,
  repl,
  trait,
  reg = NULL,
  year = NULL,
  res.het = FALSE,
  iter = 2000,
  cores = 1,
  chains = 4,
  pars = NA,
  warmup = floor(iter/2),
  thin = 1,
  seed = sample.int(.Machine$integer.max, 1),
  init = "random",
  verbose = FALSE,
  algorithm = c("NUTS", "HMC", "Fixed_param"),
  control = NULL,
  include = TRUE,
  show_messages = TRUE,
  ...
)

Arguments

data

A data frame in which to interpret the variables declared in the other arguments.

gen, loc

A string. The name of the columns that contain the evaluated candidates and locations (or environments, if you are working with factor combinations), respectively.

repl

A string, a vector, or NULL. If the trial is randomized in complete blocks design, repl will be a string representing the name of the column that corresponds to the blocks. If the trial is randomized in incomplete blocks design, repl will be a string vector containing the name of the columns that correspond to the replicate and block effects on the first and second positions, respectively (c(replicate, block)). If the data does not have replicates, repl must be NULL.

trait

A string. The analysed variable. Currently, only single-trait models are fitted.

reg

A string or NULL. The name of the column that contain information on regions or mega-environments. NULL (default) if not applicable.

year

A string or NULL. The name of the column that contain information on years (or seasons). NULL (default) if not applicable.

res.het

Should the model consider heterogeneous residual variances? Defaults for FALSE. If TRUE, the model will estimate one residual variance per location (or environmnet).

iter

A positive integer specifying the number of iterations for each chain (including warmup). The default is 2000.

cores

Number of cores to use when executing the chains in parallel, which defaults to 1 but we recommend setting the mc.cores option to be as many processors as the hardware and RAM allow (up to the number of chains).

chains

A positive integer specifying the number of Markov chains. The default is 4.

pars

A vector of character strings specifying parameters of interest. The default is NA indicating all parameters in the model. If include = TRUE, only samples for parameters named in pars are stored in the fitted results. Conversely, if include = FALSE, samples for all parameters except those named in pars are stored in the fitted results.

warmup

A positive integer specifying the number of warmup (aka burnin) iterations per chain. If step-size adaptation is on (which it is by default), this also controls the number of iterations for which adaptation is run (and hence these warmup samples should not be used for inference). The number of warmup iterations should be smaller than iter and the default is iter/2.

thin

A positive integer specifying the period for saving samples. The default is 1, which is usually the recommended value.

seed

The seed for random number generation. The default is generated from 1 to the maximum integer supported by R on the machine. Even if multiple chains are used, only one seed is needed, with other chains having seeds derived from that of the first chain to avoid dependent samples. When a seed is specified by a number, as.integer will be applied to it. If as.integer produces NA, the seed is generated randomly. The seed can also be specified as a character string of digits, such as "12345", which is converted to integer.

init

Initial values specification. See the detailed documentation for the init argument in stan.

verbose

TRUE or FALSE: flag indicating whether to print intermediate output from Stan on the console, which might be helpful for model debugging.

algorithm

One of sampling algorithms that are implemented in Stan. Current options are "NUTS" (No-U-Turn sampler, Hoffman and Gelman 2011, Betancourt 2017), "HMC" (static HMC), or "Fixed_param". The default and preferred algorithm is "NUTS".

control

A named list of parameters to control the sampler's behavior. See the details in the documentation for the control argument in stan.

include

Logical scalar defaulting to TRUE indicating whether to include or exclude the parameters given by the pars argument. If FALSE, only entire multidimensional parameters can be excluded, rather than particular elements of them.

show_messages

Either a logical scalar (defaulting to TRUE) indicating whether to print the summary of Informational Messages to the screen after a chain is finished or a character string naming a path where the summary is stored. Setting to FALSE is not recommended unless you are very sure that the model is correct up to numerical error.

...

Additional arguments can be chain_id, init_r, test_grad, append_samples, refresh, enable_random_init. See the documentation in stan.

Value

An object of S4 class stanfit representing the fitted results. Slot mode for this object indicates if the sampling is done or not.

Details

The function has nine available models, which will be fitted according to the options set in the arguments:

  1. Entry-mean model : fitted when repl = NULL, reg = NULL and year = NULL: $$y = \mu + g + l + \varepsilon$$ Where \(y\) is the phenotype, \(\mu\) is the intercept, \(g\) is the genotypic effect, \(l\) is the location (or environment) effect, and \(\varepsilon\) is the error (which contains the genotype-by-location interaction, in this case).

  2. Randomized complete blocks design : fitted when repl is a single string. It will fit different models depending if reg and year are NULL:

    • reg = NULL and year = NULL : $$y = \mu + g + l + gl + r + \varepsilon$$ where \(gl\) is the genotype-by-location effect, and \(r\) is the replicate effect.

    • reg = "reg" and year = NULL : $$y = \mu + g + m + l + gl + gm + r + \varepsilon$$ where \(m\) is the region effect, and \(gm\) is the genotype-by-region effect.

    • reg = NULL and year = "year" : $$y = \mu + g + t + l + gl + gt + r + \varepsilon$$ where \(t\) is the year effect, and \(gt\) is the genotype-by-year effect.

    • reg = "reg" and year = "year" : $$y = \mu + g + m + t + l + gl + gm + gt + r + \varepsilon$$

  3. Incomplete blocks design : fitted when repl is a string vector of size 2. It will fit different models depending if reg and year are NULL:

    • reg = NULL and year = NULL : $$y = \mu + g + l + gl + r + b + \varepsilon$$ where \(b\) is the block within replicates effect.

    • reg = "reg" and year = NULL : $$y = \mu + g + m + l + gl + gm + r + b + \varepsilon$$

    • reg = NULL and year = "year" : $$y = \mu + g + t + l + gl + gt + r + b + \varepsilon$$

    • reg = "reg" and year = "year" : $$y = \mu + g + m + t + l + gl + gm + gt + r + b + \varepsilon$$

The models described above have predefined priors: $$x \sim \mathcal{N} \left( 0, S^{[x]} \right)$$ $$\sigma \sim \mathcal{HalfCauchy}\left( 0, S^{[\sigma]} \right)$$ where \(x\) can be any effect but the error, and \(\sigma\) is the standard deviation of the likelihood. If res.het = TRUE, then \(\sigma_k \sim \mathcal{HalfCauchy}\left( 0, S^{\left[ \sigma_k \right]} \right)\). The hyperpriors are set as follows: $$S^{[x]} \sim \mathcal{HalfCauchy}\left( 0, \phi \right)$$ where \(\phi\) is the known global hyperparameter defined such as \(\phi = max(y) \times 10\).

More details about the usage of bayes_met and other functions of the ProbBreed package can be found at https://saulo-chaves.github.io/ProbBreed_site/. Solutions to convergence or mixing issues can be found at https://mc-stan.org/misc/warnings.html.

Methods

sampling

signature(object = "stanmodel") Call a sampler (NUTS, HMC, or Fixed_param depending on parameters) to draw samples from the model defined by S4 class stanmodel given the data, initial values, etc.

See also

rstan::sampling, rstan::stan, rstan::stanfit

Examples

# \donttest{
mod = bayes_met(data = maize,
                gen = "Hybrid",
                loc = "Location",
                repl = c("Rep","Block"),
                trait = "GY",
                reg = "Region",
                year = NULL,
                res.het = TRUE,
                iter = 2000, cores = 2, chain = 4)
#>             495.776 seconds (Total)
#> Chain 1: 
#> Warning: There were 2 divergent transitions after warmup. See
#> https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
#> to find out why this is a problem and how to eliminate them.
#> Warning: Examine the pairs() plot to diagnose sampling problems
#> Warning: The largest R-hat is 1.06, indicating chains have not mixed.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#r-hat
#> Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#bulk-ess
#> Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#tail-ess
# }