Type: Package
Title: Probabilistic Latent Variable Models for Metabolomic Data
Version: 1.3.1
Date: 2010-05-12
Author: Nyamundanda Gift, Isobel Claire Gormley and Lorraine Brennan.
Maintainer: Claire Gormley <claire.gormley@ucd.ie>
Description: Fits probabilistic principal components analysis, probabilistic principal components and covariates analysis and mixtures of probabilistic principal components models to metabolomic spectral data.
Depends: mclust, mvtnorm, ellipse, gtools, gplots
License: GPL-2
LazyLoad: yes
Packaged: 2019-08-31 10:22:13 UTC; hornik
Repository: CRAN
Date/Publication: 2019-08-31 10:24:07 UTC
NeedsCompilation: no

Probabilistic latent variable models for metabolomic data.

Description

Fits probabilistic principal components analysis (PPCA), probabilistic principal components and covariates analysis (PPCCA) and mixtures of probabilistic principal component analysis (MPPCA) models to metabolomic spectral data. Estimates of the uncertainty associated with the model parameter estimates are provided.

Details

Package: MetabolAnalyze
Type: Package
Version: 1.0
Date: 2010-05-12
License: GPL-2
LazyLoad: yes

Author(s)

Nyamundanda Gift, Isobel Claire Gormley and Lorraine Brennan.

Claire Gormley <claire.gormley@ucd.ie>

References

Nyamundanda, G., Gormley, I.C. and Brennan, L. (2010) Probabilistic principal components analysis for metabolomic data. Technical Report. University College Dublin.

Assess convergence of an EM algorithm.

Description

This function assesses convergence of the EM algorithm using Aitken's acceleration method, when fitting a PPCA based model.

Usage

Aitken(ll, lla, v, q, epsilon)

Arguments

ll

A vector of log likelihoods from the current and previous iterations.

lla

A vector containing the asympototic estimates of the maximized log likelihoods from the current and previous iterations.

v

Iteration number.

q

The dimension of the latent principal subspace for the PPCA based model currently being fitted.

epsilon

The value on which convergence of the EM algorithm is based.

Details

This function assesses convergence of the EM algorithm using Aitken's acceleration method in which an estimate of the maximized log likelihood at each iteration is evaluated. Convergence is achieved when the absolute difference between contiguous estimates, tol, is less than some user defined level, epsilon.

Value

A list containing:

tol

The absolute difference between contiguous estimates of the asymptotic maximized log likelihood.

la

The asymptotic estimate of the maximized log likelihood at the current iteration.

Note

This is used internally in functions which fit PPCA based models via the EM algorithm within the package MetabolAnalyze.

Author(s)

Nyamundanda Gift, Isobel Claire Gormley and Lorraine Brennan

References

McLachlan, G.J. and Krishnan, T. (1997) The EM algorithm and Extensions. Wiley, New York.

See Also

ppca.metabol, ppcca.metabol, mppca.metabol

NMR spectral data from brain tissue samples.

Description

NMR spectral data from brain tissue samples of 33 rats, where each tissue sample originates in one of four known brain regions. Each spectrum has 164 spectral bins, measured in parts per million (ppm).

Usage

data(BrainSpectra)

Format

A list containing

  1. a matrix with 33 rows and 164 columns

  2. a vector indicating the brain region of origin of each sample where:

    • 1 = Brain stem

    • 2 = Cerebellum

    • 3 = Hippocampus

    • 4 = Pre-frontal cortex

Details

This is simulated data, based on parameter estimates from a mixture of PPCA models with 4 groups and 7 principal components fitted to a similar real data set.

Source

Nyamundanda, G., Gormley, I.C. and Brennan, L. (2010) Probabilistic principal components analysis for metabolomic data. Technical report. University College Dublin, Ireland.

NMR metabolomic spectra from urine samples of 18 mice.

Description

NMR metabolomic spectra from urine samples of 18 mice, each belonging to one of two treatment groups. Each spectrum has 189 spectral bins, measured in parts per million (ppm).

Covariates associated with the mice were also recorded: the weight of each mouse is provided.

Usage

data(UrineSpectra)

Format

A list containing

  1. a matrix with 18 rows and 189 columns

  2. a data frame with 18 observations on 2 variables:

    • Treatment group membership of each animal.

    • Weight (in grammes) of each animal.

Details

This is simulated data, based on parameter estimates from a PPCA model with two prinicipal components fitted to a similar real data set.

Source

Nyamundanda, G., Gormley, I.C. and Brennan, L. (2010) Probabilistic principal components analysis for metabolomic data. Technical report. University College Dublin, Ireland.

First E step of the AECM algorithm when fitting a mixture of PPCA models.

Description

Internal function required for fitting a mixture of PPCA models.

Usage

estep1(Y, Tau, Pi, mu, W, Sig, g, p, reset)

Arguments

Y

A N x p data matrix.

Tau

A N x G matrix of posterior group membership probabilities.

Pi

A G vector of mixing proportions.

mu

A p x G matrix containing the mean for each group.

W

An p x q x G array of loadings for each group.

Sig

A scalar; the error covariance.

g

The number of groups currently being fitted.

p

Number of spectral bins in the NMR spectra.

reset

Logical indicating computational instability.

Details

First E step of the AECM algorithm when fitting a mixture of PPCA models. An internal function.

Value

A list containing

Tau

The N x G matrix of posterior group membership probablities.

logTau

An N x G matrix of the log of the numerator of posterior group membership probablities.

reset

Logical indicating computational instability.

Note

An internal function.

Author(s)

Nyamundanda Gift, Isobel Claire Gormley and Lorraine Brennan

References

Nyamundanda, G., Gormley, I.C. and Brennan, L. (2010) Probabilistic principal components analysis for metabolomic data. Technical report. University College Dublin, Ireland.

See Also

mppca.metabol

Second E step of the AECM algorithm when fitting a mixture of PPCA models.

Description

Internal function required for fitting a mixture of PPCA models.

Usage

estep2(Y, Tau, Pi, mu, W, Sig, g, p, reset)

Arguments

Y

A N x p data matrix.

Tau

An N x g matrix of posterior group membership probabilities.

Pi

A g vector of group probabilities.

mu

A p x g matrix containing the mean for each group.

W

An p x q x g array of loadings for each group.

Sig

A scalar; the error covariance.

g

The number of groups currently being fitted.

p

Number of spectral bins in the NMR spectra.

reset

Logical indicating computational instability.

Details

Second E step of the AECM algorithm when fitting a mixture of PPCA models. An internal function.

Value

A list containing

Tau

The N x G matrix of posterior group membership probablities.

logTau

An N x G matrix of the log of the numerator of posterior group membership probablities.

reset

Logical indicating computational instability.

Note

An internal function.

Author(s)

Nyamundanda Gift, Isobel Claire Gormley and Lorraine Brennan

References

Nyamundanda, G., Gormley, I.C. and Brennan, L. (2010) Probabilistic principal components analysis for metabolomic data. Technical report. University College Dublin, Ireland.

See Also

mppca.metabol

Function to plot a heatmap of BIC values.

Description

Function to plot a heat map of BIC values where lighter colours indicate larger values and optimal models. A black cross indicates the optimal model.

The function is a modified version of heatmap.

Usage

ht(x, Rowv = NULL, Colv = if (symm) "Rowv" else NULL, distfun = dist,
   hclustfun = hclust, reorderfun = function(d, w) reorder(d, w),
   add.expr, symm = FALSE, revC = identical(Colv, "Rowv"),
   scale = c("row", "column", "none"), na.rm = FALSE, margins = c(5, 5),
   ColSideColors, RowSideColors, cexRow = 1, cexCol = 1, labRow = NULL,
   labCol = NULL, main = NULL, xlab = NULL, ylab = NULL,
   keep.dendro = FALSE, verbose = getOption("verbose"), q, g)

Arguments

See the help file for heatmap.

Details

This function is used internally in mppca.metabol.

Value

See the help file for heatmap.

Note

An internal function.

Author(s)

Nyamundanda Gift, Isobel Claire Gormley and Lorraine Brennan

References

Nyamundanda, G., Gormley, I.C. and Brennan, L. (2010) Probabilistic principal components analysis for metabolomic data. Technical report. University College Dublin, Ireland.

See Also

mppca.metabol

Plot loadings and their associated confidence intervals.

Description

A function to plot the loadings and confidence intervals resulting from fitting a PPCA model or a PPCCA model to metabolomic data.

Usage

loadings.jack.plot(output)

Arguments

output

An object resulting from fitting a PPCA model or a PPCCA model.

Details

The function produces a plot of those loadings on the first principal component which are significantly different from zero, and higher than a user specified cutoff point. Error bars associated with the estimates, derived using the jackknife, are also plotted.

Author(s)

Nyamundanda Gift, Isobel Claire Gormley and Lorraine Brennan

References

Nyamundanda, G., Gormley, I.C. and Brennan, L. (2010) Probabilistic principal components analysis for metabolomic data. Technical report. University College Dublin, Ireland.

See Also

ppca.metabol.jack, ppcca.metabol.jack

Plot loadings.

Description

A function to plot the loadings resulting from fitting a PPCA model or a PPCCA model to metabolomic data. A barplot or a scatterplot can be produced.

Usage

loadings.plot(output, barplot = FALSE, labelsize = 0.3)

Arguments

output

An object resulting from fitting a PPCA model or a PPCCA model.

barplot

Logical indicating whether a barplot of the loadings is required rather than a scatter plot. By default a scatter plot is produced.

labelsize

Size of the text of the spectral bin labels on the resulting plot.

Details

A function to plot the loadings resulting from fitting a PPCA model or a PPCCA model to metabolomic data. A barplot or a scatterplot can be produced. The size of the text of the spectral bin labels on the bar plot can also be adjusted if the number of bins plotted is large.

Author(s)

Nyamundanda Gift, Isobel Claire Gormley and Lorraine Brennan

References

Nyamundanda, G., Gormley, I.C. and Brennan, L. (2010) Probabilistic principal components analysis for metabolomic data. Technical report. University College Dublin, Ireland.

See Also

ppca.metabol, ppcca.metabol

Plot loadings resulting from fitting a MPPCA model.

Description

A function to plot the loadings resulting from fitting a MPPCA model to metabolomic data. A barplot or a scatterplot can be produced.

Usage

mppca.loadings.plot(output, Y, barplot = FALSE, labelsize = 0.3)

Arguments

output

An object resulting from fitting a MPPCA model.

Y

The N x p matrix of observations to which the MPPCA model is fitted.

barplot

Logical indicating whether a barplot of the loadings is required rather than a scatter plot. By default a scatter plot is produced.

labelsize

Size of the text of the spectral bin labels on the resulting plot.

Details

A function which produces a series of plots illustrating the loadings resulting from fitting a MPPCA model to metabolomic data. A barplot or a scatterplot can be produced. The size of the text of the spectral bin labels on the bar plot can also be adjusted if the number of bins plotted is large.

Author(s)

Nyamundanda Gift, Isobel Claire Gormley and Lorraine Brennan

References

Nyamundanda, G., Gormley, I.C. and Brennan, L. (2010) Probabilistic principal components analysis for metabolomic data. Technical report. University College Dublin, Ireland.

See Also

mppca.metabol

Fit a mixture of probabilistic principal components analysis (MPPCA) model to a metabolomic data set via the EM algorithm to perform simultaneous dimension reduction and clustering.

Description

This function fits a mixture of probabilistic principal components analysis model to metabolomic spectral data via the EM algorithm.

Usage

mppca.metabol(Y, minq=1, maxq=2, ming, maxg, scale = "none", 
epsilon = 0.1, plot.BIC = FALSE)

Arguments

Y

An N x p data matrix where each row is a spectrum.

minq

The minimum number of principal components to be fit. By default minq is 1.

maxq

The maximum number of principal components to be fit. By default maxq is 2.

ming

The minimum number of groups to be fit.

maxg

The maximum number of groups to be fit.

scale

Type of scaling of the data which is required. The default is "none". Options include "pareto' and "unit" scaling. See scaling for further details.

epsilon

Value on which the convergence assessment criterion is based. Set by default to 0.1.

plot.BIC

Logical indicating whether or not a plot of the BIC values for the different models fitted should be provided. By default, the plot is not produced.

Details

This function fits a mixture of probabilistic principal components analysis models to metabolomic spectral data via the EM algorithm. A range of models with different numbers of groups and different numbers of principal components can be fitted. The model performs simultaneous clustering of observations into unknown groups and dimension reduction simultaneously.

Value

A list containing:

q

The number of principal components in the optimal MPPCA model, selected by the BIC.

g

The number of groups in the optimal MPPCA model, selected by the BIC.

sig

The posterior mode estimate of the variance of the error terms.

scores

A list of length g, each entry of which is a n_g x q matrix of estimates of the latent locations of each observation in group g in the principal subspace.

loadings

An array of dimension p x q x g, each sheet of which contains the maximum likelihood estimate of the p x q loadings matrix for a group.

Pi

The vector indicating the probability of belonging to each group.

mean

A p x g matrix, each column of which contains a group mean.

tau

An N x g matrix, each row of which contains the posterior group membership probabilities for an observation.

clustering

A vector of length N indicating the group to which each observation belongs.

BIC

A matrix containing the BIC values for the fitted models.

AIC

A matrix containing the AIC values for the fitted models.

Author(s)

Nyamundanda Gift, Isobel Claire Gormley and Lorraine Brennan.

References

Nyamundanda G., Gormley, I.C. and Brennan, L. (2010) Probabilistic principal components analysis for metabolomic data. Technical report, University College Dublin.

See Also

mppca.scores.plot, mppca.loadings.plot

Examples

data(BrainSpectra)
## Not run: 
mdlfit<-mppca.metabol(BrainSpectra[[1]], minq=7, maxq=7, ming=4, maxg=4, 
plot.BIC = TRUE)
mppca.scores.plot(mdlfit)
mppca.loadings.plot(mdlfit, BrainSpectra[[1]])

## End(Not run)

Plot scores from a fitted MPPCA model

Description

A function to plot the scores resulting from fitting a MPPCA model to metabolomic data.

Usage

mppca.scores.plot(output, group = FALSE, gplegend = TRUE)

Arguments

output

An object resulting from fitting a MPPCA model.

group

Should it be relevant, a vector indicating the known treatment group membership of each observation prior to clustering.

gplegend

Logical indicating whether a legend should be plotted.

Details

This function produces a series of scatterplots, for each group uncovered. For group g, each scatterplot illustrates the estimated score for each observation allocated to that group within the reduced q dimensional space. The uncertainty associated with the score estimate is also illustrated through its 95

It is often the case that observations are known to belong to treatment groups, for example, and the MPPCA model is employed to uncover any underlying subgroups, possibly related to disease subtypes. The treatment group membership of each observation can be illustrated on the plots produced by utilizing the ‘group’ argument.

Author(s)

Nyamundanda Gift, Isobel Claire Gormley and Lorraine Brennan

References

Nyamundanda, G., Gormley, I.C. and Brennan, L. (2010) Probabilistic principal components analysis for metabolomic data. Technical report. University College Dublin, Ireland.

See Also

mppca.metabol

First M-step of the AECM algorithm when fitting a mixture of PPCA models.

Description

Internal function required for fitting a mixture of PPCA models.

Usage

mstep1(Y, Tau, Pi, mu, g)

Arguments

Y

A N x p data matrix.

Tau

An N x G matrix of posterior group membership probabilities.

Pi

A g vector of group probabilities.

mu

A p x g matrix containing the mean for each group.

g

The number of groups currently being fitted.

Details

First M-step of the AECM algorithm when fitting a mixture of PPCA models. An internal function.

Value

A list containing

Pi

A g vector of group probabilities

Mu

A p x g matrix each column of which contains a group mean.

Note

An internal function.

Author(s)

Nyamundanda Gift, Isobel Claire Gormley and Lorraine Brennan

References

Nyamundanda, G., Gormley, I.C. and Brennan, L. (2010) Probabilistic principal components analysis for metabolomic data. Technical report. University College Dublin, Ireland.

See Also

mppca.metabol

Second M-step of the AECM algorithm when fitting a mixture of PPCA models.

Description

Internal function required for fitting a mixture of PPCA models.

Usage

mstep2(Y, Tau, Pi, mu, W, Sig, g, p, q)

Arguments

Y

A N x p data matrix.

Tau

An N x G matrix of posterior group membership probabilities.

Pi

A g vector of group probabilities.

mu

A p x g matrix containing the mean for each group.

W

A p x q x g array, each sheet of which contains a group specific loadings matrix.

Sig

The variance parmeter.

g

The number of groups currently being fitted.

p

The number of spectral bins in the NMR spectrum.

q

The number of principal components in the model being fitted.

Details

Second M-step of the AECM algorithm when fitting a mixture of PPCA models. An internal function.

Value

A list containing

W

A p x q x g array, each sheet of which contains a group specific loadings matrix.

Sig

The variance parameter.

Note

An internal function.

Author(s)

Nyamundanda Gift, Isobel Claire Gormley and Lorraine Brennan

References

Nyamundanda, G., Gormley, I.C. and Brennan, L. (2010) Probabilistic principal components analysis for metabolomic data. Technical report. University College Dublin, Ireland.

See Also

mppca.metabol

Fit a probabilistic principal components analysis (PPCA) model to a metabolomic data set via the EM algorithm.

Description

This function fits a probabilistic principal components analysis model to metabolomic spectral data via the EM algorithm.

Usage

ppca.metabol(Y, minq=1, maxq=2, scale = "none", epsilon = 0.1, 
plot.BIC = FALSE, printout=TRUE)

Arguments

Y

An N x p data matrix where each row is a spectrum.

minq

The minimum number of principal components to be fit. By default minq is 1.

maxq

The maximum number of principal components to be fit. By default maxq is 2.

scale

Type of scaling of the data which is required. The default is "none". Options include "pareto' and "unit" scaling. See scaling for further details.

epsilon

Value on which the convergence assessment criterion is based. Set by default to 0.1.

plot.BIC

Logical indicating whether or not a plot of the BIC values for the different models fitted should be provided. By default, the plot is not produced.

printout

Logical indicating whether or not a statement is printed on screen detailing the progress of the algorithm.

Details

This function fits a probabilistic principal components analysis model to metabolomic spectral data via the EM algorithm. A range of models with different numbers of principal components can be fitted.

Value

A list containing:

q

The number of principal components in the optimal PPCA model, selected by the BIC.

sig

The posterior mode estimate of the variance of the error terms.

scores

An N x q matrix of estimates of the latent locations of each observation in the principal subspace.

loadings

The maximum likelihood estimate of the p x q loadings matrix.

BIC

A vector containing the BIC values for the fitted models.

AIC

A vector containing the AIC values for the fitted models.

Author(s)

Nyamundanda Gift, Isobel Claire Gormley and Lorraine Brennan.

References

Nyamundanda G., Gormley, I.C. and Brennan, L. (2010) Probabilistic principal components analysis for metabolomic data. Technical report, University College Dublin.

See Also

ppca.metabol.jack, loadings.plot, ppca.scores.plot

Examples

data(UrineSpectra)
## Not run: 
mdlfit<-ppca.metabol(UrineSpectra[[1]], minq=2, maxq=2, scale="none")
loadings.plot(mdlfit)
ppca.scores.plot(mdlfit, group=UrineSpectra[[2]][,1])

## End(Not run)

Fit a probabilistic principal components analysis model to a metabolomic data set, and assess uncertainty via the jackknife.

Description

Fit a probabilistic principal components analysis (PPCA) model to a metabolomic data set via the EM algorithm, and assess uncertainty in the obtained loadings estimates via the jackknife.

Usage

ppca.metabol.jack(Y, minq=1, maxq=2, scale ="none", 
epsilon = 0.1, conflevel = 0.95)

Arguments

Y

An N x p data matrix where each row is a spectrum.

minq

The minimum number of principal components to be fit. By default minq is 1.

maxq

The maximum number of principal components to be fit. By default maxq is 2.

scale

Type of scaling of the data which is required. The default is "none". Options include "pareto' and "unit" scaling. See scaling for further details.

epsilon

Value on which the convergence assessment criterion is based. Set by default to 0.1.

conflevel

Level of confidence required for the loadings confidence intervals. By default 95\% confidence intervals are computed.

Details

A (range of) PPCA model(s) are fitted and an optimal model (i.e. number of principal components, q) is selected. Confidence intervals for the obtained loadings are then obtained via the jackknife i.e. a model with q principal components is fitted to the dataset N times, where an observation is removed from the dataset each time.

On convergence of the algorithm, the number of loadings significantly different from zero is printed on screen. The user may then further examine the significant loadings when prompted by selecting a cutoff value from the table printed on screen. Bar plots detailing the resulting significantly high loadings are provided.

Value

A list containing:

q

The number of principal components in the optimal PPCA model, selected by the BIC.

sig

The posterior mode estimate of the variance of the error terms.

scores

An N x q matrix of estimates of the latent locations of each observation in the principal subspace.

loadings

The maximum likelihood estimate of the p x q loadings matrix.

SignifW

The maximum likelihood estimate of the loadings matrix for those loadings significantly different from zero.

SignifHighW

The maximum likelihood estimate of the loadings matrix for those loadings significantly different from zero and higher than a user selected cutoff point.

Lower

The lower limit of the confidence interval for those loadings significantly different from zero.

Upper

The upper limit of the confidence interval for those loadings significantly different from zero.

Cutoffs

A table detailing a range of cutoff points and the associated number of selected spectral bins.

number

The number of spectral bins selected by the user.

cutoff

The cutoff value selected by the user.

BIC

A vector containing the BIC values for the fitted models.

AIC

A vector containing the AIC values for the fitted models.

Author(s)

Nyamundanda Gift, Isobel Claire Gormley and Lorraine Brennan.

References

Nyamundanda G., Gormley, I.C. and Brennan, L. (2010) Probabilistic principal components analysis for metabolomic data. Technical report, University College Dublin.

See Also

ppca.metabol, loadings.jack.plot, ppca.scores.plot

Examples

data(UrineSpectra)
## Not run: 
mdlfit<-ppca.metabol.jack(UrineSpectra[[1]], minq=2, maxq=2, scale="none")
loadings.jack.plot(mdlfit)
ppca.scores.plot(mdlfit, group=UrineSpectra[[2]][,1])
## End(Not run)

Plot scores from a fitted PPCA model

Description

A function to plot the scores resulting from fitting a PPCA model to metabolomic data.

Usage

ppca.scores.plot(output, group = FALSE)

Arguments

output

An object resulting from fitting a PPCA model.

group

Should it be relevant, a vector indicating the known treatment group membership of each observation.

Details

This function produces a series of scatterplots each illustrating the estimated score for each observation within the reduced q dimensional space. The uncertainty associated with the score estimate is also illustrated through its 95

It is often the case that observations are known to belong to treatment groups; the treatment group membership of each observation can be illustrated on the plots produced by utilizing the ‘group’ argument.

Author(s)

Nyamundanda Gift, Isobel Claire Gormley and Lorraine Brennan

References

Nyamundanda, G., Gormley, I.C. and Brennan, L. (2010) Probabilistic principal components analysis for metabolomic data. Technical report. University College Dublin, Ireland.

See Also

ppca.metabol, ppca.metabol.jack

Fit a probabilistic principal components and covariates analysis (PPCCA) model to a metabolomic data set via the EM algorithm.

Description

This function fits a probabilistic principal components and covariates analysis model to metabolomic spectral data via the EM algorithm.

Usage

ppcca.metabol(Y, Covars, minq=1, maxq=2, scale = "none", epsilon = 0.1, 
plot.BIC = FALSE, printout=TRUE)

Arguments

Y

An N x p data matrix in which each row is a spectrum.

Covars

An N x L covariate data matrix in which each row is a set of covariates.

minq

The minimum number of principal components to be fit.

maxq

The maximum number of principal components to be fit.

scale

Type of scaling of the data which is required. The default is "none". Options include "pareto' and "unit" scaling. See scaling for further details.

epsilon

Value on which the convergence assessment criterion is based. Set by default to 0.1.

plot.BIC

Logical indicating whether or not a plot of the BIC values for the different models fitted should be provided. By default, the plot is not produced.

printout

Logical indicating whether or not a statement is printed on screen detailing the progress of the algorithm.

Details

This function fits a probabilistic principal components and covariates analysis model to metabolomic spectral data via the EM algorithm. A range of models with different numbers of principal components can be fitted.

Care should be taken with the form of covariates supplied. All covariates are standardized (to lie in [0,1]) within the ppcca.metabol function for stability reasons. Hence continuous covariates and binary valued categorical covariates are easily handled. For a categorical covariate with V levels, the equivalent V-1 dummy variables representation should be passed as an argument to ppcca.metabol.

Value

A list containing:

q

The number of principal components in the optimal PPCCA model, selected by the BIC.

sig

The posterior mode estimate of the variance of the error terms.

scores

An N x q matrix of estimates of the latent locations of each observation in the principal subspace.

loadings

The maximum likelihood estimate of the p x q loadings matrix.

coefficients

The maximum likelihood estimates of the regression coefficients associated with the covariates in the PPCCA model.

BIC

A vector containing the BIC values for the fitted models.

AIC

A vector containing the AIC values for the fitted models.

Author(s)

Nyamundanda Gift, Isobel Claire Gormley and Lorraine Brennan.

References

Nyamundanda G., Gormley, I.C. and Brennan, L. (2010) Probabilistic principal components analysis for metabolomic data. Technical report, University College Dublin.

See Also

ppcca.metabol.jack, ppcca.scores.plotloadings.plot

Examples

data(UrineSpectra)
## Not run: 
mdlfit<-ppcca.metabol(UrineSpectra[[1]], UrineSpectra[[2]][,2], minq=2, maxq=2)
loadings.plot(mdlfit)
ppcca.scores.plot(mdlfit, UrineSpectra[[2]][,2], group=UrineSpectra[[2]][,1], covarnames="Weight")

## End(Not run)

Fit a probabilistic principal components and covariates analysis model to a metabolomic data set, and assess uncertainty via the jackknife.

Description

Fit a probabilistic principal components and covariates analysis (PPCCA) model to a metabolomic data set via the EM algorithm, and assess uncertainty in the obtained loadings estimates and the regression coefficients via the jackknife.

Usage

ppcca.metabol.jack(Y, Covars, minq=1, maxq=2, scale="none", epsilon=0.1, 
conflevel=0.95)

Arguments

Y

An N x p data matrix in which each row is a spectrum.

Covars

An N x L covariate data matrix where each row is a set of covariates.

minq

The minimum number of principal components to be fit. By default minq is 1.

maxq

The maximum number of principal components to be fit. By default maxq is 2.

scale

Type of scaling of the data which is required. The default is "none". Options include "pareto' and "unit" scaling. See scaling for further details.

epsilon

Value on which the convergence assessment criterion is based. Set by default to 0.1.

conflevel

Level of confidence required for the loadings and regression coefficients confidence intervals. By default 95\% confidence intervals are computed.

Details

A (range of) PPCCA model(s) are fitted and an optimal model (i.e. number of principal components, q) is selected. Confidence intervals for the obtained loadings and regression coefficients are then obtained via the jackknife i.e. a model with q principal components is fitted to the data N times, where an observation is removed from the dataset each time.

Care should be taken with the form of covariates supplied. All covariates are standardized (to lie in [0,1]) within the ppcca.metabol.jack function for stability reasons. Hence continuous covariates and binary valued categorical covariates are easily handled. For a categorical covariate with V levels, the equivalent V-1 dummy variables representation should be passed as an argument to ppcca.metabol.jack.

On convergence of the algorithm, the number of loadings significantly different from zero is printed on screen. The user may then further examine the significant loadings when prompted by selecting a cutoff value from the table printed on screen. Bar plots detailing the resulting significantly high loadings are provided.

Value

A list containing:

q

The number of principal components in the optimal PPCCA model, selected by the BIC.

sig

The posterior mode estimate of the variance of the error terms.

scores

An N x q matrix of estimates of the latent locations of each observation in the principal subspace.

loadings

The maximum likelihood estimate of the p x q loadings matrix.

SignifW

The maximum likelihood estimate of the loadings matrix for those loadings significantly different from zero.

SignifHighW

The maximum likelihood estimate of the loadings matrix for those loadings significantly different from zero and above the user selected cutoff point.

LowerCI_W

The lower limit of the confidence interval for those loadings significantly different from zero.

UpperCI_W

The upper limit of the confidence interval for those loadings significantly different from zero.

coefficients

The maximum likelihood estimates of the regression coefficients.

coeffCI

A matrix detailing the upper and lower limits of the confidence intervals for the regression parameters.

Cutoffs

A table detailing a range of cutoff points and the associated number of selected spectral bins.

number

The number of spectral bins selected by the user.

cutoff

The cutoff value selected by the user.

BIC

A vector containing the BIC values for the fitted models.

AIC

A vector containing the AIC values for the fitted models.

Author(s)

Nyamundanda Gift, Isobel Claire Gormley and Lorraine Brennan.

References

Nyamundanda G., Gormley, I.C. and Brennan, L. (2010) Probabilistic principal components analysis for metabolomic data. Technical report, University College Dublin.

See Also

ppcca.metabol, ppcca.scores.plot,loadings.jack.plot

Examples

data(UrineSpectra)
## Not run: 
mdlfit<-ppcca.metabol.jack(UrineSpectra[[1]], UrineSpectra[[2]][,2], minq=2, maxq=2)
loadings.jack.plot(mdlfit)
ppcca.scores.plot(mdlfit, UrineSpectra[[2]][,2], group=UrineSpectra[[2]][,1], covarnames="Weight")

## End(Not run)

Plot scores from a fitted PPCCA model.

Description

A function to plot the scores resulting from fitting a PPCCA model to metabolomic data.

Usage

ppcca.scores.plot(output, Covars, group = FALSE, covarnames=NULL)

Arguments

output

An object resulting from fitting a PPCCA model.

Covars

An N x L covariate data matrix where each row is a set of covariates.

group

Should it be relevant, a vector indicating the known treatment group membership of each observation.

covarnames

Should it be relevant, a vector string indicating the names of the covariates.

Details

This function produces a series of scatterplots each illustrating the estimated score for each observation within the reduced q dimensional space. The uncertainty associated with the score estimate is also illustrated through its 95

It is often the case that observations are known to belong to treatment groups; the treatment group membership of each observation can be illustrated on the plots produced by utilizing the ‘group’ argument.

Author(s)

Nyamundanda Gift, Isobel Claire Gormley and Lorraine Brennan

References

Nyamundanda, G., Gormley, I.C. and Brennan, L. (2010) Probabilistic principal components analysis for metabolomic data. Technical report. University College Dublin, Ireland.

See Also

ppcca.metabol, ppcca.metabol.jack

Function to scale metabolomic spectral data.

Description

This function provides the options of Pareto scaling, unit scaling or no scaling of metabolomic data.

Usage

scaling(Y, type = "none")

Arguments

Y

An N x p matrix of metabolomic spectra. Each row of Y is an observation's spectrum.

type

Default is "none" meaning the data are not altered. If "pareto", the data are Pareto scaled. If "unit", the data are unit scaled.

Details

Pareto scaling, frequently utilised in metabolomic analyses, scales data by dividing each variable by the square root of the standard deviation. Unit scaling divides each variable by the standard deviation so that each variable has variance equal to 1.

Value

The function returns the requested scaled version of the input matrix Y.

Author(s)

Nyamundanda Gift, Isobel Claire Gormley and Lorraine Brennan.

References

van den Berg, R.A., Hoefsloot, H.C.J, Westerhuis, J.A. and Smilde, A.K. and van der Werf, M.J. (2006) Centering, scaling, and transformations: improving the biological information content of metabolomics data. BMC Genomics, 7, 1, 142.

Nyamundanda G., Gormley, I.C. and Brennan, L. (2010) Probabilistic principal components analysis for metabolomic data. Technical report, University College Dublin.

Function to scale covariates.

Description

A function to scale covariates so that they lie in [0,1] for reasons of stability and convergence of the EM algorithm.

Usage

standardize(Covars)

Arguments

Covars

An N x L matrix containing the L covariates of each of N observations.

Details

A function to scale covariates so that they lie in [0,1] for reasons of stability and convergence of the EM algorithm. Care must be taken with categorical covariates: see ppcca.metabol for further information.

Value

Covars

A standardized version of the input matrix of covariates.

Author(s)

Nyamundanda Gift, Isobel Claire Gormley and Lorraine Brennan