overdispersedGFM | R Documentation |

This function is to implement the overdispersed generalized factor model.

```
overdispersedGFM(XList, types, q, offset=FALSE, epsELBO=1e-5,
maxIter=30, verbose=TRUE)
```

`XList` |
a list consisting of matrices with the same rows n, and different columns (p1,p2, ..., p_d),observational mixed data matrix list, d is the types of variables, p_j is the dimension of varibles with the j-th type. |

`types` |
a d-dimensional character vector, specify the type of variables. For example, |

`q` |
a positive integer or empty, specify the number of factors. |

`offset` |
a logical value, whether add an offset term (the total counts for each row in the count component of XList) when there are Poisson variables. |

`epsELBO` |
a positive real, specify the relative tolerance of ELBO function in the algorithm. Optional parameter with default as |

`maxIter` |
a positive integer, specify the times of iteration. Optional parameter with default as 30. |

`verbose` |
a logical value with TRUE or FALSE, specify whether ouput the information in iteration process, (optional) default as TRUE. |

Overdispersion is prevalent in practical applications, particularly in fields like biomedical and genomics studies. To address this practical demand, we propose an overdispersed generalized factor model (OverGFM) for performing high-dimensional nonlinear factor analysis on overdispersed mixed-type data.

return a list with class name 'overdispersedGFM' and including following components,

`hH` |
a n*q matrix, the estimated factor matrix. |

`hB` |
a p*q matrix, the estimated loading matrix. |

`hmu` |
a p-dimensional vector, the estimated intercept terms. |

`obj` |
a real number, the value of objective function when the convergence achieves. |

`q` |
an integer, the used or estimated factor number. |

`history` |
a list including the following 7 components: (1)dB: the varied quantity of B in each iteration; (2)dH: the varied quantity of H in each iteration; (3)dc: the varied quantity of the objective function in each iteration; (4)c: the objective value in each iteration; (5) realIter: the real iterations to converge; (6)maxIter: the tolerance of maximum iterations; (7)elapsedTime: the elapsed time. |

nothing

Liu Wei

nothing

```
## mix of normal and Poisson
dat <- gendata(seed=1, n=60, p=60, type='norm_pois', q=2, rho=2)
## we set maxIter=2 for example.
gfm2 <- overdispersedGFM(dat$XList, dat$types, q=2, verbose = FALSE, maxIter=2)
measurefun(gfm2$hH, dat$H0, type='ccor')
measurefun(gfm2$hB, dat$B0, type='ccor')
```

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