Description Usage Arguments Details Value Author(s) References See Also Examples

`ifa.em`

is used to perform Independent Factor Analysis on a matrix of data by the Expectation Maximization algorithm.

1 |

`y` |
A data matrix with |

`ni` |
A vector containing the number of mixture components for modeling each factor. The number of factors is equal to the length of this vector. |

`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 |

`init` |
A list containing initial values for the factor loading matrix (specified by |

`scaling` |
If TRUE (default) the data are scaled before fitting the IFA model |

Independent Factor Analysis is a latent variable model with
independent and non gaussian factors. The `p`

observed
variables `x`

are modelled in terms of a smaller set of `k`

unobserved independent latent variables, `y`

, and an additive
specific term u: x=Hy+u,
where `u`

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

and the factor loading
matrix `H`

is also
termed as `mixing matrix`

. The density of each
factor is modelled by a mixture of gaussians. The model is fitted by the EM algorithm.
This version can be computationally slow in the complex cases.
A faster R package for window which is based on fortran code can be downloaded at the home:
$www2.stat.unibo.it/viroli$ in the section Software and Data.

A list containing the components:

`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 mixtures. Each row contains the weights of each factor |

`mu` |
A matrix with the estimated component means of the mixtures. Each row contains the vector means for each factor |

`vu` |
A matrix with the estimated component variances of the mixtures. Each row contains the vector variances for each factor |

`psi` |
The noise diagonal variance matrix |

`ni` |
The input vector specifying the number of components for each mixture |

`L` |
The number of factors |

`numvar` |
The number of observed variables |

`numobs` |
The number of observations |

Cinzia Viroli

Attias H. (1999), Independent Factor Analysis, Neural Computation, 11, 803–851.

Montanari A. and Viroli C. (2010), The Independent Factor Analysis approach to latent variable modeling, Statistics, 44, 397–416.

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