knitr::opts_chunk$set(echo = TRUE)

`mixtCompLearn`

returns an object of class *MixtCompLearn* and *MixtComp* whereas `mixtCompPredict`

returns an object of class *MixtComp*.

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 | |_ IDClassBar | |_ 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 |_ ...

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

A copy of *algo* parameter.

**nbBurnInIter**Number of iterations of the burn-in part of the SEM algorithm.**nbIter**Number of iterations of the SEM algorithm.**nbGibbsBurnInIter**Number of iterations of the burn-in part of the Gibbs algorithm.**nbGibbsIter**Number of iterations of the Gibbs algorithm.**nInitPerClass**Number of individuals used to initialize each cluster.**nSemTry**Number of try of the algorithm for avoiding an error.**confidenceLevel**Confidence level for confidence bounds for parameter estimation.**ratioStableCriterion**Stability partition required to stop earlier the SEM .**nStableCriterion**Number of iterations of partition stability to stop earlier the SEM.**nInd**number of samples in the dataset**nClass**number of class of the mixture**mode**"predict" for`mixtCompPredict`

or "learn" for`mixtCompLearn`

**basicMode**If TRUE, mixtCompLearn has run in basic mode (mode using classic R formatting for missing data and with automatic detection of model)**hierarchicalMode**If TRUE, mixtCompLearn has run in hierarchical mode (learn a model with two classes, then split each classes in two and so on)

**BIC**value of BIC**ICL**value of ICL**nbFreeParameters**number of free parameters of the mixture model**lnObservedLikelihood**observed loglikelihood**lnCompletedLikelihood**completed loglikelihood**IDClass**entropy used to compute the discriminative power (see computeDiscrimPowerVar function)**IDClassBar**entropy used to compute the discriminative power (see computeDiscrimPowerVar function)**delta**entropy used to compute the similarities between variables (see heatmapVar function)**completedProbabilityLogBurnIn**evolution of the completed log-probability during the burn-in period (can be used to check the convergence and determine the ideal number of iteration)**completedProbabilityLogRun**evolution of the completed log-probability after the burn-in period (can be used to check the convergence and determine the ideal number of iteration)**runTime**a list containing the execution time in seconds of different part of the algorithm**lnProbaGivenClass**log-probability of each sample for each class times the proportion): $\log(\pi_k)+\log(P(X_i|z_i=k))$

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

Except for functional models and LatentClass, data contains, for each variable, two elements: *completed* and *stat*. *completed* contains the completed data and *stat* contains statistics about completed data.
The format is detailed 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.

**Gaussian/Poisson/NegativeBinomial/Weibull**

*stat* is a matrix where each row corresponds to a missing data and contains 4 elements: index of the missing data, median, 2.5% quantile, 97.5% quantile (if the confidenceLevel parameter is set to 0.95) of imputed values during the Gibbs at the end of each iteration after the burn-in phase of the algorithm.

**Multinomial**

*stat* is a named list where each element corresponds to a missing data. The name of the element corresponds to the index of the missing data. It contains a matrix containing the imputed values, during the Gibbs at the end of each iteration after the burn-in phase of the algorithm, and their frequency.

**Rank_ISR**

*stat* is a named list where each element corresponds to a missing data. The name of the element corresponds to the index of the missing data. It contains a matrix containing the imputed values, during the Gibbs at the end of each iteration after the burn-in phase of the algorithm, and their frequency.

**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.

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.

A *MixtCompLearn* object is the output of `mixtCompLearn`

function. It contains one or several $MixtComp$ object.

**nClass**A vector containing the number of classes tested**crit**ICL and BIC values for each value of*nClass***criterion**"BIC" or "ICL", the criterion used to choose the number of classes**algo**,**mixture**,**variable**,**warnLog**MixtComp object associated with the best number of classes**res**A list containing one*MixtComp*object per number of class. The first element (res[[1]]) corresponds to the*MixtComp*object for a number of classes of*nClass[1]***nRun**Number of runs for each number of classes**totalTime**Total running time

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