Calculates the Maximum likelihood Factor analysis with a dataset.

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`data` |
The dataset. It is a n*p numeric matrix, where n is the number of observations and p is the number of variables. |

`rnk` |
Rank constraint for the Factor analysis problem. It must a positive integer less than the number of variables p |

`Psi_init` |
The initial value of Psi. It is a p*1 numeric vetor, where p is the number of variables. Default value is a vector of uniform random numbers. |

`lb` |
The lower bound on the Psi values. The default value is set to 0.05 |

`index` |
This option is for modified version of factmle.The default value is a null vector. If assigned a zero vector, it will perform MLFA keeping some of the Psi values specified by the index at a specifed level *lb2* |

`lb2` |
This option of modified version of factmle algorithm. The default value is 0.001. The Psi values specified by the *index* is kept constant at *lb2* while doing MLFA. |

`tol` |
Precision parameter. Default is 10^-7 |

`Max_iter` |
Maximum number of iterations. Default is 1000. |

A list with the following components

`Psi` |
A vector containing the unique variances. |

`Lambda` |
A p*rnk matrix containing the factor loadings in the columns. |

`Nll` |
A vector containing the negative Log-likelihood values at every iteration. |

`Nllopt` |
The value of the negative log-likelihood upon convergence. |

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