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

Spatial analysis (M4b) {#spatial-analysis}

Theory of the model

The experimental design used is the row-column design (D3). The following model is based on frequentist statistics (section \@ref(section-freq)). The model allows taking into account environmental variation within a block with few control replicated in rows and columns.

It is based on a SpATS (Spatial Analysis of Field Trials with Splines) model proposed by @rodriguez_spatial_2016 :

$Y_{ijk} = \alpha_{i} + r_{j} + c_{k} + f(u,v) + \varepsilon_{ijk}; \quad \varepsilon_{ijk} \sim \mathcal{N} (0,\sigma^2)$

With,

• $Y_{ijk}$ the phenotypic value for germplasm $i$, row $j$ and column $k$
• $\alpha_{i}$ the random effect of germplasm $i$
• $r_{j}$ the effect of row $j$
• $c_{k}$ the effect of col $k$
• $f(u,v)$ the smooth bivariate function that simultaneously accounts for the spatial trend across both directions of the fiel (i.e. rows and columns)
• $\varepsilon_{ijk}$ the residuals

Note that $f(u,v)$ is divided into 8 components excluding the intercept [@rodriguez_spatial_2016]:

• the linear effect of the rows (row),
• the linear effect of the columns (col),
• the linear interaction of rows and columns (row:col),
• the main row effect (f(row)),
• the main column effect (f(col)),
• the smooth varying coefficient term regarding rows (f(col):row),
• the smooth varying coefficient term regarding columns (row:f(col))),
• the smooth-by-smooth interaction component (f(col):f(row))

Much more information regarding the model as well as example of R package SpATS can be found in @rodriguez_spatial_2016.

Steps with PPBstats

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

Format the data

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

Run the model

By default, germplasm are settled as random.

out_spatial = model_spatial(data = data_model_spatial, variable = "y1")

out_spatial is a list containing two elements :

• info : a list with variable and data

out_spatial$info$variable

head(out_spatial$info$data)

• model a list with four elements :
  • model r out_spatial$model$model
  • summary r out_spatial$model$summary
  • var_res the variance of the residuals r out_spatial$model$df_residual r out_spatial$model$MSerror

Check and visualize model outputs

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

Check the model

out_check_spatial = check_model(out_spatial)

out_check_spatial is a list containing two elements :

• spatial the output from the model
• data_ggplot a list containing information for ggplot:
  • data_ggplot_residuals a list containing :
    • data_ggplot_normality
    • data_ggplot_skewness_test
    • data_ggplot_kurtosis_test
    • data_ggplot_shapiro_test
    • data_ggplot_qqplot
  • data_ggplot_variability_repartition_pie

Visualize outputs

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

p_out_check_spatial = plot(out_check_spatial)

p_out_check_spatial is a list with:

• residuals

  • histogram : histogram with the distribution of the residuals r p_out_check_spatial$residuals$histogram

  • qqplot r p_out_check_spatial$residuals$qqplot

  • points r p_out_check_spatial$residuals$points

• variability_repartition : pie with repartition of variance for each factor

p_out_check_spatial$variability_repartition

Get and visualize mean comparisons

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

Get mean comparisons

Get mean comparisons with mean_comparisons.

out_mean_comparisons_spatial = mean_comparisons(out_check_spatial, p.adj = "bonferroni")

out_mean_comparisons_spatial is a list of two elements:

• info : a list with variable and data
• data_ggplot_LSDbarplot_germplasm

Visualize mean comparisons

p_out_mean_comparisons_spatial = plot(out_mean_comparisons_spatial)

p_out_mean_comparisons_spatial is a list of two elements

• germplasm_blup whih represent the BLUPs with their confidence intervalle

p_out_mean_comparisons_spatial$germplasm_blup

• germplasm_barplot. For each element of the list, there are as many graph as needed with nb_parameters_per_plot parameters per graph. Letters are displayed on each bar. Parameters that do not share the same letters are different regarding type I error (alpha) and alpha correction. The error I (alpha) and the alpha correction are displayed in the title.

pg = p_out_mean_comparisons_spatial$germplasm_barplot
pg$`23`

Get and vizualise groups of parameters

Get groups of parameters

In order to cluster locations or germplasms, you may use mulivariate analysis on a matrix with several variables in columns and parameter in rows.

This is done with parameter_groups() which do a PCA on this matrix.

Clusters are done based on HCPC method as explained here

Lets' have an example with three variables.

First run the models

out_spatial_2 = model_spatial(data_model_spatial, variable = "y2")
out_spatial_3 = model_spatial(data_model_spatial, variable = "y3")

Then check the models

out_check_spatial_2 = check_model(out_spatial_2)
out_check_spatial_3 = check_model(out_spatial_3)

Then run the function for germplasm.

list_out_check_model = list("spatial_1" = out_check_spatial, "spatial_2" = out_check_spatial_2, "spatial_3" = out_check_spatial_3)
out_parameter_groups = parameter_groups(list_out_check_model, "germplasm")

out_parameter_groups is list of two elements:

• obj.pca : the PCA object from FactoMineR::PCA()
• clust, a list of two elements:
  • res.hcpc : the HCPC object from FactoMineR::HCPC()
  • clust : the dataframe with cluster assigned to each individual

Visualize groups of parameters

Visualize outputs with plot

p_germplasm_group = plot(out_parameter_groups)

p_germplasm_group is list of two elements :

• pca : a list with three elements on the PCA on the group of parameters :

  • composante_variance : variance caught by each dimension of the PCA r p_germplasm_group$pca$composante_variance

  • ind : graph of individuals r p_germplasm_group$pca$ind

  • var : graph of variables r p_germplasm_group$pca$var

• clust : output from factextra::fviz_cluster(), a list of number of cluster + 1 element

cl = p_germplasm_group$clust
names(cl)

cl$cluster_all

cl$cluster_1

post hoc analysis to visualize variation repartition for several variables

list_out_check_model = list("spatial_1" = out_check_spatial, "spatial_2" = out_check_spatial_2, "spatial_3" = out_check_spatial_3)
post_hoc_variation(list_out_check_model)

Apply the workflow to several variables

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

workflow_spatial = function(x, data){
  out_spatial = model_spatial(data = data, variable = x)

  out_check_spatial = check_model(out_spatial)
  p_out_check_spatial = plot(out_check_spatial)

  out_mean_comparisons_spatial = mean_comparisons(out_check_spatial, p.adj = "bonferroni")
  p_out_mean_comparisons_spatial = plot(out_mean_comparisons_spatial)

  out = list(
    out_spatial = out_spatial,
    out_check_spatial = out_check_spatial,
    p_out_check_spatial = p_out_check_spatial,
    out_mean_comparisons_spatial = out_mean_comparisons_spatial,
    p_out_mean_comparisons_spatial = p_out_mean_comparisons_spatial
    )
  return(out)
}

vec_variables = c("y1", "y1", "y1")
out = lapply(vec_variables, workflow_spatial, data_model_spatial)
names(out) = vec_variables


list_out_check_model = list("spatial_1" = out_check_spatial, "spatial_2" = out_check_spatial_2, "spatial_3" = out_check_spatial_3)

out_parameter_groups = parameter_groups(list_out_check_model, "germplasm" )
p_germplasm_group = plot(out_parameter_groups)

p_post_hoc_variation = post_hoc_variation(list_out_check_model)

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