Description Usage Arguments Details Value Author(s) References Examples

`fma`

is used to perform Factor Mixture Analysis (with covariates) on a matrix of data by the Expectation Maximization algorithm.

1 |

`y` |
A data matrix with |

`k` |
The number of the mixture components. |

`r` |
The number of factors. |

`x.z` |
A matrix of covariates with |

`x.w` |
A matrix of covariates with |

`it` |
The maximum number of iterations of the EM algorithm. By default it is set to 15. |

`eps` |
The lower bound for relative variation of the likelihood. It is used as alternative stopping rule for the EM algorithm: if the relative increment of the likelihood is lower than |

`seed` |
Fix the seed of the running. Default is 4. |

`scaling` |
If TRUE (FALSE is default) the data are scaled before fitting the FMA model. |

`init` |
A list containing initial values for all (of some) model parameters. If |

Factor Mixture Analysis is a particular factor model with
non Gaussian factors modelled by a multivariate Gaussian mixture. The `p`

observed
variables `y`

are modelled in terms of the smaller set of `r`

factors, `z`

, and an additive
specific term `u`

: `y=Hz+u`

,
where `u`

is assumed
to be normally distributed with diagonal variance matrix `Psi`

. `H`

is the factor loading matrix.
The model is fitted by the EM algorithm.
The code implements also factor mixture model with covariates. Covariates may affect the observed variables into two manners:
they are assumed to linearly affect the factor means (`x.z`

) and \ or they can differently affect the a priori probability of group membership
(`x.w`

). The default is NULL which means that covariates are not incorporated in the model.

`H` |
The estimated factor loading matrix. |

`lik` |
The log-likelihood computed at each iteration of the EM algorithm. |

`w` |
A matrix with the estimated weights of the mixture. |

`Beta` |
An array of dimension |

`phi` |
A matrix of dimension |

`sigma` |
An array of dimension |

`psi` |
The noise diagonal variance matrix. |

`ph.y` |
The posterior distribution of each mixture components. |

`z` |
The reconstructed factor scores by Thomposon method. |

`index` |
The allocation vector. |

`bic` |
The BIC value. |

`aic` |
The AIC value. |

`elapsed` |
Computational time in seconds. |

Cinzia Viroli

A. Montanari and C. Viroli (2010), Heteroscedastic Factor Mixture Analysis, Statistical Modelling, 10(4), 441-460.

A. Montanari and C. Viroli (2011), Dimensionally reduced mixtures of regression models, Journal of Statistical Planning and Inference, 141, 1744-1752.

C. Viroli (2011), Using factor mixture analysis to model heterogeneity, cognitive structure and determinants of dementia: an application to the Aging, Demographics, and Memory Study, Statistics in Medicine, to appear.

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```
Loading required package: MASS
Loading required package: mvtnorm
[1] 0.42
```

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