An R6 Class to represent a PLNfit in a standard, general framework

The function PLN() fit a model which is an instance of a object with class PLNfit. Objects produced by the functions PLNnetwork(), PLNPCA(), PLNmixture() and PLNLDA() also enjoy the methods of PLNfit() by inheritance.

This class comes with a set of R6 methods, some of them being useful for the user and exported as S3 methods. See the documentation for coef(), sigma(), predict(), vcov() and standard_error().

Fields are accessed via active binding and cannot be changed by the user.

Active bindings

n

number of samples

q

number of dimensions of the latent space

p

number of species

d

number of covariates

nb_param

number of parameters in the current PLN model

model_par

a list with the matrices of the model parameters: B (covariates), Sigma (covariance), Omega (precision matrix), plus some others depending on the variant)

var_par

a list with the matrices of the variational parameters: M (means) and S2 (variances)

optim_par

a list with parameters useful for monitoring the optimization

latent

a matrix: values of the latent vector (Z in the model)

latent_pos

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

fitted

a matrix: fitted values of the observations (A in the model)

vcov_coef

matrix of sandwich estimator of the variance-covariance of B (need fixed -ie known- covariance at the moment)

vcov_model

character: the model used for the residual covariance

weights

observational weights

loglik

(weighted) variational lower bound of the loglikelihood

loglik_vec

element-wise variational lower bound of the loglikelihood

BIC

variational lower bound of the BIC

entropy

Entropy of the variational distribution

ICL

variational lower bound of the ICL

R_squared

approximated goodness-of-fit criterion

criteria

a vector with loglik, BIC, ICL and number of parameters

Methods

Public methods

• PLNfit$new()

• PLNfit$update()

• PLNfit$optimize()

• PLNfit$optimize_vestep()

• PLNfit$postTreatment()

• PLNfit$predict()

• PLNfit$predict_cond()

• PLNfit$show()

• PLNfit$print()

• PLNfit$clone()

---

Method new()

Initialize a PLNfit model

Usage

PLNfit$new(responses, covariates, offsets, weights, formula, control)

Arguments

responses

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

covariates

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

offsets

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

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-like structure for controlling the fit, see PLN_param().

---

Method update()

Update a PLNfit object

Usage

PLNfit$update(
  B = NA,
  Sigma = NA,
  Omega = NA,
  M = NA,
  S = NA,
  Ji = NA,
  R2 = NA,
  Z = NA,
  A = 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.

M

matrix of variational parameters for the mean

S

matrix of variational parameters for the variance

Ji

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

R2

approximate R^2 goodness-of-fit criterion

Z

matrix of latent vectors (includes covariates and offset effects)

A

matrix of fitted values

monitoring

a list with optimization monitoring quantities

Returns

Update the current PLNfit object

---

Method optimize()

Call to the NLopt or TORCH optimizer and update of the relevant fields

Usage

PLNfit$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-class

covariates

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

offsets

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

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 (Sigma, B). Intended to position new data in the latent space.

Usage

PLNfit$optimize_vestep(
  covariates,
  offsets,
  responses,
  weights,
  B = self$model_par$B,
  Omega = self$model_par$Omega,
  control = PLN_param(backend = "nlopt")
)

Arguments

covariates

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

offsets

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

responses

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

weights

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

B

Optional fixed value of the regression parameters

Omega

precision matrix of the latent variables. Inverse of Sigma.

control

a list-like structure for controlling the fit, see PLN_param().

Sigma

variance-covariance matrix of the latent variables

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 postTreatment()

Update R2, fisher and std_err fields after optimization

Usage

PLNfit$postTreatment(
  responses,
  covariates,
  offsets,
  weights = rep(1, nrow(responses)),
  config_post,
  config_optim,
  nullModel = NULL
)

Arguments

responses

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

covariates

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

offsets

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

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 optimization (optional bootstrap, jackknife, R2, etc.). 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 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 predict()

Predict position, scores or observations of new data.

Usage

PLNfit$predict(
  newdata,
  responses = NULL,
  type = c("link", "response"),
  level = 1,
  envir = parent.frame()
)

Arguments

newdata

A data frame in which to look for variables with which to predict. If omitted, the fitted values are used.

responses

Optional data frame containing the count of the observed variables (matching the names of the provided as data in the PLN function), assuming the interest in in testing the model.

type

Scale used for the prediction. Either link (default, predicted positions in the latent space) or response (predicted counts).

level

Optional integer value the level to be used in obtaining the predictions. Level zero corresponds to the population predictions (default if responses is not provided) while level one (default) corresponds to predictions after evaluating the variational parameters for the new data.

envir

Environment in which the prediction is evaluated

Details

Note that level = 1 can only be used if responses are provided, as the variational parameters can't be estimated otherwise. In the absence of responses, level is ignored and the fitted values are returned

Returns

A matrix with predictions scores or counts.

---

Method predict_cond()

Predict position, scores or observations of new data, conditionally on the observation of a (set of) variables

Usage

PLNfit$predict_cond(
  newdata,
  cond_responses,
  type = c("link", "response"),
  var_par = FALSE,
  envir = parent.frame()
)

Arguments

newdata

a data frame containing the covariates of the sites where to predict

cond_responses

a data frame containing the count of the observed variables (matching the names of the provided as data in the PLN function)

type

Scale used for the prediction. Either link (default, predicted positions in the latent space) or response (predicted counts).

var_par

Boolean. Should new estimations of the variational parameters of mean and variance be sent back, as attributes of the matrix of predictions. Default to FALSE.

envir

Environment in which the prediction is evaluated

Returns

A matrix with predictions scores or counts.

---

Method show()

User friendly print method

Usage

PLNfit$show(
  model = paste("A multivariate Poisson Lognormal fit with", self$vcov_model,
    "covariance model.\n")
)

Arguments

model

First line of the print output

---

Method print()

User friendly print method

Usage

PLNfit$print()

---

Method clone()

The objects of this class are cloneable with this method.

Usage

PLNfit$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Examples

if (FALSE) { # \dontrun{
data(trichoptera)
trichoptera <- prepare_data(trichoptera$Abundance, trichoptera$Covariate)
myPLN <- PLN(Abundance ~ 1, data = trichoptera)
class(myPLN)
print(myPLN)
} # }