how to perform - station biologique de...
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HOW TO PERFORM
MULTIVARIATE ANALYZES?
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W4M Core Team
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The "Multivariate" module
The "Multivariate" module on W4M allows you
to perform:
• Principal Component Analysis (PCA)
• Partial Least-Squares regression (PLS) and
discriminant analysis (PLS-DA)
• Orthogonal Partial Least-Squares regression
(OPLS) and discriminant analysis (OPLS-DA)
The original algorithms for PCA, PLS and
OPLS with the NIPALS algorithm have been
implemented by using the R environment
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Chaining the statistical modules
The Multivariate module can be chained with the Univariate module,
and also the Filters module (either to filter out pool or blank samples
before the statistics, or filter out the variables according to a statistical
threshold after the analysis)
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Preparing your files (1/9)
Your data must be split into 3 files:
• dataMatrix.tsv
• sampleMetadata.tsv
• variableMetadata.tsv
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Preparing your files (2/9)
Each file can be prepared by using Excel and saved using the
tabulated type format:
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Preparing your files (3/9)
You can then rename your file with the .tsv extension (instead of .txt)
by right-clicking on the file:
.tsv files (i.e. tabular separated) can be handled correctly both by
Excel and Galaxy.
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Preparing your files (4/9)
Decimal separator must be "."
Missing values must be indicated as "NA"
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Preparing your files (5/9)
Note: you can switch your default language in Excel to English in order
to have your decimal separator automatically set to "."
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Preparing your files (6/9)
The dataMatrix.tsv file must contain:
• the names of your samples in the first row
• the names of your variables in the first column
• numbers (or NA) in all the other cells
Note: the name in the topleft (A1) cell does not matter; avoid using "ID"
for Excel compatibility
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Preparing your files (7/9) The sampleMetadata.tsv file must contain:
• the names of the factors to be used in statistical analyzes in the first row
• the columns must be either characters (resp. numbers) for qualitative (resp.
quantitative) factors
• the names of your samples in the first column which must exactly match
those of the dataMatrix.tsv file
Note:
• 1) the name in the topleft (A1) cell does not matter; avoid using "ID" for Excel
compatibility
• 2) you can add columns for storing metadata about your samples even
though it is not used in your Galaxy analysis
• 3) results from statistical analyzes (e.g. scores) will be added as
supplementary columns in this file 10
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Preparing your files (8/9)
The variableMetadata.tsv file must contain:
• the names of the metadata (e.g. mzmed, rtmed) in the first row (there must
be at least one column in addition to the variable names)
• the names of your variables in the first column which must exactly match
those of the dataMatrix.tsv file
Note:
• 1) the name in the topleft (A1) cell does not matter; avoid using "ID" for Excel
compatibility
• 2) you can add columns for storing metadata about your variables even
though it is not used in your Galaxy analysis
• 3) results from the statistical analyzes (e.g. loadings, VIPs) will be added as
new columns in this file
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Preparing your files (9/9)
Sample and variable names:
• should not start with a digit
• should contain only
• a b c d e f g h i j k l m n o p q r s t u v w x y z
• A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
• 0 1 2 3 4 5 6 7 8 9
• , [comma]
• - [dash]
• _ [underscore]
• [blank]
• other punctuations and accents should not be used
• your sample and variable names should not contain any duplicate
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Loading your files into Galaxy (1/2)
Upload your three files (dataMatrix.tsv, sampleMetadata.tsv and
variableMetadata.tsv)
• either by using the icon
and drag & dropping the file:
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Loading your files into Galaxy (2/2)
• or with the Get Data / Upload File
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Check that your data have been
uploaded correctly
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Rename your history (optional)
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Open the "Multivariate" module
and select your 3 files of interest:
you are now ready to start your multivariate analyzes!
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Principal component analysis (PCA)
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Select
• the total number of components
• the scaling
• the logarithm (log10) transformation of the values (optional)
• the components for display
• and launch the computation
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Graphical results
Look at the "figure.pdf" file to see the scree plot, extreme observations,
and the loading and score plots
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Observation diagnostics
The "observation diagnostics" plot highlights observations with large
distance from the center in the score plane (score distance) or large
distance to their projection in the score plane (orthogonal distance)
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score distance
orthogonal distance
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Graphical results
The figure can be downloaded as a .pdf file
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Numerical results
Numerical results (including the percentage of explained inertia) can
be viewed in the "information.txt" file
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Score and loading values
The score (resp. loading) values of the selected components have been added
as columns in the sampleMetadata.tsv (resp. variableMetadata.tsv) files
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Tuning the parameters
You can recall the page with your parameters, modify them, and restart
the analysis
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Advanced parameters (1/2)
• Default algorithm is svd (faster) except if there are missing values (nipals will be
used instead)
• The number of extreme values on the loading plots (coloured in red) can be
modified
• The type of graphic can be modified
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Advanced parameters (2/2)
• A factor (column of the sampleMetadata.tsv) can be indicated to color the samples
• In case of a qualitative factor, it can be used to draw the Mahalanobis ellipses of
each class
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References
• Husson F., Le S. and Pages J. (2011). Exploratory multivariate analysis by
example using R. Chapman & Hall/CRC
• Ringner M. (2008). What is principal component analysis? Nature
Biotechnology, 26:303-304. http://dx.doi.org/10.1038/nbt0308-303
• Baccini A. (2010). Statistique descriptive multidimensionnelle (pour les
nuls). www.math.univ-toulouse.fr/~baccini/zpedago/asdm.pdf
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Partial Least Squares (PLS)
and
Partial Least Squares Discriminant
Analysis (PLS-DA)
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Select (1/2)
• the Y response to be modelled (column of the sampleMetadata.tsv file)
• Note: in the case of a qualitative response, Mahalanobis ellipses can be
drawn for each class by indicating the same factor as Y
• the number of random permutations of the labels to estimate the
significance of the model
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Select (2/2)
• the total number of components
• the scaling
• the logarithm (log10) transformation of the values (optional)
• the components for display
• and launch the computation
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Graphical results
Look at the "figure.pdf" file to see the results of the permutation testing,
extreme observations, and the loading and score plots
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Diagnostic metrics
0 ≤ R2X ≤ 1: percentage of X inertia explained by the model
0 ≤ R2Y ≤ 1: percentage of Y inertia explained by the model
0 ≤ Q2Y ≤ 1: estimation of the predictive performance of the model by
cross-validation
R2X and R2Y increase with the number of components while Q2Y
reaches a maximum (due to overfitting limitation), as can be visualized
with the "overview" graphic:
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Permutation testing
The algorithm randomly permutates the Y labels, builds the models
and computes the R2X, R2Y, Q2Y
Counting the number of R2Y (and Q2Y) metrics from random models
which are superior to the values of the true model gives an indication
of the significance of the PLS modelling
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Numerical results
The details of the R2X, R2Y, and Q2Y values are stored in the
"information.txt" file
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Scores, loadings and VIPs
The score (resp. loading and VIPs) of the selected components have been
added as columns in the sampleMetadata.tsv (resp. variableMetadata.tsv) files
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Advanced parameters (1/2)
• Use the icon to view your last parameters, modify them
and start a new computation
• The optimal number of components can be estimated
• The dataset can be split into a reference and test subsets
(the latter comprising samples with odd indices)
in this case, an estimation of the error on the test subset
(RMSEP) is computed in addition to the estimation of the error
on the reference test (RMSEE)
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Advanced parameters (2/2)
• Several other types of graphics are available:
• XY-scores
• predict-train and predict-test (the latter being
available only if the test set of odd-indices has
been defined)
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Orthogonal Partial Least Squares
(OPLS)
and
Orthogonal Partial Least Squares
Discriminant Analysis (OPLS-DA)
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Select (1/2)
• the Y response to be modelled (as in PLS)
• set the number of predictive components to 1
• the number of orthogonal components
• the number of random permutations of the labels to estimate the
significance of the model (as in PLS)
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Select (2/2)
• the scaling
• the logarithm (log10) transformation of the values (optional)
• the components for display
• and launch the computation
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http://workflow4metabolomics.org
Graphical results
Look at the "figure.pdf" file to see the results of the permutation testing,
extreme observations, and the loading and score plots
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http://workflow4metabolomics.org
Diagnostic metrics and
permutation testing
Diagnostics are similar to PLS (see above)
Note: OPLS improves the interpretation of the components but not the
overall predictive performance of the model
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http://workflow4metabolomics.org
Numerical results
The details of the R2X, R2Y, and Q2Y values are stored in the
"information.txt" file
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http://workflow4metabolomics.org
Advanced parameters
• Use the icon to view your last parameters, modify them
and start a new computation
• The optimal number of orthogonal components can be
estimated
• Note: Care should be taken to avoid too many orthogonal
components (which would result in overfitting) by
thoroughly examining the R2Y and Q2Y values in the
"overview" graphic
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http://workflow4metabolomics.org
References
• Trygg J., Holmes E. and Lundstedt T. (2007). Chemometrics in
Metabonomics. Journal of Proteome Research, 6:469-479.
http://dx.doi.org/10.1021/pr060594q
• Wheelock A. and Wheelock C.E. (2013). Trials and tribulations of omics data
analysis: Assessing quality of SIMCA-based multivariate models using
examples from pulmonary medicine. Molecular BioSystems, 9:2589-2596.
http://dx.doi.org/10.1039/C3MB70194H
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