PLNPCAfit {PLNmodels}

An R6 Class to represent a PLNfit in a PCA framework

Description

The function PLNPCA() produces a collection of models which are instances of object with class PLNPCAfit. This class comes with a set of methods, some of them being useful for the user: See the documentation for the methods inherited by PLNfit and the plot() methods for PCA visualization

Super class

PLNmodels::PLNfit -> PLNPCAfit

Active bindings

rank

the dimension of the current model

vcov_model

character: the model used for the residual covariance

nb_param

number of parameters in the current PLN model

entropy

entropy of the variational distribution

latent_pos

a matrix: values of the latent position vector (Z) without covariates effects or offset

model_par

a list with the matrices associated with the estimated parameters of the pPCA model: B (covariates), Sigma (covariance), Omega (precision) and C (loadings)

percent_var

the percent of variance explained by each axis

corr_circle

a matrix of correlations to plot the correlation circles

scores

a matrix of scores to plot the individual factor maps (a.k.a. principal components)

rotation

a matrix of rotation of the latent space

eig

description of the eigenvalues, similar to percent_var but for use with external methods

var

a list of data frames with PCA results for the variables: coord (coordinates of the variables), cor (correlation between variables and dimensions), cos2 (Cosine of the variables) and contrib (contributions of the variable to the axes)

ind

a list of data frames with PCA results for the individuals: coord (coordinates of the individuals), cos2 (Cosine of the individuals), contrib (contributions of individuals to an axis inertia) and dist (distance of individuals to the origin).

call

Hacky binding for compatibility with factoextra functions

Methods

Public methods

• PLNPCAfit$new()

• PLNPCAfit$update()

• PLNPCAfit$optimize()

• PLNPCAfit$optimize_vestep()

• PLNPCAfit$project()

• PLNPCAfit$setVisualization()

• PLNPCAfit$postTreatment()

• PLNPCAfit$plot_individual_map()

• PLNPCAfit$plot_correlation_circle()

• PLNPCAfit$plot_PCA()

• PLNPCAfit$show()

• PLNPCAfit$clone()

Inherited methods

• PLNmodels::PLNfit$predict()
• PLNmodels::PLNfit$predict_cond()
• PLNmodels::PLNfit$print()

Method new()

Initialize a PLNPCAfit object

Usage

PLNPCAfit$new(rank, responses, covariates, offsets, weights, formula, control)

Arguments

rank

rank of the PCA (or equivalently, dimension of the latent space)

responses

the matrix of responses (called Y in the model). Will usually be extracted from the corresponding field in PLNfamily

covariates

design matrix (called X in the model). Will usually be extracted from the corresponding field in PLNfamily

offsets

offset matrix (called O in the model). Will usually be extracted from the corresponding field in PLNfamily

weights

an optional vector of observation weights to be used in the fitting process.

formula

model formula used for fitting, extracted from the formula in the upper-level call

control

a list for controlling the optimization. See details.

Method update()

Update a PLNPCAfit object

Usage

PLNPCAfit$update(
  B = NA,
  Sigma = NA,
  Omega = NA,
  C = NA,
  M = NA,
  S = NA,
  Z = NA,
  A = NA,
  Ji = NA,
  R2 = NA,
  monitoring = NA
)

Arguments

B

matrix of regression matrix

Sigma

variance-covariance matrix of the latent variables

Omega

precision matrix of the latent variables. Inverse of Sigma.

C

matrix of PCA loadings (in the latent space)

M

matrix of mean vectors for the variational approximation

S

matrix of variance vectors for the variational approximation

Z

matrix of latent vectors (includes covariates and offset effects)

A

matrix of fitted values

Ji

vector of variational lower bounds of the log-likelihoods (one value per sample)

R2

approximate R^2 goodness-of-fit criterion

monitoring

a list with optimization monitoring quantities

Returns

Update the current PLNPCAfit object

Method optimize()

Call to the C++ optimizer and update of the relevant fields

Usage

PLNPCAfit$optimize(responses, covariates, offsets, weights, config)

Arguments

responses

the matrix of responses (called Y in the model). Will usually be extracted from the corresponding field in PLNfamily

covariates

design matrix (called X in the model). Will usually be extracted from the corresponding field in PLNfamily

offsets

offset matrix (called O in the model). Will usually be extracted from the corresponding field in PLNfamily

weights

an optional vector of observation weights to be used in the fitting process.

config

part of the control argument which configures the optimizer

Method optimize_vestep()

Result of one call to the VE step of the optimization procedure: optimal variational parameters (M, S) and corresponding log likelihood values for fixed model parameters (C, B). Intended to position new data in the latent space for further use with PCA.

Usage

PLNPCAfit$optimize_vestep(
  covariates,
  offsets,
  responses,
  weights = rep(1, self$n),
  control = PLNPCA_param(backend = "nlopt")
)

Arguments

covariates

design matrix (called X in the model). Will usually be extracted from the corresponding field in PLNfamily

offsets

offset matrix (called O in the model). Will usually be extracted from the corresponding field in PLNfamily

responses

the matrix of responses (called Y in the model). Will usually be extracted from the corresponding field in PLNfamily

weights

an optional vector of observation weights to be used in the fitting process.

control

a list for controlling the optimization. See details.

Returns

A list with three components:

• the matrix M of variational means,

• the matrix S2 of variational variances

• the vector log.lik of (variational) log-likelihood of each new observation

Method project()

Project new samples into the PCA space using one VE step

Usage

PLNPCAfit$project(newdata, control = PLNPCA_param(), envir = parent.frame())

Arguments

newdata

A data frame in which to look for variables, offsets and counts with which to predict.

control

a list for controlling the optimization. See PLN() for details.

envir

Environment in which the projection is evaluated

Returns

• the named matrix of scores for the newdata, expressed in the same coordinate system as self$scores

Method setVisualization()

Compute PCA scores in the latent space and update corresponding fields.

Usage

PLNPCAfit$setVisualization(scale.unit = FALSE)

Arguments

scale.unit

Logical. Should PCA scores be rescaled to have unit variance

Method postTreatment()

Update R2, fisher, std_err fields and set up visualization

Usage

PLNPCAfit$postTreatment(
  responses,
  covariates,
  offsets,
  weights,
  config_post,
  config_optim,
  nullModel
)

Arguments

responses

the matrix of responses (called Y in the model). Will usually be extracted from the corresponding field in PLNfamily

covariates

design matrix (called X in the model). Will usually be extracted from the corresponding field in PLNfamily

offsets

offset matrix (called O in the model). Will usually be extracted from the corresponding field in PLNfamily

weights

an optional vector of observation weights to be used in the fitting process.

config_post

a list for controlling the post-treatments (optional bootstrap, jackknife, R2, etc.). See details

config_optim

a list for controlling the optimizer (either "nlopt" or "torch" backend). See details

nullModel

null model used for approximate R2 computations. Defaults to a GLM model with same design matrix but not latent variable.

Details

The list of parameters config_post controls the post-treatment processing, with the following entries:

• jackknife boolean indicating whether jackknife should be performed to evaluate bias and variance of the model parameters. Default is FALSE.

• bootstrap integer indicating the number of bootstrap resamples generated to evaluate the variance of the model parameters. Default is 0 (inactivated).

• variational_var boolean indicating whether variational Fisher information matrix should be computed to estimate the variance of the model parameters (highly underestimated). Default is FALSE.

• rsquared boolean indicating whether approximation of R2 based on deviance should be computed. Default is TRUE

• trace integer for verbosity. should be > 1 to see output in post-treatments

Method plot_individual_map()

Plot the factorial map of the PCA

Usage

PLNPCAfit$plot_individual_map(
  axes = 1:min(2, self$rank),
  main = "Individual Factor Map",
  plot = TRUE,
  cols = "default"
)

Arguments

axes

numeric, the axes to use for the plot when map = "individual" or "variable". Default it c(1,min(rank))

main

character. A title for the single plot (individual or variable factor map). If NULL (the default), an hopefully appropriate title will be used.

plot

logical. Should the plot be displayed or sent back as ggplot object

cols

a character, factor or numeric to define the color associated with the individuals. By default, all individuals receive the default color of the current palette.

Returns

a ggplot graphic

Method plot_correlation_circle()

Plot the correlation circle of a specified axis for a PLNLDAfit object

Usage

PLNPCAfit$plot_correlation_circle(
  axes = 1:min(2, self$rank),
  main = "Variable Factor Map",
  cols = "default",
  plot = TRUE
)

Arguments

axes

numeric, the axes to use for the plot when map = "individual" or "variable". Default it c(1,min(rank))

main

character. A title for the single plot (individual or variable factor map). If NULL (the default), an hopefully appropriate title will be used.

cols

a character, factor or numeric to define the color associated with the variables. By default, all variables receive the default color of the current palette.

plot

logical. Should the plot be displayed or sent back as ggplot object

Returns

a ggplot graphic

Method plot_PCA()

Plot a summary of the PLNPCAfit object

Usage

PLNPCAfit$plot_PCA(
  nb_axes = min(3, self$rank),
  ind_cols = "ind_cols",
  var_cols = "var_cols",
  plot = TRUE
)

Arguments

nb_axes

scalar: the number of axes to be considered when map = "both". The default is min(3,rank).

ind_cols

a character, factor or numeric to define the color associated with the individuals. By default, all variables receive the default color of the current palette.

var_cols

a character, factor or numeric to define the color associated with the variables. By default, all variables receive the default color of the current palette.

plot

logical. Should the plot be displayed or sent back as ggplot object

Returns

a grob object

Method show()

User friendly print method

Usage

PLNPCAfit$show()

Method clone()

The objects of this class are cloneable with this method.

Usage

PLNPCAfit$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

See Also

The function PLNPCA, the class PLNPCAfamily

Examples

data(trichoptera)
trichoptera <- prepare_data(trichoptera$Abundance, trichoptera$Covariate)
myPCAs <- PLNPCA(Abundance ~ 1 + offset(log(Offset)), data = trichoptera, ranks = 1:5)
myPCA <- getBestModel(myPCAs)
class(myPCA)
print(myPCA)