Package 'DrBats' reference manual

Title:	Data Representation: Bayesian Approach That's Sparse
Description:	Feed longitudinal data into a Bayesian Latent Factor Model to obtain a low-rank representation. Parameters are estimated using a Hamiltonian Monte Carlo algorithm with STAN. See G. Weinrott, B. Fontez, N. Hilgert and S. Holmes, "Bayesian Latent Factor Model for Functional Data Analysis", Actes des JdS 2016.
Authors:	Gabrielle Weinrott [aut], Brigitte Charnomordic [ctr], Benedicte Fontez [cre, aut], Nadine Hilgert [ctr], Susan Holmes [ctr], Isabelle Sanchez [ctr]
Maintainer:	Benedicte Fontez <[email protected]>
License:	GPL-3
Version:	0.1.6
Built:	2024-10-30 04:01:59 UTC
Source:	https://github.com/cran/DrBats

Convert a STAN objet to MCMC list

Description

Convert a STAN objet to MCMC list

Usage

coda.obj(stanfit)
coda.obj(stanfit)

Arguments

stanfit

a STAN object

Value

codafit an mcmc.list

Author(s)

Gabrielle Weinrott

Examples

data(stanfit) # output of modelFit or main.modelFit
coda.fit <- coda.obj(stanfit)
head(coda.fit)

data(stanfit) # output of modelFit or main.modelFit
coda.fit <- coda.obj(stanfit)
head(coda.fit)

Perform Coinertia Analysis on the PCA of the Weighted PCA and Deville's PCA

Description

Perform Coinertia Analysis on the PCA of the Weighted PCA and Deville's PCA

Usage

coinertia.drbats(
  X.histo = NULL,
  Qp = NULL,
  X = NULL,
  t = NULL,
  t.range = c(0, 1000),
  breaks
)
coinertia.drbats(
  X.histo = NULL,
  Qp = NULL,
  X = NULL,
  t = NULL,
  t.range = c(0, 1000),
  breaks
)

Arguments

`X.histo`	the data matrix projected onto the histogram basis
`Qp`	a matrix of weights, if Qp = NULL the function specifies a diagonal weight matrix
`X`	a data matrix, if X.histo is NULL and needs to be built
`t`	a matrix of observation times, if X.histo is NULL and needs to be built
`t.range`	the range of observation times in vector form, if X.histo is NULL and needs to be built (default: t.range = c(0, 1000))
`breaks`	integer number of histogram windows

Value

co_weight the co-inertia object

Author(s)

Gabrielle Weinrott

Examples

res <- drbats.simul(N = 5, P = 100, t.range = c(5, 100), breaks = 8)
res.coinertia <- coinertia.drbats(X = res$X, t = res$t.simul, t.range = c(5, 100), breaks = 8)
res.coinertia

res <- drbats.simul(N = 5, P = 100, t.range = c(5, 100), breaks = 8)
res.coinertia <- coinertia.drbats(X = res$X, t = res$t.simul, t.range = c(5, 100), breaks = 8)
res.coinertia

Main simulation function

Description

Main simulation function

Usage

drbats.simul(
  N = 10,
  P = 150,
  t.range = c(0, 1000),
  b.range = c(0.2, 0.4),
  c.range = c(0.6, 0.8),
  b.sd = 2,
  c.sd = 2,
  a.range = c(-0.4, 0.4),
  y.range = c(0, 10),
  amp = 10,
  per = 12,
  data.type = "sparse",
  breaks = 15,
  sigma2 = 0.2,
  seed = NULL
)
drbats.simul(
  N = 10,
  P = 150,
  t.range = c(0, 1000),
  b.range = c(0.2, 0.4),
  c.range = c(0.6, 0.8),
  b.sd = 2,
  c.sd = 2,
  a.range = c(-0.4, 0.4),
  y.range = c(0, 10),
  amp = 10,
  per = 12,
  data.type = "sparse",
  breaks = 15,
  sigma2 = 0.2,
  seed = NULL
)

Arguments

`N`	integer number of functions to simulate (default = 10)
`P`	a number of observation times (default = 150)
`t.range`	a range of times in which to place the P observations (default = c(1, 1000))
`b.range`	a vector giving the range of values for the mean of the first mode (default b.range = c(0.2, 0.4))
`c.range`	a vector giving the range of values for the mean of the second mode (default c.range = c(0.6, 0.8))
`b.sd`	the standard deviation for the first mode (default b.sd = 2)
`c.sd`	the standard deviation for the second mode (default c.sd = 2)
`a.range`	a vector giving the range of values for the slope (default a.range = c(-0.4, 0.4))
`y.range`	a vector giving the range of values for the intercept (default y.range = c(0, 10))
`amp`	the amplitude of the cosine function (default = 10)
`per`	the periodicity of the cosine function (default = 12)
`data.type`	string indicating type of functions (options :sparse, sparse.tend, sparse.tend.cos)
`breaks`	number of breaks in the histogram basis
`sigma2`	the precision of the error terms (default = 0.2)
`seed`	integer specification of a seed (default = NULL)

Value

Y.simul a list containing a matrix Y, a matrix beta, and a matrix epsilon

t.simul a matrix of simulated observation times

X the underlying signal to build the data, see DataSimulationandProjection vignette

proj.pca the outputs of the function pca.proj.Xt

wlu the outputs of the function W.QR

Author(s)

Gabrielle Weinrott

Examples

res <- drbats.simul(N = 5, P = 100, t.range = c(5, 100), breaks = 8)
X <- res$X
t <- res$t.simul
# To plot the observations, ie the rows
matplot(t(t), t(X), type = 'l', xlab = "Time", ylab = "X")

res <- drbats.simul(N = 5, P = 100, t.range = c(5, 100), breaks = 8)
X <- res$X
t <- res$t.simul
# To plot the observations, ie the rows
matplot(t(t), t(X), type = 'l', xlab = "Time", ylab = "X")

Project a set of curves onto a histogram basis

Description

Project a set of curves onto a histogram basis

Usage

histoProj(X, t, t.range, breaks)
histoProj(X, t, t.range, breaks)

Arguments

`X`	a matrix
`t`	a matrix of observation times
`t.range`	a range of times in which to place the P projections (default = c(0, 1000))
`breaks`	the number of intervals in the histogram basis

Value

X.proj the matrix X after projection

X.count a matrix containing the number of observations used to build the projection onto the histogram basis

windows a vector containing the first time of each window of the histogram intervals

X.max the matrix of minimum values in each window

X.min the matrix of maximum values in each window

Author(s)

Gabrielle Weinrott

Examples

res <- drbats.simul(N = 5, P = 100, t.range = c(5, 100), breaks = 8)
res.proj <- histoProj(res$X, res$t.simul, t.range = c(5, 100), breaks = 8)
res.proj

res <- drbats.simul(N = 5, P = 100, t.range = c(5, 100), breaks = 8)
res.proj <- histoProj(res$X, res$t.simul, t.range = c(5, 100), breaks = 8)
res.proj

Fit a Bayesian Latent Factor to a data set using STAN

Description

Fit a Bayesian Latent Factor to a data set using STAN

Usage

modelFit(
  model = "PLT",
  var.prior = "IG",
  prog = "stan",
  parallel = TRUE,
  Xhisto = NULL,
  nchains = 4,
  nthin = 10,
  niter = 10000,
  R = NULL
)
modelFit(
  model = "PLT",
  var.prior = "IG",
  prog = "stan",
  parallel = TRUE,
  Xhisto = NULL,
  nchains = 4,
  nthin = 10,
  niter = 10000,
  R = NULL
)

Arguments

`model`	a string indicating the type of model ("PLT", or sparse", default = "PLT")
`var.prior`	the family of priors to use for the variance parameters ("IG" for inverse gamma, or "cauchy")
`prog`	a string indicating the MCMC program to use (default = "stan")
`parallel`	true or false, whether or not to parelleize (done using the package "parallel")
`Xhisto`	matrix of simulated data (projected onto the histogram basis)
`nchains`	number of chains (default = 2)
`nthin`	the number of thinned interations (default = 1)
`niter`	number of iterations (default = 1e4)
`R`	rotation matrix of the same dimension as the number of desired latent factors

Value

stanfit, a STAN object

Author(s)

Gabrielle Weinrott

References

The Stan Development Team Stan Modeling Language User's Guide and Reference Manual. http://mc-stan.org/

Perform a PCA using Deville's method

Description

Perform a PCA using Deville's method

Usage

pca.Deville(X, t, t.range, breaks)
pca.Deville(X, t, t.range, breaks)

Arguments

`X`	a data matrix
`t`	a matrix of observation times corresponding to X
`t.range`	the range of observation times in vector form (ex. t.range = c(0, 1000))
`breaks`	integer number of histogram windows

Value

X.histo the matrix projected onto the histogram basis

U.histo a matrix of eigenvectors in the histogram basis

Cp a matrix of principal components

lambda a vector of eigenvalues

perc.lambda a vector of the percentage of total inertia explained by each principal component

Author(s)

Gabrielle Weinrott

References

JC Deville, "Methodes statisiques et numeriques de l'analyse harmonique", Annales de l'INSEE, 1974.

Examples

res <- drbats.simul(N = 5, P = 100, t.range = c(5, 100), breaks = 8)
res.pca <- pca.Deville(res$X, res$t.simul, t.range = c(5, 100), breaks = 8)
res.pca

res <- drbats.simul(N = 5, P = 100, t.range = c(5, 100), breaks = 8)
res.pca <- pca.Deville(res$X, res$t.simul, t.range = c(5, 100), breaks = 8)
res.pca

PCA data projected onto a histogram basis

Description

PCA data projected onto a histogram basis

Usage

pca.proj.Xt(X, t, t.range = c(0, 1000), breaks = 15)
pca.proj.Xt(X, t, t.range = c(0, 1000), breaks = 15)

Arguments

`X`	the data matrix
`t`	the matrix of observation times
`t.range`	a vector specifying the observation time range (default : c(0, 1000))
`breaks`	the number of breaks in the histogram basis (default : breaks = 15)

Value

Xt.proj a matrix of projected observations

U a matrix of eigenvectors

lambda a vector of eigenvalues

lambda.perc the percentage of inertia captured by each axis

Author(s)

Gabrielle Weinrott

Examples

res <- drbats.simul(N = 5, P = 100, t.range = c(5, 100), breaks = 8)
pca.proj.Xt(res$X, res$t.simul, t.range = c(0, 100), breaks = 8)

res <- drbats.simul(N = 5, P = 100, t.range = c(5, 100), breaks = 8)
pca.proj.Xt(res$X, res$t.simul, t.range = c(0, 100), breaks = 8)

Calculate the unnormalized posterior density of the model

Description

Calculate the unnormalized posterior density of the model

Usage

postdens(mcmc.output, Y, D, chain = 1)
postdens(mcmc.output, Y, D, chain = 1)

Arguments

`mcmc.output`	an mcmc list as produced by clean.mcmc
`Y`	the data matrix
`D`	the number of latent factors
`chain`	the chain to plot (default = 1)

Value

post a vector containing the posterior density at each iteration##' @examples

Author(s)

Gabrielle Weinrott

Examples

data("toydata")
data("stanfit")
dens <- postdens(coda.obj(stanfit), Y = toydata$Y.simul$Y, D = 2, chain = 1)
hist(dens)

data("toydata")
data("stanfit")
dens <- postdens(coda.obj(stanfit), Y = toydata$Y.simul$Y, D = 2, chain = 1)
hist(dens)

A stanfit object fitted to the toydata

Description

A stanfit object fitted to the toydata

Usage

stanfit
stanfit

Format

A large stanfit object

A toy longitudinal data set

Description

A toy longitudinal data set

Usage

toydata
toydata

Format

A list with 5 elements :

Y.simul: a list of simulated data with 3 elements
t.simul: a matrix with 5 rows and 150 columns giving the observation times of the original data
X: the original data matrix with 5 rows and 150 columns
proj.pca: a list with 4 elements : results of the function histoProj(X, t, t.range = c(0, 1000), breaks = 8)
wlu: a list with 4 elements : results of the function W.QR(U, lambda) where U and lambda are the results of the PCA of X

Format scores output for visualization

Description

Format scores output for visualization

Usage

visbeta(mcmc.output, Y, D, chain = 1, axes = c(1, 2), quant = NULL)
visbeta(mcmc.output, Y, D, chain = 1, axes = c(1, 2), quant = NULL)

Arguments

`mcmc.output`	an mcmc list as produced by clean.mcmc
`Y`	the matrix of data
`D`	the number of latent factors
`chain`	the chain to use (default = 1)
`axes`	the axes to use (default = c(1, 2))
`quant`	a vector of quantiles to retain (default = NULL)

Value

mean.df are the MCMC estimates for the parmeters

points.df contains all of the estimates of the chain

contour.df contains the exterior points of the convex hull of the cloud of estimates

Author(s)

Gabrielle Weinrott

Examples

data("toydata")
data("stanfit")
codafit <- coda.obj(stanfit) ## convert to mcmc.list
beta.res <- visbeta(codafit, Y = toydata$Y.simul$Y, D = toydata$wlu$D, chain = 1,
axes = c(1, 2), quant = c(0.05, 0.95))

ggplot2::ggplot() +
  ggplot2::geom_path(data = beta.res$contour.df, ggplot2::aes(x = x, y = y, colour = ind)) +
  ggplot2::geom_point(data = beta.res$mean.df, ggplot2::aes(x = x, y = y, colour = ind))

data("toydata")
data("stanfit")
codafit <- coda.obj(stanfit) ## convert to mcmc.list
beta.res <- visbeta(codafit, Y = toydata$Y.simul$Y, D = toydata$wlu$D, chain = 1,
axes = c(1, 2), quant = c(0.05, 0.95))

ggplot2::ggplot() +
  ggplot2::geom_path(data = beta.res$contour.df, ggplot2::aes(x = x, y = y, colour = ind)) +
  ggplot2::geom_point(data = beta.res$mean.df, ggplot2::aes(x = x, y = y, colour = ind))

Plot the estimates for the latent factors

Description

Plot the estimates for the latent factors

Usage

visW(mcmc.output, Y, D, chain = 1, factors = c(1, 2))
visW(mcmc.output, Y, D, chain = 1, factors = c(1, 2))

Arguments

`mcmc.output`	an mcmc list as produced by clean.mcmc
`Y`	the matrix of data
`D`	the number of latent factors
`chain`	the chain to plot (default = 1)
`factors`	a vector indicating the factors to plot (default = c(1, 2))

Value

res.W a data frame containing the estimates for the factors, and their lower and upper bounds

Inertia the percentage of total inertia captured by each of the factors

Author(s)

Gabrielle Weinrott

Examples

data("toydata")
data("stanfit")
codafit <- coda.obj(stanfit) ## convert to mcmc.list
W.res <- visW(codafit, Y = toydata$Y.simul$Y, D = toydata$wlu$D,
chain = 1, factors = c(1, 2))

## plot the results

data <- data.frame(time = rep(1:9, 2), W.res$res.W)
ggplot2::ggplot() +
  ggplot2::geom_step(data = data, ggplot2::aes(x = time, y = Estimation, colour = Factor)) +
  ggplot2::geom_step(data = data, ggplot2::aes(x = time, y = Lower.est, colour = Factor),
  linetype = "longdash") +
  ggplot2::geom_step(data = data, ggplot2::aes(x = time, y = Upper.est, colour = Factor),
  linetype = "longdash")

data("toydata")
data("stanfit")
codafit <- coda.obj(stanfit) ## convert to mcmc.list
W.res <- visW(codafit, Y = toydata$Y.simul$Y, D = toydata$wlu$D,
chain = 1, factors = c(1, 2))

## plot the results

data <- data.frame(time = rep(1:9, 2), W.res$res.W)
ggplot2::ggplot() +
  ggplot2::geom_step(data = data, ggplot2::aes(x = time, y = Estimation, colour = Factor)) +
  ggplot2::geom_step(data = data, ggplot2::aes(x = time, y = Lower.est, colour = Factor),
  linetype = "longdash") +
  ggplot2::geom_step(data = data, ggplot2::aes(x = time, y = Upper.est, colour = Factor),
  linetype = "longdash")

Build and decompose a low-rank matrix W

Description

Build and decompose a low-rank matrix from a matrix of eigenvectors and eigenvalues from principal component analysis

Usage

W.QR(U, lambda)
W.QR(U, lambda)

Arguments

`U`	a matrix of eigenvectors
`lambda`	a vector of corresponding eigenvalues

Value

W a low-rank matrix

D the number of latent factors

Q the orthogonal matrix of the W = QR matrix decomposition

R the upper triangular matrix of the W = QR matrix decomposition

Author(s)

Gabrielle Weinrott

Examples

res <- drbats.simul(N = 5, P = 100, t.range = c(5, 100), breaks = 8)
res.pca <- pca.Deville(res$X, res$t.simul, t.range = c(5, 100), breaks = 8)
Wres.pca <- W.QR(res.pca$U, res.pca$lambda)
Wres.pca

res <- drbats.simul(N = 5, P = 100, t.range = c(5, 100), breaks = 8)
res.pca <- pca.Deville(res$X, res$t.simul, t.range = c(5, 100), breaks = 8)
Wres.pca <- W.QR(res.pca$U, res.pca$lambda)
Wres.pca

Perform a weighted PCA using Deville's method on a data matrix X that we project onto a histogram basis and weighted

Description

Perform a weighted PCA using Deville's method on a data matrix X that we project onto a histogram basis and weighted

Usage

weighted.Deville(X, t, t.range, breaks, Qp = NULL)
weighted.Deville(X, t, t.range, breaks, Qp = NULL)

Arguments

`X`	a data matrix
`t`	a matrix of observation times corresponding to X
`t.range`	the range of observation times in vector form (ex. t.range = c(a, b))
`breaks`	integer number of histogram windows
`Qp`	a matrix of weights, if Qp = NULL the function specifies a diagonal weight matrix

Value

X.histo the matrix projected onto the histogram basis

U.histo a matrix of eigenvectors in the histogram basis

Cp a matrix of principal components

lambda a vector of eigenvalues

perc.lambda a vector of the percentage of total inertia explained by each principal component

Author(s)

Gabrielle Weinrott

Examples

res <- drbats.simul(N = 5, P = 100, t.range = c(5, 100), breaks = 8)
res.weighted <- weighted.Deville(res$X, res$t.simul, t.range = c(5, 100), breaks = 8, Qp = NULL)
res.weighted

res <- drbats.simul(N = 5, P = 100, t.range = c(5, 100), breaks = 8)
res.weighted <- weighted.Deville(res$X, res$t.simul, t.range = c(5, 100), breaks = 8, Qp = NULL)
res.weighted

Package 'DrBats'

Help Index

Convert a STAN objet to MCMC list

Description

Usage

Arguments

Value

Author(s)

Examples

Perform Coinertia Analysis on the PCA of the Weighted PCA and Deville's PCA

Description

Usage

Arguments

Value

Author(s)

Examples

Main simulation function

Description

Usage

Arguments

Value

Author(s)

Examples

Project a set of curves onto a histogram basis

Description

Usage

Arguments

Value

Author(s)

Examples

Fit a Bayesian Latent Factor to a data set using STAN

Description

Usage

Arguments

Value

Author(s)

References

Perform a PCA using Deville's method

Description

Usage

Arguments

Value

Author(s)

References

Examples

PCA data projected onto a histogram basis

Description

Usage

Arguments

Value

Author(s)

Examples

Calculate the unnormalized posterior density of the model

Description

Usage

Arguments

Value

Author(s)

Examples

A stanfit object fitted to the toydata

Description

Usage

Format

A toy longitudinal data set

Description

Usage

Format

Format scores output for visualization

Description

Usage

Arguments

Value

Author(s)

Examples

Plot the estimates for the latent factors

Description

Usage

Arguments

Value

Author(s)