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

Hedonic analysis (M9b) {#hedonic}

Method description

The hedonic evaluation test involves asking consumers to :

1. to rate their preference from 1 (I dislike extremely) to 9 (I like very much) for three to four sensory attributes specific to the test product. The overall preference is ascertained at the beginning of the questionnaire in order not to influence the consumer and be closer to typical conditions of consumption.
2. give additional information such as sex, age and organic consumption frequency in order to characterise the population sample.
3. give additional sensory descriptors to describe products are asked after evaluation of each product.

Determine differences of appreciation for each samples

Regarding samples, the objectives of the hedonic tests are to

1. determine differences of appreciation for a given attribute between the set of samples bsed on the note given by the juges and
2. determine appreciation of samples based on descriptors given by the juges

Differences of sample regarding the note given by the juges.

The data distribution determines the type of tests that should be used to analyze the data set.

• If the distribution is Normal, one-way analysis of variance (ANOVA) can be performed:

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

with $Y_{ij}$ the note from 1 to 9 given by a person to a sample, $\alpha_i$ the person (i.e. assessor) that taste the sample, $\beta_j$ the germplasm tasted, $\varepsilon_{ijkl}$ the residuals.

Then, multiple comparison of mean on germplasm are performed. The aim is to obtain a final ranking based on consumers’ preferences.

• If the data set doesn’t follow a Normal distribution, a Friedman test on the rank should be used to indicate if the varieties are perceived differently by assessors.

Appreciation of sample regarding the descriptors given by the juges.

To do so, Correspondance Analysis (CA) is done on the data with descriptors.

Juges profiles

Another objective of the analysis is to determine juges profiles based on the note given and the additional information such as sex, age and organic consumption frequency, etc.

It is done with a Hierarchical Clustering on Principle Components (HCPC) that can be implement to identify groups of juges preferences after a Principal Component Analysis (PCA).

Steps with PPBstats

For hedonic analysis, you can follow these steps (Figure \@ref(fig:main-workflow-organo)):

• Format the data with format_data_PPBstats()
• Describe the data with plot()
• Run the model with model_hedonic()
• Check model outputs with graphs to know if you can continue the analysis with check_model()
• Get mean comparisons on the note given by the juges for each factor with mean_comparisons() and vizualise it with plot()
• Format data for CA and HCPC analysis with biplot_data() and visualise it with plot()

Format the data

data(data_hedonic)
head(data_hedonic)

The data frame has the following columns: sample, germplasm, location, juges, note, descriptors. The descriptors must be separated by ";". Any other column can be added as supplementary variables.

Then, you must format your data with format_data_PPBstats() and type = "data_organo_hedonic". Argument threshold can be set in order to keep only descriptors that have been cited several time. For exemple with threshold = 2, only descriptors cited at least twice are kept.

data_hedonic = format_data_PPBstats(data_hedonic, type = "data_organo_hedonic", threshold = 2)
names(data_hedonic)

data_hedonic is a list of four elements :

• data the data formated to run the anova and the multivariate analysis regarding
  • sample

head(data_hedonic$data$data_sample)

- sample_mean which gathers for each sample a mean for note and descriptors

head(data_hedonic$data$data_sample_mean)

- juges which gathers for each juge a mean for note

head(data_hedonic$data$data_juges)

• var_sup the supplementary variables used in the multivariate analysis

data_hedonic$var_sup

• descriptors the vector of descriptors cited knowing the threshold applyed when formated the data.

data_hedonic$descriptors

Describe the data

First, you can describe the data regarding the note given

p_note = plot(data_hedonic, plot_type = "boxplot", x_axis = "germplasm",
               in_col = "location", vec_variables = "note"
               )
p_note

As well as the descriptors for each germplasm for example:

descriptors = data_hedonic$descriptors

p_des = plot(data_hedonic, plot_type = "radar", in_col = "germplasm", 
                         vec_variables = descriptors
                         )
p_des

Run the model

To run the model on the dataset, used the function model_hedonic.

out_hedonic = model_hedonic(data_hedonic)

out_hedonic is a list with three elements:

• model : the result of the anova run on note

out_hedonic$model
anova(out_hedonic$model)

• CA : the result of the correspondance analysis run on the data set with the supplementary variables with FactoMineR::CA

out_hedonic$CA

• HCPC : the result of the correspondane analysis run on the data set with the supplementary variables with FactoMineR::PCA follow by FactoMineR::HCPC. It is a list of three elements:

out_hedonic$HCPC$res.pca

out_hedonic$HCPC$res.hcpc

head(out_hedonic$HCPC$clust)

Check and visualize model outputs

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

Check the model

out_check_hedonic = check_model(out_hedonic)

out_check_hedonic is list with two elements:

• hedonic which it the same objet as out_hedonic
• 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
  • data_ggplot_var_intra

Visualize outputs

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

p_out_check_hedonic = plot(out_check_hedonic)

p_out_check_hedonic is a list with:

• residuals of the ANOVA model

  • histogram : histogram with the distribution of the residuals r p_out_check_hedonic$residuals$histogram
  • qqplot r p_out_check_hedonic$residuals$qqplot
  • points r p_out_check_hedonic$residuals$points

• variability_repartition : pie with repartition of SumSq for each factor of the ANOVA model

p_out_check_hedonic$variability_repartition

• variance_intra_germplasm : repartition of the residuals for each germplasm which represent the person assessor variation plus the intra-germplasm variance of the ANOVA model.

p_out_check_hedonic$variance_intra_germplasm

• CA_composante_variance : variance caught by each dimension of the CA

p_out_check_hedonic$CA_composante_variance

• HCPC_composante_variance : variance caught by each dimension of the PCA previous to the HCPC

p_out_check_hedonic$PCA_composante_variance

Get and visualize mean comparisons on note

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

Get mean comparisons on note

Get mean comparisons with mean_comparisons().

out_mean_comparisons_hedonic = mean_comparisons(out_check_hedonic)

out_mean_comparisons_hedonic is a list of one element for futher ggplot : data_ggplot_LSDbarplot_germplasm

Visualize mean comparisons on note

p_out_mean_comparisons_hedonic = plot(out_mean_comparisons_hedonic)

p_out_mean_comparisons_hedonic is a list of on elements with barplots :

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.

• germplasm : mean comparison for germplasm

pg = p_out_mean_comparisons_hedonic$germplasm
names(pg)
pg$`1`

Get and visualize biplot regarding samples (CA) and juges (HCPC)

The biplot represents information about the percentages of total variation explained by the two axes. It has to be linked to the total variation caught by the interaction. If the total variation is small, then the biplot is useless. If the total variation is high enought, then the biplot is useful if the two first dimension represented catch enought variation (the more the better).

Get biplot

Get biplot regading samples (CA) and juges (HCPC)

out_biplot_hedonic = biplot_data(out_check_hedonic)

Visualize biplot

p_out_biplot_hedonic = plot(out_biplot_hedonic)

p_out_biplot_hedonic is a list of two elements with

• the CA biplot where descriptors are represented by a triangle in red and samples are represented by text in blue and point in color refering to the sample.

p_out_biplot_hedonic$ca_biplot

• the HCPC biplot is a list of two elements : one with the variable ans the additionnal variables and the other with the groups of juges detected by the HCPC.

p_out_biplot_hedonic$hcpc_biplot

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