Description Usage Arguments Value References See Also Examples

Maximum likelihood estimates exist for *N > max(p/q,q/p)+1* and are
unique for *N > max(p,q)*. This finds the estimate for the mean and then
alternates between estimates for the *U* and *V* matrices until
convergence. An AR(1), compound symmetry, correlation matrix, or independence
restriction can be proposed for either or both variance matrices. However, if
they are inappropriate for the data, they may fail with a warning.

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`data` |
Either a list of matrices or a 3-D array with matrices in dimensions 1 and 2, indexed by dimension 3. |

`row.mean` |
By default, |

`col.mean` |
By default, |

`row.variance` |
Imposes a variance structure on the rows. Either
'none', 'AR(1)', 'CS' for 'compound symmetry', 'Correlation' for a
correlation matrix, or 'Independence' for
independent and identical variance across the rows.
Only positive correlations are allowed for AR(1) and CS covariances.
Note that while maximum likelihood estimators are available (and used) for
the unconstrained variance matrices, |

`col.variance` |
Imposes a variance structure on the columns. Either 'none', 'AR(1)', 'CS', 'Correlation', or 'Independence'. Only positive correlations are allowed for AR(1) and CS. |

`tol` |
Convergence criterion. Measured against square deviation between iterations of the two variance-covariance matrices. |

`max.iter` |
Maximum possible iterations of the algorithm. |

`U` |
(optional) Can provide a starting point for the |

`V` |
(optional) Can provide a starting point for the |

`...` |
(optional) additional arguments can be passed to |

Returns a list with a the following elements:

`mean`

the mean matrix

`scaling`

the scalar variance parameter (the first entry of the covariances are restricted to unity)

`U`

the between-row covariance matrix

`V`

the between-column covariance matrix

`iter`

the number of iterations

`tol`

the squared difference between iterations of the variance matrices at the time of stopping

`logLik`

vector of log likelihoods at each iteration.

`convergence`

a convergence flag,

`TRUE`

if converged.`call`

The (matched) function call.

Pierre Dutilleul. The MLE algorithm for the matrix normal distribution. Journal of Statistical Computation and Simulation, (64):105–123, 1999.

1 2 | ```
Gupta, Arjun K, and Daya K Nagar. 1999. Matrix Variate Distributions.
Vol. 104. CRC Press. ISBN:978-1584880462
``` |

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