Overview of MixtComp Object

Quentin Grimonprez

2020-01-07

mixtCompLearn returns an object of class MixtCompLearn and MixtComp whereas mixtCompPredictreturns an object of class MixtComp.

MixtComp Object

Overview of output object with variables named categorical, gaussian, rank, functional, poisson, nBinom and weibull with model respectively Multinomal, Gaussian, Rank_ISR, Func_CS (or Func_SharedAlpha_CS), Poisson, NegativeBinomial and Weibull. In case of a successfull run, the output object is a list of list organized as follows:

output
|_______ algo __ nbBurnInIter
|             |_ nbIter
|             |_ nbGibbsBurnInIter
|             |_ nbGibbsIter
|             |_ nInitPerClass
|             |_ nSemTry
|             |_ mode
|             |_ nInd
|             |_ confidenceLevel
|             |_ nClass
|             |_ ratioStableCriterion
|             |_ nStableCriterion
|             |_ basicMode
|             |_ hierarchicalMode
|
|_______ mixture __ BIC
|                |_ ICL
|                |_ lnCompletedLikelihood
|                |_ lnObservedLikelihood
|                |_ IDClass
|                |_ delta
|                |_ runTime
|                |_ nbFreeParameters
|                |_ completedProbabilityLogBurnIn
|                |_ completedProbabilityLogRun
|                |_ lnProbaGivenClass
|
|_______ variable __ type __ z_class
                  |       |_ categorical
                  |       |_ gaussian
                  |       |_ ...
                  |
                  |_ data __ z_class __ completed
                  |       |          |_ stat
                  |       |_ categorical __ completed
                  |       |              |_ stat
                  |       |_ ...
                  |       |_ functional __ data
                  |                     |_ time
                  |
                  |_ param __ z_class __ stat
                          |           |_ log
                          |           |_ paramStr
                          |_ functional __ alpha __ stat
                          |             |        |_ log
                          |             |_ beta __ stat
                          |             |       |_ log
                          |             |_ sd __ stat
                          |             |     |_ log
                          |             |_ paramStr
                          |_ rank __ mu __ stat
                          |       |     |_ log
                          |       |_ pi __ stat
                          |       |     |_ log
                          |       |_ paramStr
                          |
                          |_ gaussian __ stat
                          |           |_ log
                          |           |_ paramStr
                          |_ poisson __ stat
                          |          |_ log
                          |          |_ paramStr
                          |_ ...

warnLog

In case of an unsuccessfull run, the output object is a list containing an element warnLog with all the warnings returned by MixtComp.

algo

A copy of algo parameter.

mixture

variable

type

Named list (according to variable names) containing model used for each variable (e.g. “Gaussian”).

data

The format is detailled below according to the model.

  • LatentClass

Two elements: completed and stat. completed contains the completed data. stat is a matrix with the same number of columns as the number of class. For each sample, it contains the \(t_{ik}\) (probability of \(x_i\) to belong to class k) estimated with the imputed values during the Gibbs at the end of each iteration after the burn-in phase of the algorithm.

  • Func_CS and Func_SharedAlpha_CS

Two elements: data and time. time (resp. data) is a list containing the time (resp. value) vector of the functional for each sample.

  • Other Models

One element: completed, a matrix/vector containing the completed version of the dataset.

param

For one variable, it contains a list with estimated parameters (param), log recorded during the SEM (log) and hyperparameters if any (paramStr). The output format depends of the model but in most of the case, stat is a matrix with 3 columns containing the median values of estimated parameters and quantile ate the desired confidence level, log is matrix containing the estimated proportion during the M step of each iteration of the algorithm after the burn-in phase and paramStr is a string. For the meaning of the parameters, user can refer to the documentation data format.

  • LatentClass

A list of 3 elements: stat, log, paramStr. log is matrix containing the estimated proportion during the M step of each iteration of the algorithm after the burn-in phase. stat is a matrix containing the median (and quantiles corresponding to the confidenceLevel parameter) of the estimated proportion. The median proportions are the returned proportions. paramStr contains "".

  • Gaussian

The stat matrix has 2*nClass rows. For a class \(k\), parameters are mean (\(\mu_k\)) and sd (\(\sigma_k\)).

  • Poisson

The stat matrix has nClass rows. For a class \(k\), the parameter is lambda (\(\lambda_k\)).

  • NegativeBinomial

The stat matrix has 2*nClass rows. For a class \(k\), parameters are n (\(n_k\)) and p (\(p_k\)).

  • Weibull

The stat matrix has 2*nClass rows. For a class \(j\), parameters are k (shape) (\(k_j\)) and lambda (scale) (\(\lambda_j\)).

  • Multinomial

paramStr contains "nModality: J" where \(J\) is the number of modalities.

The stat matrix has J*nClass rows. For a class \(k\), parameters are probabilities to belong to modality \(J\).

  • Rank_ISR

paramStr contains "nModality: J" where \(J\) is the length of the rank (number of sorted objects).

Two lists (named mu and pi) of 2 elements: stat, log.

For pi, stat is a matrix with nClass rows. For a class \(k\), parameter is pi (\(pi_k\)).

For mu, stat is a list with nClass elements. For a class \(k\), a list is returned with the mode of the parameter (\(\mu_k\)), and the frequency of the mode during the SEM algorithm after the burn-in phase.

  • Func_CS and Func_SharedAlpha_CS

paramStr contains "nSub: S, nCoeff: C" where \(S\) is the number of subregressions and \(C\) the number of coefficients of each regression.

Three lists (named alpha, beta and sd) of 2 elements: stat, log.

For alpha, stat is a matrix with 2*S*nClass rows. For a class \(k\) and a subregression \(s\), parameters are the estimated coefficients of a logistic regression controlling the transition between subregressions.

For beta, stat is a matrix with S*C*nClass rows. For a class \(k\) and a subregression \(s\), parameters are the estimated coefficient of the regression.

For sd, stat is a matrix with S*nClass rows. For a class \(k\) and a subregression \(s\), the parameter is the standard deviation of the residuals of the regression.

MixtCompLearn Object

A MixtCompLearn object is the output of mixtCompLearn function. It contains one or several \(MixtComp\) object.