Asca

Purpose

ANOVA-simultaneous component analysis (ASCA) is a method to determine which factors within a fixed effects experimental design are significant relative to the residual error. ASCA permits an ANOVA-like analysis even when there are many more variables than samples. ASCA is implemented following Smilde et al, "ANOVA-simultaneous component analysis (ASCA): a new tool for analyzing designed metabolomics data", Bioinformatics, 2005.

Synopsis

[model] = asca(x, F);

[model] = asca(x, F, ncomp);

[model] = asca(x, F, ncomp, options);

Description

Build an ASCA model by applying ASCA to X-block data, X, measured according to an experimental design, F. An ASCA model is intended to show which factors have a significant in explaining the experimental data. A P-value estimating the significance of each factor or interaction is calculated based on a permutation test of the factor's levels.

Inputs

• X = the experimental value determined for each experiment/row of F.
• F = array or dataset experiment design matrix describing the settings of each X variable (cols) for each sample (row). Note, When F is a dataset then the origin/identity of each column should be described in the options field, "interactions", or in the userdata.DOE.col_ID field.

Optional Inputs

• ncomp = a cell array of integer values indicating the number of Principal Components to use in each sub-model, or a single integer value which will be used as the number of Principal Components for each sub-model. If omitted, the maximum

number of components for each submodel will be calculated.

Outputs

• model = an ASCA standard model structure containing fields (when input matrix x has size mxn):

submodel: {1xnsub cell} of evrimodels

combinedscores: [mxp dataset]

combinedprojected: [mxp dataset]

details, which contains field:

data: cell array containing input x and F

decomp: [1x1 struct] containing internal quantities

decompdata: {1x(nsub+1) cell} of ANOVA decomposed arrays, each size [mxn]

decompnames: {mx1 cell} names of the ANOVA factor levels

effects: The percentage each effect (overall mean, factors, interactions and residuals) contributes to the sum of squares of the data matrix X.

decompresiduals: [mxn] containing the residuals term in the ANOVA model. This is the variability not modeled by the factors and interactions.

pvalues: P-values for significance of the factor or interaction's effect obtained by using a permutation test.

Options

options = a structure array with the following fields:

• display: [{'off'}| 'on' ] governs output to the command window.
• interactions: vector indicating which factors contribute to columns of F, or an integer which specifies the max. order of interactions to include, for example, 3 includes two-way and three-way interactions.
• npermutations: [{0}] Number of permutations to use when applying permutation test to each main factor to get P-value using Null Hypothesis that the factor has no effect on the experimental outcome. P-values are in model.detail.pvalues.
• nocenterpoints: [ 'off' |{'on'}] governs automatic filtering of center points. If a design contains additional added center points, these are typically removed before calculating the factor effects. However, some other packages do not do this filtering and the only way to match their results is to disable the filtering by setting this option to 'off'. Note that filtering can only be done if the input F is a DOE DataSet object.

Example

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See Also

baselinew, deresolv