In priviere/PPBstats: An R package to perform analysis found within PPB programmes

Study variance within germplasm {#variance-intra}

Theory of the model

The model is based on bayesian statistics (section \@ref(section-bayes)).

The phenotypic value $Y_{ijkl}$ for a given variable $Y$, germplasm $i$, environment $j$, plot $k$ and individual $l$ is modeled as :

$Y_{ijkl} = \mu_{ijk} + \varepsilon_{ijkl} ; \quad \varepsilon_{ijkl} \sim \mathcal{N} (0,\sigma^2_{ij})$,

Where $Y_{ijkl}$ is the phenotypic value for germplasm $i$, environment $j$, plot $k$ and individual $l$; $\mu_{ijk}$ is the mean of population $i$ in environnement $j$ and plot $k$ (nested in environment $j$); $\varepsilon_{ijkl}$ is what is not explained by the model in germplasm $i$, environment $j$, plot $k$ and individual $l$.

$\varepsilon_{ijkl}$ is taken from a normal distribution, centered on 0 with variance $\sigma^2_{ij}$

With priors : $\sigma^2_{ij} \sim 1/Gamma(10^{-6},10^{-6})$ and $\mu_{ijk} \sim N(\mu_{.j.},10^{6})$

$\sigma^2_{ij}$ correspond to the intra-germplasm variance.

No specific experimental design is needed as long as there are several individuals measured for a given germplasm.

Steps with PPBstats

For variance intra analysis, you can follow these steps (Figure \ref(fig:main-workflow)) :

• Format the data with format_data_PPBstats()
• Run the model with model_bh_intra_location()
• Check model outputs with graphs to know if you can continue the analysis with check_model()
• Get mean comparisons for each factor with mean_comparisons() and vizualise it with plot()

Format the data

data(data_model_bh_variance_intra)
data_model_bh_variance_intra = format_data_PPBstats(data_model_bh_variance_intra, type = "data_agro")

Run the model

To run the model , used the function model_bh_intra_location. You can run it on one variable.

#out_vi = model_bh_intra_location(data_model_bh_variance_intra, variable = "spike_weight", nb_iterations = 100)

Check and visualize model outputs

The tests to check the model are explained in section \@ref(check-model-bayes).

Check the model

Once the model is run, it is necessary to check if the outputs can be taken with confidence. This step is needed before going ahead in the analysis (in fact, object used in the next functions must come from check_model).

#out_check_vi = check_model(out_vi)

Visualize outputs

Once the computation is done, you can visualize the results with plot

#p_out_check_vi = plot(out_check_vi)

Get and visualize mean comparisons

The method to compute mean comparison are explained in section \@ref(mean-comp-check-bayes).

Get mean comparisons

Get mean comparisons with mean_comparisons.

#out_mean_comparisons_vi = mean_comparisons(out_check_vi, parameter = "mu", p.adj = "soft.bonf")

Visualize outputs

Once the computation is done, you can visualize the results with plot

#p_out_mc_vi = plot(out_mean_comparisons_vi)

Apply the workflow to several variables

If you wish to apply the variance_intra workflow to several variables, you can use lapply with the following code :

workflow_model_variance_intra = function(x){
  out_vi = model_bh_intra_location(data_variance_intra, variable = x)

  out_check_vi = check_model(out_vi)
  p_out_check_vi = plot(out_check_vi)

  out_mean_comparisons_vi = mean_comparisons(out_check_vi, p.adj = "bonferroni")
  p_out_mean_comparisons_vi = plot(out_mean_comparisons_vi)

  out = list(
    "out_vi" = out_vi,
    "out_check_vi" = out_check_vi,
    "p_out_check_vi" = p_out_check_vi,
    "out_mean_comparisons_vi" = out_mean_comparisons_vi,
    "p_out_mean_comparisons_vi" = p_out_mean_comparisons_vi
  )

  return(out)
}

## Not run because of memory and time issues !
# vec_variables = c("y1", "y2", "y3")
#
# out = lapply(vec_variables, workflow_model_variance_intra)
# names(out) = vec_variables

priviere/PPBstats documentation built on May 6, 2021, 1:20 a.m.